Language: C++

{1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,4,11,26,57,120,247,502,1013,2036,4083,8178,16369,32752,65519,131054,262125,524268,1048555,2097130,4194281,8388584,16777191,33554406,67108837,134217700,268435427,536870882,73741786,147483602,294967235,589934502,179869030,359738094,719476223,438952475,877904987,755810005,511620042,23240117,46480275,92960592,185921227,371842498,743685041,487370121,974740289,949480619,898961280,797922603,595845250,191690545,383381143,766762340,533524728,67049505,134099067,268198192,536396443,72792939,145585939,291171940,582343943,164687943,329375951,658751968,317503996,635008060,270016182,540032434,80064932,160129936,320259945,640519964,281039996,562080068,124160206,248320490,496641059,993282198,986564470,973129015,946258106,892516289,785032656,570065391,140130862,280261812,560523713,121047509,242095109,484190310,968380713,936761513,873523114,747046317,494092724,988185546,976371184,952742461,905485016,810970127,621940350,243880797,487761699,975523504,951047108,902094317,804188736,608377575,216755254,433510620,867021353,734042813,468085734,936171584,872343278,744686667,489373446,978747012,957494138,914988391,829976898,659953913,319907944,639816014,279632148,559264424,118528970,237058070,474116271,948232674,896465474,792931075,585862278,171724685,343449507,686899152,373798436,747597012,495194158,990388458,980777052,961554241,923108620,846217379,692434898,384869937,769740023,539480189,78960522,157921196,315842545,631685244,263370636,526741428,53483006,106966170,213932499,427865158,855730477,711461109,422922374,845844912,691689982,383380123,766760413,533520987,67042136,134084442,268169055,536338282,72676730,145353634,290707443,581415062,162830294,325660766,651321711,302643595,605287371,210574917,421150017,842300218,684600614,369201407,738403001,476806183,953612555,907225293,814450770,628901725,257803636,515607466,31215120,62430436,124861069,249722336,499444871,998889942,997780078,995560351,991120898,982241993,964484184,928968567,857937334,715874869,431749940,863500090,727000384,454000973,908002159,816004525,632009258,264018725,528037667,56075545,112151309,224302838,448605897,897212016,794424248,588848713,177697644,355395514,710791255,421582731,843165691,686331605,372663434,745327100,490654426,981309086,962618400,925237029,850474288,700948807,401897846,803795932,607592098,215184431,430369105,860738454,721477146,442954531,885909309,771818859,543637960,87276163,174552577,349105406,698211065,396422377,792845009,585690267,171380784,342761826,685523911,371048075,742096411,484193077,968386417,936773091,873546440,747093139,494186538,988373344,976746950,953494163,906988590,813977445,627955156,255910579,511821433,23643135,47286547,94573372,189147023,378294326,756588933,513178141,26356558,52713400,105427085,210854456,421709199,843418686,686837654,373675591,747351473,494703231,989406755,978813797,957627882,915256053,830512396,661025083,322050458,2,18,96,404,1494,5118,16724,53040,165018,507050,1545384,4684908,14152574,42653814,128354076,385848008,159116155,480493389,447770730,355894123,92847124,328871864,87277627,463158117,792126066,181682973,155659955,688203512,507059498,406078232,988036108,503713182,590351468,929480567,105296470,949601582,116231800,883552438,720374411,300560641,180560122,99440299,413844468,472584411,879859304,563794279,539820010,316338991,342779711,815869616,22675002,218162757,954769391,464876224,595770852,189603188,373397347,729374335,406494548,656233951,842209909,273653527,315016147,933167772,775750414,279754164,744277342,42870960,748700305,486285544,939235993,778477062,256980024,614048728,528374739,957592893,617727882,343094241,9116409,987029420,880461740,480145642,117971569,708998126,837175652,931904303,636482748,591003431,136136516,134678215,856588548,474890357,234937816,325364624,217214274,133902065,366243506,27824341,941680292,541475386,57315601,37746518,844860209,997843548,920078543,613353913,546321226,51505987,979626369,589120095,67866924,804639166,616019803,252290025,565357778,313075645,173258949,987868737,899818292,571907852,460658811,871876725,595461010,746075473,157642555,311791717,613135513,194960024,296020345,310375381,775789164,16728368,428942269,44377035,648268032,975114928,986003986,79368457,480857053,928113716,755466017,208688131,510685479,301340074,442629560,405149988,370015805,419222912,876064139,865028216,68801855,153886222,356666798,860064090,160367698,641502657,245356381,377815912,416991836,818114915,588675394,34739982,641700712,117439,150437401,751537483,855118773,766425422,701471608,908863322,335545444,224606484,109819621,201519760,348742324,534655012,580883774,696552173,997522310,808363312,56748236,433627591,827715510,536879709,718173956,369660718,539329813,478755445,157869796,916888531,637296820,685226663,602426900,900849808,889763690,43796441,880477725,139688359,415654682,240223249,707268969,95086945,231903357,589078347,554055636,235892977,855216788,860812592,172849601,699460688,460294862,104800084,762322007,182901102,340665946,606016430,986180652,294899721,557510650,18251717,746292395,622050220,632596202,430780049,358424297,207543350,887274040,191214047,632530912,15476064,282301598,318759247,900095232,588030176,539689959,170380138,613873295,47198921,552869105,481267185,89237464,558701359,258200095,938911414,145476529,94035228,597438991,423106581,531022975,116600389,396990118,285475257,45563602,515095514,302225994,420687972,290215994,927085280,894264584,908946454,179281015,442863674,138770611,36810417,351568876,537123383,576346237,659134542,837740017,234038633,143899973,315416042,713829430,676801043,101179892,445245582,619302009,425191121,410299247,500506316,40894020,201591273,762752423,604375775,445526801,601542961,334718737,64501821,314363739,184975962,38866745,84648488,190213668,443350284,75643455,718290824,137769787,379281627,6,96,840,5496,30426,151800,707772,3153648,13622526,57588528,239782512,987643272,36484294,404234584,392585814,898035315,575174284,246600375,811470459,683273579,944530613,160687311,186367318,966928663,310745792,324184017,434061165,714573914,483689558,307015431,567362584,193004171,274985556,915274348,403348465,799225682,405433523,14870867,704622880,546316043,675087455,225205435,471115501,356259091,900702010,226723475,324665304,947812436,137322984,597972995,984590057,460472940,596881918,430181760,203915682,574447624,389109735,852317608,123612518,855437931,68495933,596187816,622755010,761272022,993730422,145847900,842962989,836003776,489234413,660001590,805783322,875110110,846453416,363345822,581274596,729532896,430752283,372448434,684396850,857365410,944554814,799571630,540392369,392464380,965207669,35658377,807860052,831147989,972883282,812856553,520271269,996925726,148403839,286517473,410407674,328965389,207456569,240356186,812128620,328429934,182376492,733874979,20350791,22940747,370754501,382789190,657165974,455110543,379293914,710511643,163327571,507103250,176259662,926185969,124051284,658235013,702836284,730427441,171657008,559799959,371084747,425741832,650021638,738703811,57894029,88420714,353979209,933376931,620786705,405665909,80427942,399875203,879108560,702396856,561397755,873667459,78977783,363423390,958788513,606496445,297842569,997509740,922540189,764483334,314242385,34012245,347923187,499104790,663708797,130247951,441281262,587709095,68524780,158910624,195761506,137175482,661030905,462935933,12430912,397747995,257725642,33246612,632835130,967997003,933073447,145030297,704757626,793202539,922645994,819789493,847245701,266778576,642663025,341198637,52238962,567212415,991850093,512832686,567068228,793594527,110514318,743630512,375542684,681512445,147123735,441319571,111880305,242721139,186212011,648196973,972780422,640158966,522291968,353501666,823052172,422143830,180800894,953079080,59074087,145613289,710656091,103952767,56827023,22028872,480536029,594689568,292685992,463984572,302982936,562409806,14257096,110547840,732186726,220519949,868686980,133639886,802602204,323121500,638051012,321969731,436592300,553864657,660797455,559406693,148988611,592502279,690167423,923948642,604457281,936640798,726783718,298490090,401546305,485171466,392424689,82086598,157048481,572742725,712198889,547984693,599124055,31392524,360996641,734650708,738919015,645048876,305745,426327371,141158365,763532868,481288942,869123655,541481230,547033143,46368014,776719033,987460018,851948313,626133597,62957762,388210014,87151168,500925010,49404814,382811790,813561931,703966828,556043494,483267106,184829507,121269346,121367441,729784127,911155473,192910968,545493499,605522862,458440217,469869573,704111259,716790015,476812361,531533951,411044714,829593134,411471856,610730625,791607334,144845241,283885158,451565185,340778172,354293024,445819703,387963770,67727697,396543733,24,600,7800,73080,563520,3833664,23971920,141379920,799912200,391998892,589053863,633370852,417646250,541423106,757493114,431489194,428336475,858221594,779364999,411758941,690637662,455909089,202043375,335225318,532490102,752877327,489903171,923050462,654940208,658979559,921678977,860940004,781229911,199637891,337407319,565543420,959799161,248689121,815676548,404255500,206752852,576047552,913303870,446575473,684280501,54655197,572584133,245025535,597566734,491775558,145314279,913549308,676433463,149864140,478122964,704007200,802113697,620985678,983028646,831941730,161421607,603137771,883561722,699229104,433777014,436564343,162645407,98807483,365341035,938291843,697514765,566176481,463450137,261722084,851431052,238388681,742360301,694252827,716967554,885533770,216840373,47457646,115041453,284472507,769243034,709386519,274506682,377059193,472129616,14426764,330292484,504168654,385777718,413226517,924256735,648863054,94949758,514654214,330224998,295928122,125704995,538046304,401854422,329399476,225768581,984585674,79650286,13670773,3991665,754470252,494856643,105924144,903016664,652822448,704836345,259624083,284310671,387255231,345610136,671820863,907438014,754498922,900855722,339263084,862670516,979882475,273332120,588795946,282602898,263854230,983047111,912034069,572693091,372371838,202500409,640781999,134549867,417670571,177436612,854567353,873158382,91129483,669357444,102347442,579285019,383842571,744355790,191661858,290713202,107879871,256222713,802154822,362004325,870244054,458913963,870683346,670869516,428418274,870435523,465958438,428776433,135449258,626363684,307363590,202314662,610793311,181823113,697501213,280591323,87641994,86719192,634625766,100384866,72830507,292974063,177400929,16886333,105750952,842847101,85609310,714127780,800812151,103983022,837373315,885816101,940187165,537957623,311710220,259588677,482651528,798538099,982771085,24981830,305096707,787457211,529311305,998136489,354039733,267910004,936432370,139261339,130872764,300949795,301079012,815024892,823471427,484001705,269294690,153418964,941450978,913275415,682004978,192962345,922642560,816955151,412926391,249279987,706663694,10970186,725493130,483723746,896010433,420479186,600497443,494690926,661652147,477226150,396344072,148867221,616979326,519355833,549717674,587810647,351078412,696045083,274348515,41317673,374172366,209695250,633663256,446242419,74577656,116154006,807711630,336224862,333265091,259645162,378689983,20729993,363641205,843986532,506739994,319458282,681475042,347496302,781637479,575965124,947763910,962902582,903708135,65727750,822483637,416293503,199907936,654582417,347818704,62711589,776578117,263271607,556519630,906027637,679543377,370254026,664191768,786198120,933068610,234939176,587308802,101570903,159182172,435777722,908668953,481344579,314590159,197377786,131138488,484454046,569614420,225558353,799463087,819337963,488010305,425894417,523757626,984114310,415843263,120,4320,78120,991200,10134720,89898480,723071760,425009885,693502814,807873985,993200662,763557054,937617417,741205186,739337431,494346025,551112102,896053759,132509474,303202615,431401663,509855662,504142796,336176078,367703485,747353373,36582066,292722178,799834725,15586346,467171775,498199762,506019104,329326861,59294786,571267948,528644178,875066071,279709700,710678837,718772754,622809704,526125880,408449688,332005688,731857351,237768129,984717748,18799551,314675867,996403637,997700872,28790562,493796558,502899655,663629163,335544672,764292932,104478349,918023221,149183295,810556926,726991082,451559356,520932931,634759347,503000123,632621410,639555119,739366406,679968312,237089453,199429060,971370614,273857599,628957439,947417725,812705632,719542344,561830702,309450389,137024945,992499568,999007252,177909604,477246526,872397041,193992824,511275579,122301688,564179000,313917727,741024213,595512690,743087411,302353923,484576798,444478608,611058851,177879593,934441760,428164689,947326673,737925913,427394951,915101948,300651338,848216487,174460945,177116416,709638725,872370342,397262492,294278222,239301124,454973600,133193679,137027430,630755046,78202010,434184179,616961862,686297185,881924575,296537574,527742893,718597760,824970814,666575806,694101156,549394790,630200330,562970607,851217086,946759058,446671415,30564964,143438162,490104077,229482877,182938174,35168304,386216377,269462928,402470567,514306817,770618612,544724567,89791757,542373173,260719788,377494664,582406471,264719308,5711407,535455414,652868198,532398107,128631283,380018022,13822783,854275218,284791205,543386771,587373779,364792160,511548532,168441548,446901662,406058690,883647232,128903686,240967110,934624771,150598203,143019517,780358357,352100145,412737435,663450223,720879892,38642574,384605127,742225619,699843213,553488192,28608744,179754750,245221973,310149760,552735727,328003462,930262377,846697424,804510472,514476300,379057978,589262517,875569712,631119354,834939328,237167909,493215965,145474402,616336889,425353438,390729549,172256176,424511755,803857484,831650444,499793344,924245799,526268730,190731443,977159067,23027956,793704269,77769732,454326094,648406459,418851041,900935548,464667657,185941508,275213381,609435349,699411271,33095042,636555249,258753501,911234251,929530874,339391288,309439321,155644908,470771673,438774770,554326872,53211897,752152622,265479423,814866379,173087637,920686207,250214385,264148253,848363634,97203521,452438960,306059730,660848303,485085679,440055877,976771013,460658171,587407838,176792134,197318966,799929206,187444900,386090177,239286395,776312664,307897921,214892229,483639513,60265843,67503327,176264290,494701990,636856252,390351021,766832382,710066624,816131883,678602462,426568393,473321745,704416302,828520593,697047687,440375904,58835085,578939213,729292605,598559793,216657020,71733029,224609733,661284578,102363928,164813068,554845263,247876116,720,35280,846720,13970880,182710080,44959826,521408180,302038030,468138032,592835864,279674406,582287211,500552478,205760233,582465321,321278099,408954205,616415881,820861742,12291245,407421818,855361524,276849506,539990494,247287344,509875502,976245968,949651388,435125744,601246379,994872099,467155323,328885184,264904969,202971997,662550468,811878010,23032868,757966597,197835515,872040588,229013859,235026974,257316480,780625432,808954254,654396757,241811990,276472060,899834809,835697796,225661484,555506872,200941772,816479789,443910946,116696701,263332588,655040747,841758106,398256206,984683518,527098279,418102644,448650662,383652558,530894137,962358465,593538176,155012782,608729554,866247171,7954508,778897097,226844944,185054046,495973904,741836323,332231129,936186889,207096777,615853866,272174792,72088658,388816594,497585571,546049892,10807705,560152241,960768056,294099026,974781391,779420078,991036992,566791223,374777072,417401600,146075747,835140836,887400919,490456394,167509276,712013011,966320686,607920327,627113110,936708418,621224394,645621981,679399816,517171384,987035707,441803379,774756836,336428709,481654262,252140718,803706324,558938880,993847189,880635861,63937743,923633704,463025719,242414484,797348885,675799520,957901570,298074842,633228021,953751329,476065024,457876189,931251615,970612674,8936971,266799652,782150738,205641764,950839248,741445967,933953012,965099683,446961752,649377656,659919648,211740822,824088802,882782068,274067185,453728433,948918936,864222323,510860433,548656263,847802662,654123313,727991591,765160111,973068772,169287288,563945142,258057621,113688842,672662363,470819847,229498971,947952944,319164316,476278015,92901171,286848566,244904035,213654244,91639260,807353534,433372320,448749645,301013765,404214742,796417973,696057209,220480846,606420100,44851746,880524010,375897278,531049390,243437237,326212317,670270796,1420088,178930143,161558626,954201374,466336561,646826957,467032594,141701655,589575114,894495465,741093946,931578507,59441817,98086615,14138881,472624963,429627033,861870489,979610060,295732856,218815877,238057260,656045637,368443054,515162438,498857298,739113893,343918911,850584091,261966484,927169734,122662508,47821176,672670179,873860947,316986449,44839224,874367141,459334626,750617873,894615372,872438697,647135148,698688618,772727353,315519344,673644875,663647791,778274617,885761533,940525684,924500398,599222766,352967961,48064355,534473509,469612156,254963808,491216879,625376673,720138055,440822857,454174788,2883981,226501078,880004196,384714798,929453440,3099952,512502592,925350253,659220779,705376188,374852613,308318218,702712418,257153253,628164217,586674774,651381961,683288802,670974398,4128961,893945972,926396997,367877010,719221601,776866712,454628753,348846792,738132087,324051745,262266387,944878236,782625437,247470003,561348077,814391728,60784488,771628213,95201254,522768874,681272204,5040,322560,9918720,206357760,357668139,234742078,443099725,198293547,891695996,87770789,741418274,447536170,53549533,769331153,378023569,82380412,665111263,533749554,589514765,659358297,565747517,169434766,810908155,98947215,361031932,58322852,321930746,130588930,927357537,824916436,804889142,989208059,220678087,833371222,434899753,784248532,863183532,520997006,929254942,544936272,493601184,450677897,186572987,495964652,187294171,977682027,134212951,48233465,625445741,241777920,832367831,77635749,385509885,156846963,597052630,225657216,413191954,969895067,369081260,377550865,402572293,757814299,794346323,961342249,588698740,122923442,198719117,920555601,527731216,646122381,621667535,924408936,58576559,941040727,243106309,853944017,169258953,553860945,936504033,373143581,449113787,786830795,433504641,477536043,762744709,342986507,228141079,646800131,870293813,374809383,81263423,86192102,234092693,641274654,464514690,671066201,436229126,272521449,827474293,919663889,840031392,103215138,280357435,342087305,624403083,6959725,511273159,497081940,660643793,790910784,73262828,522910984,252998351,477341624,750917342,622955322,341825649,190134723,49224806,630146060,620133882,930433530,691997502,828730443,108508359,81331889,863468776,449677907,462213093,69179585,998393927,427867261,23488868,622661839,859220470,27998242,814930697,81147153,906066958,568037974,214710114,629182730,714295552,623138598,103754788,923487567,342379790,505427796,66243655,640054156,800766995,461979508,810036431,48175826,91224383,393372421,855027948,540383361,570891758,560181897,812094434,400823353,835573507,219142144,373472665,321117281,104233234,267326682,758891393,931060089,999839596,807116728,735219890,545802672,494587881,60255068,773595402,951818196,204585125,479920189,962425641,562612728,207590961,541503166,922698021,318431066,571483259,689546704,294442743,831550358,895610496,723294356,322619352,154670831,455111998,397176905,394587759,485133405,498196181,956861510,900573087,329975708,169017708,492444345,66723741,165540072,142691410,91127970,733317174,737483743,124891022,416912802,758061533,878215823,770597967,457956916,699028758,279549337,362344314,886583462,821703296,498207096,249641065,522348673,504737285,837120787,57398797,109512148,889348630,943470115,347938975,9763339,526411988,968704833,712922566,204968442,711814641,151503593,232137360,101678543,747114839,324458099,280303654,509615525,549764917,768450172,828290061,747917825,563625590,495584110,715209784,365814533,221227398,884968858,249891640,889986981,769914483,749913889,694759625,838305097,714431171,951916179,649512564,154181818,784496635,581448419,804699689,229036444,169624646,732899036,520640860,638246734,566513548,361343836,437479792,821221855,459406726,824922478,720929166,137526193,265930366,844070424,716269666,356193298,688439971,277344361,464231081,233972843,371848388,286977942,706619883,52556586,730063671,40320,3265920,125193600,205319019,479686599,975154869,548307441,223552910,295085997,221968032,872652147,393081530,629383005,43148309,338465909,109446246,704845537,448668367,875002325,754782758,159288958,344549599,907112392,47316094,918287087,332887882,786960015,830281336,170923686,930299508,294038138,36052551,107404601,404386243,600862616,899558734,669018978,80866326,922504557,989869966,171324725,318590326,616203068,655792514,970572571,142976324,739334275,347241078,879604946,504342996,966555862,62233823,410271025,82338824,896099892,536237118,252045820,864866508,4528058,597160195,198157390,140240152,457635866,535879556,111078865,811165799,715113390,958056018,470948516,830418880,707949791,793140894,261737078,797311635,846859440,661814055,911835312,889880285,220963357,631205329,105036392,485581141,118316043,849137724,842593268,738592710,313519088,112052589,314370103,284309741,278552531,814427388,148978005,34417875,258594696,486880372,254875721,760952585,187872345,634331866,390854334,945878944,227245742,176086768,135257122,838964721,721474339,55003555,403684998,415635281,305526747,504442656,844548637,935044322,575339616,29311749,775213735,280708944,753764488,966406206,634147869,409779120,728462078,159021850,263184385,766237431,386062267,891810748,810253322,643713985,99691073,820057101,315645885,391213131,378537035,304673336,581809707,126341318,301040151,982001502,117711479,402800991,657059997,562757020,257282753,594297846,617723501,51821952,497102778,691961754,294106453,235230769,191595915,24288587,821414366,827156869,867752348,254203614,658643526,560782683,758275876,397724037,110854466,852804957,828415922,96623625,303668395,750215997,893519672,770819878,927833907,582925929,670865441,371536242,442972546,23619992,289255180,520679148,256803946,256993638,785508134,140565298,40928145,417612921,550301751,8150472,975621881,981221570,88116654,846870718,711243797,751837923,827681371,226049589,649528566,524747345,132756743,476037868,435674525,944206239,315065714,409082610,413432772,288990340,415523549,206653990,464558514,425826568,746790283,730015773,531444148,933319713,317248689,519626885,697687927,804923191,417632412,897015341,167181486,695898458,969142996,332744918,226425465,514053654,834817991,144541370,687683811,948722836,568654703,966906779,648276743,130070471,967805746,329705676,982738865,862086950,221000299,15381356,840535688,2683931,585509045,676149933,86935101,774293640,452966785,712206372,819864872,861770435,991899261,84070560,269152550,816779233,633023582,740017140,810799465,329509034,176066547,206636786,253765903,584591104,976342335,46075043,760185447,460381401,684062508,370285737,225646450,750094721,549841012,202848966,982162368,936077928,490524608,891755632,739328179,365117749,368208318,970541208,41748059,834703074,569540499,960766003,338133691,522314038,609252416,841843510,835942417,598239814,573074433,970471741,221503764,278832597,362880,36288000,696463993,410758036,993344920,877011654,630514826,259107316,977619343,384580335,649365652,684236269,242656774,392133931,886537807,723527677,590022986,686004573,707566691,229687951,949750167,55759302,812556094,416774961,974918956,811875265,969860854,38014765,813429625,682417372,645297082,316452703,374578265,905615902,619733791,985151249,630508670,432143020,819022256,228633185,121309088,908816847,120055709,244562085,770006242,129180924,345399810,350739508,321575317,152185772,42859007,158493137,648654309,930838008,520714459,505996008,705806555,410577797,922236053,446674068,326160478,584060178,920745664,497472346,29933049,750115522,614372152,20048864,275197263,767349019,721837941,618872259,148383545,283091784,595199371,938684404,192731990,880053584,924050993,903520409,601083453,965635678,235747291,763478732,790223747,900385539,494792580,461081691,699160885,298011731,200741875,301925201,718030348,693835971,758546506,319590,753291032,134225154,893347379,74508773,798259282,619877530,910376647,119435550,489033165,278287158,108778065,735335706,661088740,894898390,471151047,827870176,604057207,141634512,465680235,681269063,338095756,832737304,317357179,731039450,504739746,785523502,221702803,487794903,827097427,104999299,67049449,929675986,910779397,600415886,329978158,248772816,233948280,423764308,173941959,338280438,385041247,45252894,162917605,855303141,738425673,467794663,483579644,109324921,16768507,775271926,201133790,717640895,715523449,615581793,550500953,600215895,903040725,288114463,96383357,210802944,728635342,946562800,54441229,964194885,539812541,352346411,710215044,271267625,438544308,620066687,602877561,252842040,271783279,709519801,605405203,895423240,542087393,47261454,841093581,398497182,621394426,986395800,510256315,854423971,580742599,252458649,749881895,216555846,118756621,41663972,859763724,220357385,290527212,588386483,723221783,884493180,432597045,150825554,686435641,263567182,598313735,524960423,141743968,673327237,589502461,467866508,613886107,168239399,339064812,856778024,463539625,180488790,774803914,648542147,821648971,666805176,632151410,673481795,545159329,372080948,83775048,572550913,862463340,27995688,808551551,595758291,768224222,88875792,281501276,219310546,116002733,978347750,69710269,114631432,680369177,868529570,306049742,802953197,398956418,467067233,719200646,26801629,662479615,371778095,870003025,103534339,352510932,301980571,380753455,411002159,42020218,934575834,176995343,781553234,318645687,119996275,310993426,460092586,400805300,917972037,976089225,857939115,268287350,301494164,828950913,181626412,704485885,586186556,29031985,726794764,904520553,549243637,525151229,109501506,733926184,708895104,26505366,510330259,40582077,945598500,214292906,912372351,744006690,333966730,150601910,701724387,815091959,256283068,386902217,736894394,318914180,515154689,127793775,71406767,722679218,3628800,439084800,588748632,880172893,607100715,756922280,47047428,849443223,560291814,929724188,73346160,235387618,524996169,702134582,84534164,150158116,172121717,670689252,271115464,295708818,932138454,191604312,199227292,709525869,152666225,984279579,850085321,169179534,570872186,388695796,666712177,139527756,83628935,150290950,745651024,919808089,614623898,406630496,639737321,449563442,364158037,626942480,952555107,4115258,244788784,113962885,397009786,457194905,960586784,490253291,641799399,163227281,518860634,763737690,309373403,907821905,513914295,754927889,980300029,838392367,925320660,603789662,301678918,839709941,196454382,398338793,822834960,178575934,180326980,995432256,469291641,470054057,341103123,944261030,677558653,427699046,349656521,636549648,785420702,618295293,967472270,65152229,732028708,134512867,414285433,331920658,914512413,906757668,585290415,804481915,58140168,711783870,70370260,490559519,507023424,419355443,491008792,882088434,912113042,558837066,739783588,864705876,704942436,918508619,218098098,325494373,471711825,455314237,306711398,945692824,584096707,150441855,643053986,752680571,461550987,275804425,258838902,575548580,134374615,750927958,473648326,734363383,348947240,524774227,297791909,8776927,871630569,781127643,961144830,603194047,893153422,432385681,595689694,856045772,655578290,610216461,395728252,374844249,871556911,267555349,320298708,133059485,907250195,268677161,60544051,727750250,873366582,131027002,802604392,80170442,885431229,28102548,284320415,306912772,956432132,388747683,437976891,349095598,543970713,102427587,845875036,480285905,441295962,38687317,650827116,578009260,274175291,120123284,496406766,48280498,959689723,851029034,122652506,677677281,165710321,774279848,887117213,473440273,860061586,597469877,87361476,729219507,614667757,815850734,183346379,41140139,193891986,919788002,520461311,20241007,534665908,74451497,366627931,971135633,742535931,440954541,276199276,205660962,607467332,213837833,519267967,113287712,742048595,70251617,178729086,793233691,606771020,244936172,263999396,615007222,778003061,558046744,402410319,373553391,131934518,176584877,575116121,403651913,310243599,204041993,239072249,120360558,548988090,91326685,921617234,4019442,947289436,361590368,730945900,45599623,913600431,369730422,961677389,37039798,720289918,720562881,849498766,368130591,120830096,994373459,182208538,643186180,207638296,322754505,890009842,858268874,60160291,744588184,719326825,707622640,268167687,822003771,96950308,323887699,724268339,617451680,834604001,341644909,458377527,372143247,505057028,6614322,329965699,231420840,459846129,701928669,101643605,497769979,170149717,105695141,663275038,127625462,338790498,566176232,572632463,234671802,195774603,915466297,265910960,514529105,24757397,909731631,743969130,45747617,933885508,164303504,315216484,403609699,112697799,110754061,39916800,748019165,848266147,870055388,315506755,617885898,483232087,54430102,27300721,97635838,156927087,124616832,397233870,347699707,221169518,745220621,213824285,633571059,426909855,470332302,559791866,212969967,483022085,193337708,263029919,838022723,298279487,689251524,650224541,869407760,872322768,916528420,511402571,512851194,854359827,467995091,324799626,911241165,558827958,437151459,636873930,137154151,516541789,822014978,496816108,365706896,890909931,879503891,758489211,91639985,392754783,710262423,474798771,143379123,138272301,47115218,55421520,394572500,437692471,661276296,472169606,6666336,27285668,961148941,789485517,248213024,911392897,25466578,562504699,413401334,6909445,747982690,921862635,766818329,139698632,719850627,79157383,442589279,494638095,858293238,248412132,229166940,404917899,855503973,252554510,320361137,926339314,628463306,890200890,633469149,134227742,240069725,327936207,593865069,948176392,789612066,795050975,290681316,959588314,8435629,891154348,358881064,713715080,256944515,266372599,683695841,690196078,268832379,370123016,279545012,752752225,628431674,488471969,198906886,801063361,103618458,946768738,183082489,777148616,91328077,981127303,696473375,444424666,916342781,672094722,766874470,320652209,487505409,890053730,69658652,636698518,666509329,24182103,674961464,475388605,501268331,739556102,680657662,455954395,230755807,241346732,807671177,651018123,497574483,797976344,803860851,921965084,560371396,938641678,587105890,715721910,416787319,119009755,896382785,487991712,757769430,212372319,175659861,552218488,703240194,273574434,477903389,630239892,142282825,554999064,428473868,208181928,916770878,577190251,568860516,527892894,688337340,945080165,5709952,476933005,256818986,832201917,944106429,181279532,283620357,820900039,569662270,595774629,605661402,188089385,798167457,351485326,201271611,721227596,233195261,386684020,414058379,740927628,45721248,385924831,376373910,425756939,886412524,227308705,912770649,736091748,211839512,894332660,869422354,555945687,875477703,36568179,102471419,656329589,957917310,461156035,726371395,464531811,252523565,111303697,559286986,29703127,833797287,196498965,393568970,137749357,34647869,65195330,808002684,694621099,936472333,297962493,492386294,931889814,303238371,274803604,771452936,978040944,720939600,557206565,326940277,731790409,367068350,971785959,578471481,604625038,487916522,433344733,393964098,578491672,790717665,862568531,187083773,310490923,925626956,171124521,382335372,156907313,21583570,431285365,684049042,849758012,835395445,919386412,378202015,397503663,773380343,519343924,933475590,771449203,533072342,475042019,450121787,143933989,852645716,279320591,778853223,856706004,285895174,842894531,770574049,496291814,122293396,665985875,741663611,677577396,813503298,836479847,176966481,12822959,193650473,729870805,5257819,636352402,479001600,951269840,247777169,412191866,365850448,285421922,37954129,363959475,519709070,224492694,467505111,897175331,602478013,448784688,990279177,674010643,820876408,801231031,989625480,529016734,353032066,772943198,359398650,322839243,946245439,657171497,903165727,690671448,417303165,362493339,426009331,393255493,855812745,113633739,654275417,210761444,39066335,213947658,192493453,413411158,47063884,424548457,798386701,384435758,31762627,205232499,791636724,422891969,123563832,253562028,548369517,542465224,994535428,881861195,963935606,500637714,798374323,517359693,700251361,725548867,368316187,257240692,641090657,7118025,152087294,627475092,748434249,385176933,985969133,471162842,45106594,474412853,476191500,184267881,518909055,231885832,732415118,845251401,906780686,345584375,417479024,279791398,607466768,765185746,192983798,237743056,949428455,368650734,935363313,386600661,231819685,294942445,244745112,112316718,32615957,111355994,444346087,333881819,853311038,272240966,455525970,172935646,324890677,131061067,860694380,669807617,400366143,463527926,264464121,134219829,491041344,8116468,194047426,604174389,897023896,969066355,140121674,765321628,917727088,611300550,82325268,495885518,932325185,334351985,250703898,624386299,67428581,373950917,153464569,31684011,466666572,182498922,862459744,392822654,652443663,329939092,604550171,514505036,679225165,657216156,612686172,874130386,848600548,986488472,817662850,644897434,556178494,530976510,775555976,854427246,1314032,742362381,237893396,148248308,887091264,60321098,709338550,545297851,967246306,714625944,340053727,833319379,927905148,775925310,862121626,974497712,284197177,802806239,910307640,819086110,661851556,275384626,719361203,223456266,886377897,791128550,852470272,980319199,643032007,288888,564219738,430434279,794494863,325706073,538157938,522251068,71170872,874418666,207934691,628803181,463107060,785637743,165078494,884480200,422251439,375208031,427955631,562946120,15310126,36927413,221234308,332061955,608782035,699765051,288892686,860777566,747298450,330214579,658439435,759749356,167260223,811552598,118272771,664054244,801754408,109125681,255630937,789523136,604003940,422198529,116254365,820513777,813907609,729744362,671405672,830128112,920480785,845938498,969764297,199702757,830270728,79628019,353471407,422882109,184828473,53527768,622686319,177312863,763660278,682651466,707018685,86913300,404858377,43551929,312065802,585931338,419109219,307876833,509319744,205615935,920448747,711029608,453201798,588071851,177498559,714237700,773041141,279266897,19624884,295705,662484430,550508094,885612005,444027837,177927813,389105101,465940235,355155844,296973826,238335254,204631960,543598104,297453555,164723493,297731469,366207618,361313932,458064620,371577138,802471964,287589333,464068827,166838665,53870515,567428290,55867170,150156553,572293777,227020758,496068260,26057767,113241517,399212847,493775814,373645492,273908031,585035872,926858566,319952124,569376379,869755258,369910327,799027249,122562291,937740788,622299529,220652187,709543968,78249526,822591838,9109882,402490658,473585752,449447677,950731366,599762590,863183358,929332479,271959252,772894806,447983560,168736226,157734072,993936611,312902934,710162572,538348968,776045133,221838855,210547482,825518943,273766041,702815431,570871641,509400792,705023931,70756600,99873733,68732718,240064398,286874600,941886949,733275080,207172909,255034237,46704753,273189787,417963294,137341472,476469047,735887987,742302933,703544432,168330432,431641413,427016788,771434545,989196195,469168928,182738681,437448678,926645887,530186567,245441948,986879341,961606488,471996115,413206355,477048157,713713086,571170746,912588800,55993768,772416454,657911104,618569059,744592701,694316976,460527121,140819139,986090414,165843847,371214875,453730541,702159005,384245683,704389458,791172668,608317145,98269459,1754248,145516931,846688922,816953810,732815891,602187640,556397173,407817206,59621928,439232170,649264983,467788088,716839884,453187810,324747600,703108785,714841191,464973930,471399096,357830182,821908942,212424419,961188194,357805843,522928497,954782173,592089066,994483873,732195489,960632088,948026417,312117197,810289621,987413391,940830527,891231051,194358253,418224318,80483442,763650872,1478521,536866559,217257465,796763993,479808282,505007670,52693659,402332927,890328140,765603724,251750840,227328522,805583754,792181185,879856437,901693691,870643680,64115965,576158459,478483993,273447438,348569190,36427537,778385286,907140379,826410694,652575112,353538455,103345217,495574622,561188995,922979580,923440708,596433159,430931630,640857599,730381125,461785565,772008214,400736526,321886264,223760918,779173435,50192969,918928346,451325561,835461360,898927532,104087344,404991638,269302690,452939375,845995896,458431892,502640744,204432588,583405880,887778285,854727668,285570199,495848031,758601300,862887200,79937252,13967951,436471459,310697269,787114237,578472971,575894862,779087380,676009185,677021760,862792870,553017113,385466553,122325870,93188465,98238182,999507138,613185670,904158128,943457541,313851040,789302792,271743869,930562771,978516604,874654586,826194469,888578872,47897241,225874822,664548258,232247089,744101337,417063609,748907483,367091454,580840636,822907127,269220719,370706920,78701256,532569886,233926647,219481009,937910362,808902520,121604064,957972281,915675753,589965234,152037598,68591091,147146826,722307723,989566792,592352952,841359408,532664925,748338498,213845939,270402273,606239389,688372371,211432157,172908291,395553284,681756722,384467382,763017648,490962386,807429815,292350904,772021448,364537464,978308802,673129535,969426476,62008472,488289701,612149500,919647604,940208298,178290591,115382695,25446345,831839038,762220079,381475085,749573592,908501098,774016162,270662568,72565149,769339518,478008239,85223714,894937728,350982696,559550232,477265468,50810638,81745300,994442134,517186424,49093629,958290289,653356956,361086387,303048975,267903539,602950186,686427346,620623517,522338623,629216146,48146800,658808122,497532179,7548769,884215115,925842049,325156848,232439682,162855255,97160940,44285338,389512292,896976727,823435328,87101351,582663435,303693298,962873920,867911913,192869874,975106296,8061191,476485024,805781463,159277741,454885009,371822169,206893272,185285,349429270,776498497,133017331,564756435,605654227,116749465,552261504,187517426,664396977,147059926,617353174,225350669,91596224,190689534,170201545,511332304,367445483,445511886,460084198,810439891,501756602,419430501,313368387,17071041,898868125,504643223,518389798,656972977,18979020,966467488,693081372,857006058,675953368,897367089,954314047,135370117,470347561,965106827,581845267,754783063,326097397,103455554,197773174,519414683,628656330,626200348,882897972,698231953,693119023,659449948,919967483,242389452,607703249,782029534,361447251,524085926,698477950,523103999,809220948,411331357,285486381,966191788,705488735,60046247,790130839,572375810,50492931,880325205,621724945,14479979,997429116,873794610,170289550,261713464,333440168,579422877,116326011,842725939,387574798,86548636,933911008,997556683,373825278,304322463,671487839,591064520,505532360,593358080,492161677,741377382,250260410,266447829,355079748,975635321,785325861,997347514,448239241,206427580,598740568,56607264,83155686,162257777,243110376,865827201,364435291,464228962,745083756,550756195,760033934,552797054,415178068,341169030,583034271,743102097,955202535,978939599,959959660,892442578,509994813,213827118,469246351,837691710,52785430,358280214,403198680,552530283,419364103,210727533,277399027,689481425,709919249,673133425,189589207,562962730,206755376,537909855,183021797,716551251,14827311,925701734,288857971,891042641,578422677,13420742,475710021,900726709,527490102,608662378,483839930,127459704,158531387,270061108,373610762,823481989,768281121,718251434,687898803,429232037,140062306,439001991,100805389,999710966,302971105,92351573,551075416,520499710,914093664,62372357,795299017,441423331,618817957,118984582,470510641,849220746,47558339,428897952,471207720,853528955,706003953,223231527,290676224,720924986,72772534,863436054,4853459,122858991,972438061,962452481,66183729,954366021,41847780,777714625,187116083,991790759,350775729,473075641,42556992,453791863,826317082,635219589,941159059,153238870,573179987,726903796,741469215,426391446,138689819,714525920,878964648,115882897,763720023,539986485,556378110,694569982,38412509,219676297,403470319,875981512,210735122,265189285,578359712,260319255,437033417,162448885,674358851,635864652,965468313,479186359,194771814,460434629,745029837,165722289,35226389,966598045,240186708,51105459,557356080,789049777,409016105,84636515,323260739,720994806,569951795,939864630,141358433,747854650,122277956,143217984,989415604,6492489,625833976,274903832,596602680,432733818,263557774,835515172,511973686,901500863,170051024,35851415,354766218,484479506,401945983,415837356,479579000,542630216,718161980,855045725,849099090,590682263,340913091,788282192,141549548,958672102,755017851,587527412,425141624,334776776,469349132,772322422,349793960,275447109,972757408,93748526,803791456,890923687,249598988,417551068,677974163,703597934,199522468,617945348,678158099,143648326,596072542,896506161,27350014,356005909,490545574,690016362,830025193,198162658,474591577,71729146,92364889,834177843,397759281,895932829,780130572,725366646,100364588,461257455,435626482,637413114,795173512,660221287,604878031,17983869,822335100,799798135,1837987,93861479,56186950,542591848,496006427,340867435,234026699,809400182,322958195,477286495,161311785,139233301,934155124,347739428,584061813,611607364,742623485,93248789,886979013,321259149,926649576,582804688,998268074,706773831,523713022,389166023,663029679,616774303,535478300,641163494,33764139,420164023,234246048,827763226,213519144,616150134,870552183,447906981,458719266,394932426,596677351,21513507,331557505,539756518,83831222,455683994,974799273,770419719,407016540,683290274,135504549,737965425,399633029,885098836,653604343,863315091,683948048,397410863,257041535,153717135,138107525,579114525,948933204,750825750,94949432,140113393,403145606,647278564,922157176,621890419,712076045,96985964,794431652,5734306,669182815,138884347,769325298,360270826,950623545,852909504,393556868,324489845,749566731,797304811,782135475,553936535,73057885,756241914,402914812,192010073,386402341,272934164,928974047,164151825,329902836,985426833,593984689,266064825,770825014,430204880,260996868,405297331,606296041,447880533,777219949,621237314,769208707,498492448,480455138,954198257,890912890,581838094,567592869,659571866,302253257,248703718,358387552,181666686,525936229,95423091,327398105,648657253,622858644,22133202,484628184,368246711,530644279,655907366,729144021,637314129,429252371,873906927,956080328,53827167,220325965,864131864,533063137,539351102,930097297,622005504,476005475,965358792,143349218,336978386,418987337,530155663,327276042,69257348,100573957,396376655,235070263,438491611,431361429,948263201,400314824,446660224,909962525,559473588,683774402,592844108,519537607,590560910,907446305,654759497,932225159,937001103,56027283,886760881,725225982,114332588,362934140,733354598,885096148,769102956,72464544,333928263,576099499,160146022,998029200,169409275,213785999,791572965,651183983,175621499,526185167,625839695,37756415,416785320,428977364,789741546,235305198,354370332,293295543,753900181,682178922,141918562,714949470,490309479,110929485,133525694,526041228,589862001,487152886,348902641,134253129,472952221,762288066,199198115,717840235,903693818,714154826,45117135,229411094,727049367,315235711,364673240,262194744,925265886,112010606,354086968,225424690,308010243,222636222,135568964,107135114,313718253,342692182,145488674,596162792,205068428,882516386,879069735,937941259,61375413,563459686,79499106,84557699,416819066,392414604,349277725,725833270,851322473,583356809,941597672,534810305,90888589,765248175,168338802,979232034,655520074,153964211,867164796,157256743,569496558,513697658,768118789,573661063,160782750,189789156,291580678,517041275,98764791,166617460,641317051,335977766,827185096,19777244,393244846,316537247,457889579,801270118,913764289,716493417,109693905,132335924,586655667,424705762,581455533,545737051,887358515,442486201,698286453,26908921,415957445,524555782,236138635,655117737,413692325,67600845,907828076,663353426,504058828,745435213,300074430,390265797,760564774,447095806,10967537,211264157,645937906,915750799,425474085,450696805,97942018,624742451,685045049,735326496,514289583,119502359,9318552,440556322,658368112,672294752,469152070,816222837,717239170,188590080,613227494,749233338,213319970,127928859,766216288,343122047,764125313,486742380,771471034,773291135,586292091,888698701,864973563,846644988,148241061,499529920,627398752,279723469,42496901,543015626,599520540,471187130,854503983,289190593,213730084,280903512,932365420,978136134,167885294,842302221,282497073,658250298,960801,268121448,216088056,260191943,811340180,273167486,325758803,733021343,621947253,840927479,865396974,758206232,495168141,63467305,9312577,784701364,287275353,951827100,727063039,639846616,396372419,932741366,127719818,134125724,743849819,123408208,274265637,314741315,231082504,995592699,94220050,251481727,678283034,862255146,89674569,776988668,109364333,274210609,705978022,92479691,835176837,946275159,826060570,310316339,869061381,180159942,727326479,508528908,708756618,142004313,602950932,703795036,375057876,147986833,857123276,909040369,711778047,600232458,420747700,900879293,180982852,518194155,267565505,706885320,364037128,205802149,907578724,700172978,656935656,144311867,876041496,65869890,459562313,325537986,666184275,833271469,270738067,193305204,690599224,424764373,655064295,72206717,397088745,730118895,421735165,328144685,286009184,473744702,442083350,861514112,489221395,50208799,802648450,594433356,29551159,978392059,56576860,431042127,625966758,606293218,720527280,146280789,140710658,138246238,767441930,735215190,692482198,542176155,570538867,612138068,553158365,438370484,641765384,397713532,566532713,151498877,555372187,908909681,231455764,412077012,482158674,632347751,450032977,806917386,425606191,896404925,573675377,311168186,500784107,684124350,245309173,293361244,365815495,728207756,581296583,93206138,182393730,790316490,476638154,66946528,281493501,797916780,892247959,138410581,455947338,630520354,700654550,379032005,938850669,107171190,816526579,556885733,582816582,22604850,85626677,134403477,796896040,332594491,354441692,549583252,223432873,348736831,102849932,88284645,129118900,265648844,392486366,568380180,763562804,442133665,863219615,667347657,807799061,890089462,917449887,826764399,984105425,896036160,245718930,554334106,213564488,257467645,64956143,619972114,642115186,170792510,637320720,668601339,641001859,788600226,350494848,324306197,338853582,326224883,874686742,62177601,556006738,958512223,692500110,243994479,470490525,10598739,767453717,456089372,278083387,196054658,945988288,117685828,787451554,383540787,957144236,874030087,954447785,225834985,516843073,307625838,356121515,350156974,512609124,646634825,962019138,551516493,279237092,998906992,670679776,770170426,921965363,32954982,441441821,910401496,59514223,78345385,486160733,69347822,224759357,288101509,218376913,724148606,254576782,41122456,76805499,125168264,895055374,215187939,25677652,466037328,294162569,940564476,785381154,134116526,34699950,166350613,851414825,364992527,701842720,983465012,608782167,640847154,725483982,449822296,326122708,732046545,530878634,558931944,350991614,956149487,678406838,477849788,921968203,891974612,649493756,588302658,437526156,155916945,604982970,895522318,934380167,600396541,1192821,761022605,613607110,665440249,443449744,995787681,460406731,788986965,972321409,643642275,858510429,167366661,64961587,381743472,17379119,100154604,825204117,254993538,211619474,72130022,647912096,887383633,731762537,826871905,867815601,128199782,914724998,931802460,285927157,56139359,477738067,654164393,700996663,762451588,897447572,571809192,481796289,532408530,826428926,89656611,125881700,289756523,918205417,429505706,80291480,829300501,921189861,47858448,976364114,978733986,761706460,740788540,838621017,36553489,459829837,627925228,680035723,744795576,949784842,849197322,85832589,52309138,713412501,165505040,800696490,739225381,980963558,994974434,627937237,931204322,645932072,859455692,472006060,5963916,728048048,962666101,203610861,91742867,32360595,77971029,558350705,959733671,656433436,886163681,610581852,967717660,761471493,35885901,233965270,971523885,49992499,845954405,646035881,66319105,107808935,393225941,251619955,213971871,720736040,84656602,805909226,850288090,549370332,557880826,726180183,146865008,653008847,946584359,290960283,949131211,673303941,65961979,345072157,959059570,839482553,766451931,598527936,336250542,634099077,677738657,708197463,625483080,507213437,854256047,933352842,47774865,659678572,279777527,886239481,660911389,589009763,241561422,303254545,726981458,467581948,39915531,443996310,746312906,65936633,912554331,989300142,159822650,336966451,140961383,786293827,589154343,15733779,768515319,857872793,183107869,972784068,751521863,903215843,486463885,176791368,758607130,431778651,547032428,920879475,923488340,523359457,500628700,206878664,86667400,45891571,458067774,658163341,591488045,348427888,869956421,350032334,423742184,376618729,454166584,478648140,61016152,201915179,239894356,490261966,811022782,355021139,826457510,155436156,636122070,278226400,61588634,974703953,285744506,243074146,463182089,417445035,583415480,634189989,686447091,652981312,761336124,698784843,351282531,191254931,814484406,311681746,824528232,104772694,364708748,212481321,595331950,310339716,510533742,438344528,924250613,776298378,667190415,211472792,474187738,461648826,849977092,869983811,475206710,235992411,62154993,341523328,111988447,290533822,703322694,646094685,301267195,263296262,887065822,119493938,620332741,873226654,640795108,918278190,759494872,285514419,108225196,259599102,766233957,285233306,360352115,195857542,742312079,593302333,368784474,614594516,804384984,534639570,78097392,662740863,873220378,950924123,651682527,238692761,377523063,952292765,902886137,171408920,124664441,290334030,367228546,512228301,613976665,540415215,403988653,371427298,243703684,219131528,4270788,164830609,897506123,798077009,790957585,463937819,236960866,418309237,602915964,544174366,91169858,590100567,96471965,731821308,667601504,975564336,610472030,281366549,419375183,516838309,34543251,6603033,972486228,83088730,839881070,316836950,805841426,50519768,215535529,446116177,51374244,983085060,29997591,460650340,300511238,430449591,627133875,500102063,104886866,948647367,266400195,798452647,350813782,242600761,132939579,489453319,272639323,16917525,491847738,601090072,480703303,632587621,66171324,139666138,850500207,54681223,916941342,585068819,828778988,67764293,629526099,960519659,807789448,634354205,901332026,520220165,184128578,233217354,299017991,687940868,95089684,822490181,788405290,19050186,155856439,296274982,693338828,897543126,603108086,78273831,116881735,536390413,374132663,911097519,124193349,912471489,461888564,598154103,811283858,74724465,340098553,441198740,193470622,13333156,957324202,199671269,69419200,557725948,190905528,66773449,333988022,977785923,613866701,67005449,651439158,206306701,47996804,979130124,330724957,349771000,401709826,179333108,923259611,23027362,997818384,250109690,275115932,727813060,984438030,301468921,698633394,253569636,262917716,912905351,689977162,604931523,142870088,602496336,943195383,356895234,457619754,677731763,698368131,101398839,386772173,533780119,844398265,98295991,470581769,413684033,555476009,795052309,534420056,566686208,557316307,926521246,262629086,374790462,730916301,88036219,219315822,362083746,973118104,333896887,469038181,153131524,330588432,221456016,468061486,774866841,153767498,123084436,911849010,155509252,320925402,160309434,830102314,256966367,353008064,805622794,523879529,676943796,236314097,717038112,201892051,913569588,337350501,450222650,451501713,515900644,203936099,292944278,562827387,529000648,89379679,780936909,516146535,548284043,405782349,143906947,755960218,618436584,234980813,342045366,889271716,232844016,556013743,705573270,867117311,738573882,25672146,784883467,855293566,504316471,72841427,133164932,99623180,473299863,850503559,253745740,202274251,332187026,954873261,52843389,897380830,143757443,872273516,350109843,65698784,23836765,346861921,885121760,927605092,514885943,842294855,981952878,967357678,941389234,809176551,573947173,677973732,391607090,534246699,775822369,275316613,502205198,980092503,103924205,683192340,497350138,933825453,947842323,225676890,868462324,830483738,836116010,793873587,391449924,352458765,971877117,785405435,333654859,18650038,745621052,334963480,934599997,62808363,848059679,94327075,898024258,913863529,64723670,969055147,818961254,466388151,874895374,834670682,313106269,4687166,743518088,656852932,479222161,537614924,747767466,415519741,201676639,232193679,70716465,588444571,519940944,865636575,482943429,968440792,995378431,580215944,532571499,168612942,544956634,190342243,995536952,717679680,811560423,876076501,387558269,116500800,337112352,440563992,344508878,588666673,922817570,633781453,103786993,188282275,117817088,990911231,145483863,195984458,47999613,632314257,959728543,988504121,925541185,965113884,28744702,242863853,302817267,57585597,717727985,144665641,533432499,115334218,685698036,787659795,142015298,219535985,123865016,941092833,767552638,734709420,799205149,164718450,846708171,800494338,454013584,418439908,719126098,865675945,974531365,340300233,737320091,300331803,682373691,28914072,981448775,564865310,385808126,753163164,731291883,997653521,259989404,791018432,957738329,284688707,120044371,968176696,42750377,120778616,102180372,843687247,35621965,985593572,651974738,562271366,22469537,275064759,133633963,172064894,84832995,706164229,226777191,886977262,797679329,340414294,501361193,287147339,352007580,808851810,225258978,534263709,809916069,498036687,62923560,142197655,526419820,328203965,475636336,570436758,24318838,63127148,303952258,896584494,657927609,758477156,404291854,345190005,88191399,254575496,250869780,175287680,497638530,829239203,972844218,260200001,544460932,753394882,872114067,302585972,478151831,69485805,557071147,9044495,425947413,528812323,487752667,965224651,69133329,636009408,657513679,94107053,88868784,338087420,12515869,311292452,966896017,523766732,146326063,529793335,289837383,524053212,536712998,800766973,907010126,861460730,189677581,641130815,621145425,135250431,535750214,335010408,520766994,173347213,870166499,478312041,795959897,166174883,203822695,829030294,408108955,249963174,755483296,310457577,516400886,808916164,542659154,17801158,776470536,464990661,178057401,711469894,969146046,501019598,359032898,943609653,583804544,624973461,254027744,337528021,524798582,50627693,661467883,309303682,455793829,713329014,839943194,647844090,800814437,748066086,405510295,861646481,573975050,69171752,994361113,958924174,78734338,858174519,629558161,277431548,986511456,814326897,151507180,446285816,271267907,384162285,235732926,973036026,424134158,446634749,176363462,182456793,957480448,520060557,73762844,85735103,147959629,442807952,662639965,836281644,284016386,816875102,997433643,82746406,246310015,854974466,768931536,840095524,343849377,569270077,121316749,579516699,609861152,517538079,110960761,454924317,92284194,838354108,683268273,875937295,331869218,491022074,344049707,428653197,247976596,771601604,241341235,226058397,321294900,99273670,876886877,498296231,336392,391958421,702297463,506533483,895439698,704905835,224251607,512302621,205702945,164758717,143777623,301289903,954902383,791281822,770680236,788989438,781203988,110175751,696723911,124357744,190732056,855112370,429785997,601715013,479381762,352470931,724581327,520888775,950829081,995119264,406923996,923291124,257791748,288680218,614813077,884934760,635750363,724903005,958430710,763448081,793620073,741721746,102100093,346858656,368099148,820387714,614456662,106526131,810298566,14457976,273869039,103803900,396042351,277294187,125515045,362003673,381728071,744824445,822451677,4960519,355834309,564201728,947013150,600082116,185935124,75906132,939862132,982738821,266166573,526053933,391559282,900152106,661779636,233693690,863093280,540579562,403355016,93411928,726143701,258795285,911942786,667928141,248133517,746695862,7886741,939220275,388181950,156871895,351520652,927297241,217289872,73885702,963563741,856763749,430216718,898155810,67660467,248821235,31519482,960200522,256833,968719389,83278667,76471776,140546526,682908716,319712641,683174045,598442418,910569168,285876162,615011456,316842465,32099947,824404821,779369659,550359218,868592613,782328722,367299195,248453217,518312115,846800805,190478791,699428073,369104713,768795841,854919972,942701190,94601816,772048530,284309734,469440080,235905192,14112213,298762198,411344447,354762631,199139287,852582723,983393816,764148332,355484209,399013500,108748625,872223096,130432651,881951473,592710381,480935933,667697423,576595507,937410990,506358566,969851458,946701661,522361605,637774782,578036516,832618671,737329314,677013973,914821087,156905356,113471816,213825142,72847302,258093923,159481735,540870376,723083690,910684939,624224272,170273441,410094248,496765325,542102574,455968286,702623538,44888895,616531278,275908813,567265787,425979440,468412613,928482948,418195406,383875811,916035630,709741826,261219408,452040995,210582893,687374036,819588532,47955281,594657064,431646313,937048539,519890514,30650508,527622641,675457302,271892537,737559061,906537262,790853550,491463293,241964891,697622473,283292177,968736595,417470759,718063699,474141543,66771613,631277244,561637337,871264671,972570623,196176283,775880037,962748911,531703971,17340587,651170066,9627691,377732307,771480203,295820553,57922111,524468320,194503033,863406550,317677572,872459147,822589165,130884871,98307161,458982462,943572414,721030541,456075019,371870812,784580219,126002439,794258211,544800147,378668587,847844012,243927317,864871496,369933752,465922575,960071371,404283686,777795338,848627999,149032849,99100492,984841793,978024068,973725707,580412771,536811603,575732595,620677180,60423658,803807122,288276766,523808579,953830986,440515557,668737460,864821149,19672928,502703560,647042117,889741055,133782248,928413910,848074744,112981795,522350521,628477179,121401003,556150077,722751233,785521184,561521148,775589381,421697694,949112347,455991982,152725907,159250563,841675231,511338028,837933174,575701905,182188396,92573222,69879318,215049245,170006355,43806791,769236060,928573569,938834511,556430155,648008196,531677231,819857024,524662730,814477194,636382758,404851181,335088977,786391362,310008432,855529300,614135630,979039506,201365410,863536150,517246245,219947648,953306055,173740140,433095244,803132709,122578602,925768960,414526371,975888160,208240897,991124692,554839752,38918972,101463591,516018896,773520239,164642524,686786485,839809506,599733623,758385804,236796285,982289590,286588386,441259196,431551310,580792750,530926655,398909504,632619803,377208769,325101590,609816742,651967339,492710475,804900863,118643858,727841216,183476750,378972139,70606253,758193346,932045299,802117486,350727246,505850928,171911323,902457176,485749388,185187110,609287564,29648048,597828896,297584833,82797694,254487155,510518474,23776371,794410300,478983014,785380255,848659854,535680385,762323173,415877039,437551502,167800,78241504,952533086,702672266,779842998,795022383,196125406,812303964,28168532,34701627,330810516,59181941,690119425,914393829,914374062,969953847,97564834,564877821,25275369,628763369,162217260,403798662,536031235,983766057,935785926,99707586,892938639,818641205,763079952,756833056,319430943,190370174,532202715,512730062,579389027,437837120,767673710,778856872,31431263,770151730,46318973,453332852,17381541,255163673,252177894,522009832,55178570,460463390,813245325,674620076,106808018,792398768,362435910,602640637,796894747,879580016,849627291,981396016,953522212,743905328,549630470,609165436,640308979,876511965,717668010,951923999,897692767,723021447,507691387,636180613,934792663,278554585,242295680,731200581,707122883,611408711,228678577,768908743,10328359,507647136,45435890,736676889,306695557,247817246,34707734,318931925,316780615,412293039,28070373,345322201,137043678,80876842,218770461,197158258,464553531,264639024,693138389,790083580,475757127,832707583,995091054,963300579,481671935,501589167,590577474,602866126,77129716,505973236,757702722,417596134,986201070,847548755,874160580,638351730,475848525,305879544,899746624,78250673,812075204,830060852,196005758,736467781,584420043,278496443,831758969,103982375,984905733,190641578,323305326,632607617,68078379,411530213,273047772,457716632,428785568,448719836,766908409,168670005,386751107,390410224,483207215,515253115,466988632,978548148,337852581,74086688,385305046,823637836,580027827,786945470,880636824,169025527,122031515,900869410,234504793,297644208,230046151,185932273,869709470,952185343,994208724,96544972,30430631,294656736,249690063,819607348,370731773,852079443,223787776,351832026,135179152,813989448,269525594,604306898,977394940,782036455,125489154,992649018,497672805,229253665,577822092,895478362,865965093,541866929,755089178,131366825,436444948,809604958,638413217,992034724,997243125,506862369,578590204,148279609,356154892,346505895,207891603,514818383,302472310,144426780,221858610,940190460,575873605,383403361,971204038,764519117,788209075,990899261,384424647,494091377,38590824,148265731,6246894,394277417,130170596,87563214,461510986,521886983,330005632,844996463,241306777,963035160,110484843,16238606,261325203,341752895,516976761,365632258,885066742,374256869,548672246,67288232,447123512,132381673,19832299,555846760,409755740,319189812,943009628,547420883,932653196,439866843,760253479,612666095,639065281,84057981,719851380,456552264,45582856,266519425,621479124,605469736,8291563,273792146,287424685,100665135,385839733,512392685,72228544,613246328,325906260,53981421,555024007,543118209,825091567,153135054,721577883,124546861,187719351,209808834,181668070,301026704,255986745,571384378,934113341,505712292,257056346,136089010,382397759,329783094,382641074,157251274,262436868,972705265,329184881,558534707,677585252,953032866,59253181,789906944,886428410,506145504,945233401,128577550,519452312,230177917,883976521,914396562,13171767,436279380,569588246,869431375,559264723,67173823,724041904,202679096,817105692,228212729,742652392,413249745,62818457,739938209,327242291,496971133,499850454,729774995,872641803,650341961,209981900,926636136,213033752,64679383,631044004,529457084,339104456,509150713,305467142,422648712,691749208,422018608,310958866,860734560,783103095,657237154,70161629,375573645,922413497,635555479,222279050,751759751,273682120,694382364,43041594,903962896,337543608,73756317,877954367,704478996,21610076,498254469,862860896,388763376,177844113,312738485,158743163,825137722,911818402,806994855,837704396,906534055,34281685,773722088,800123428,286030907,112661508,511918776,747407167,881796138,520593457,425386611,911531220,664097079,701010865,636160031,530774166,277810733,981734030,913028533,788656999,29213322,878103194,230806560,849938766,134404509,278501172,435947577,520781575,859808218,416790995,138858790,211836758,780780011,806407147,440333613,122208789,233641038,701112635,850808158,433267314,146357237,81400373,900719607,921874744,710364138,375792994,384434491,533421652,823360131,225405686,978041037,682233354,162607473,975123884,304718757,977974419,472656194,722245019,841459952,218058749,914602815,940142225,179641966,952430340,551776610,409066118,496417219,806253998,34154785,199837591,629334624,438555558,52882154,668838622,706739911,467252064,457884097,973644912,735050509,43578147,68648707,545492096,530021214,339752895,166592340,788497412,412375254,962751978,895673632,216627688,336442885,88870679,149731506,24853746,821995127,490272129,212173560,701189742,995866837,539590737,339129842,738813350,55239690,669758773,769238928,207300560,37462929,797969678,421815087,432791111,893979845,895007444,673471294,414943431,938422173,547261902,540707092,322331174,984079077,405053399,247675878,36915323,981092475,450375796,622862390,45604174,860300751,878823696,512475291,499947675,19082534,104118253,759098318,378423569,408622868,462247840,775621552,42233166,271209465,150862591,746248339,258835956,226553017,19214985,712237145,92146933,773695100,990752679,620747418,701633756,373427185,166944827,667375334,953154428,253308333,60659314,24802966,137115364,462340582,219869062,86486998,78580907,151860879,341609482,514317756,215231502,600807801,498216610,677806214,834013623,265672361,529325253,981965186,182722650,267923275,639031011,495284982,139737553,130485627,592484454,214499156,124309832,593980523,179439594,750073679,844468627,85423184,251303536,929587179,971443381,190610388,269660732,267932019,337330233,605716955,924868906,151319507,640580806,83663247,856697514,138390024,80738854,481123759,304182963,748953431,780613679,926071756,410780716,532000904,972836000,731717058,566380319,726203615,570112957,759935156,6480181,218069297,509496235,178655675,247857473,311281109,46845778,816387102,971542935,816523836,269785177,804813114,699362437,603482396,377142042,123807713,613567448,565625319,619740950,813954047,497942587,13552708,303931862,406383389,848276262,8734731,8868007,64372671,345028495,18693226,105056320,155469012,886298611,742837719,657629300,18309623,998527051,836111378,155869989,206995247,640356162,219752684,767151516,129729492,318341237,290925500,883289847,942806924,372614687,240116027,581807522,572525828,630531596,641959806,161411279,466023001,757174340,322810868,355271124,414299329,164609919,432502446,516451290,433724813,136271128,35276669,480163897,788516453,147990127,380806960,423485545,170524556,915113561,910557012,159390366,952056200,548429619,771881449,253643145,120256450,638978896,554556787,181286760,518337491,849720972,725125739,673020533,665150793,923680837,236760708,792391094,287072060,376536868,1089750,475069803,468581326,900648698,895843148,921351348,165900029,876713125,387869347,504226767,909891215,667608065,220114390,800518895,578356038,518986476,505854797,458006651,695952397,547195700,609506994,170509721,154859716,982481696,633018943,197120061,707110591,407012152,319193186,689377169,564078150,261805491,684348269,435492257,400890853,384335094,210947599,111332744,745761021,433060219,273263996,139368429,488536771,564361612,970881393,260158304,715688450,67745315,586780489,967184608,194641561,101011928,646176125,952776828,57145228,615889879,42607381,933600477,320972979,196044791,825674225,92527266,403639171,764018115,780314330,595660743,869907457,245767247,124219206,328088332,559067597,896127266,128220726,131508849,795356409,853264065,353687612,769289106,743304353,694071176,884444963,146279354,81010538,620401764,217728296,799088277,842764733,700395488,295638046,299998925,666135614,75762128,945772766,456254270,202521498,456048557,584269183,755071078,806651877,718178093,593335984,936827424,439237288,59458345,186086591,705741284,531040155,655978919,38674687,298067967,903427953,484222902,679706713,8464749,969628158,981331163,552408590,666103768,722879232,866012337,584947397,899916590,200537963,992516261,673572968,417303941,760191010,196313592,688393191,888210068,849117261,542105693,975108541,353138746,90677077,972428404,137124206,805207636,472999422,779147244,495177580,570644661,317472463,176164931,632221744,303794312,300129257,826392483,212381714,747532440,859411439,4008472,522755270,232747651,524440246,285278478,136721020,775762104,789872704,195547080,573460699,419908975,679688103,380912474,846822065,952556557,161219458,759136361,822037790,983212105,441750636,459840065,256239684,91201244,85238020,980806700,702121165,806774236,272005209,627522873,235672193,93658559,867886575,858049438,7288845,394840637,297111014,553183020,241397000,335638143,934985879,181248296,190061320,311038828,143636403,404788245,135676848,350616871,368083579,838085610,493117702,149369567,843582015,380537322,52073718,967995651,575888066,115901238,312341013,485026712,161668967,886748021,251298280,793358875,521235179,53582233,781486041,440732388,935092209,368426676,786080832,127856658,530239156,927403415,355075063,919269769,778777874,629148866,350587778,490186183,305765495,229471480,277770129,419226876,897591988,261673685,348078347,885708876,790449289,224186621,560180584,810432236,517674131,983806724,109752704,546065963,674370358,554225316,250736224,411061056,377061304,340903531,8457642,617587890,737216619,681287792,722311761,229883578,789726501,995415324,834623280,351422176,134880033,422545989,811334837,598092347,370190518,511642381,991340473,580420116,89893801,382840783,688969139,915875120,723261781,116274256,68708696,464829705,938731390,210409701,417109724,278631047,712197543,786399162,300115651,937774931,826795866,473657468,533395828,318279954,574543393,859917615,267982682,414356428,496725240,695899128,168840921,577438564,197089892,49428893,885468030,574997613,236717067,639736401,549851546,832957192,545993199,332700464,589593193,94083498,988587722,407139720,543336284,376593639,649440439,157323920,458183783,29555352,438087944,966239334,287247696,169314482,487736458,331225855,346251567,642539135,925860335,355418392,735697683,666477911,219701075,336158953,613399502,625129777,787832888,451983304,540729347,35571907,937089851,120169069,826361295,574843971,93644469,236399932,948687783,424422468,118748807,34783820,934649917,786487756,64196844,227578074,594701640,547357292,542836457,283701002,694971942,595640728,884107784,323973904,425082985,188396633,333067203,671351419,610596927,294973293,302917854,830463510,472728501,778152211,167702699,974869710,645026092,416535367,997053144,194576415,544089297,73677036,238902430,983737245,102171793,14030417,127317287,293784314,697073984,283493210,260427081,529944590,841336972,80895030,432723262,328520832,552297760,504720233,612617082,983027192,278876868,801739744,130775343,506592906,897604561,544676958,13240336,56358545,17705274,725146605,760189074,316931161,122654079,682819451,582245038,560788776,133209459,247997345,882339939,103898705,112033679,913561928,383027382,748475945,763073715,991408708,986495874,34067966,714047012,892549747,282570172,75274306,359913278,127787693,466078354,522108982,8351079,790954032,264409617,633834817,656639956,483490697,465890268,76997679,226210027,500330458,606344366,164858324,134881889,299839013,188548832,781717993,344577442,127336241,967313520,667746361,757231171,828224761,270496746,476566009,869219811,970179562,106972441,165380747,694855318,685589121,927936264,825754276,981434581,302314942,260111166,741589334,695071163,212715717,917915152,801332002,596413618,533949442,298271130,438224167,483663147,712179450,718766100,739085038,286690020,275398585,847017682,856652628,622621944,918020548,194190897,550918962,487815236,57205603,437647415,333692983,459042011,641623681,941913352,601409662,565959705,977239803,229488207,572615746,36721072,315814017,545360326,344720282,212456378,635120402,695430346,17554278,581337689,93999944,332291995,447751450,619147336,785894336,802398775,893896457,188524782,587866633,414589077,395350073,442015767,199431402,103835384,177069002,787855941,347476822,146962288,247222482,198829152,175931291,38835424,518173640,974890502,75079143,345928205,104667457,179514777,147547602,769996622,680934791,353764559,74338675,898995729,740524004,329155317,330348128,835198833,307427622,725429400,977144251,806359583,527223172,396455829,52770523,101312913,289972231,223511436,125700553,814915382,451343059,799806757,832123797,685504237,751951448,146634547,255196604,176300025,971180707,745863356,221756007,162667305,438869713,877796149,190961367,375392617,867028859,586419677,705675185,269321541,870930362,262133914,699630928,361251904,900963125,108741216,135282730,656283746,864574449,955205616,643221202,582478932,918542566,416751652,166181221,186802222,319283904,958252245,598504310,590214331,625573518,566068438,22300617,954761013,828840065,512921867,835283652,801345406,262879927,793506621,366898936,148355810,717905539,833743960,227553045,336834832,192981114,556728622,468967818,20539994,736201101,458106042,958046393,475534893,848294487,367754194,375198804,922898454,384516176,256002019,25110152,282414315,472870202,183273632,791114262,883816009,903705544,569742857,336339025,188503114,892493026,533052823,926349143,530768458,836546404,165780595,651244401,909306935,436841209,86487074,679292785,995496572,175646248,833754922,585232991,846263831,789068238,379874268,316762414,273876975,818605014,528695353,746673303,559045321,764171366,55198752,538605863,492191448,770540586,650053778,736014999,318139519,538051969,996322443,866138723,703716229,978264467,15136290,714066268,473193017,318077603,58341565,982058027,43603374,366216595,301198759,250311964,314677964,587551828,488716936,793672592,636377683,226566053,62170930,997269650,750302345,446312995,277756320,436193863,842021680,913375778,649194016,638192831,289942160,145273923,612905600,949519766,928225883,792977005,820646920,65726083,153099156,233049524,589171271,23334584,528470294,659863159,175892221,740102033,846896688,551598701,157855921,261956842,592621704,243541258,318904770,373909839,438542903,244873120,84750089,670947566,950096850,712297320,187543405,49770139,754021729,540753164,921840037,898631180,715699863,222832213,722407427,329776295,866329416,859280034,159230545,387745563,458150457,257134885,604259062,587421856,346593567,978395889,176566525,756918422,898309660,354612003,351629295,952366466,225058950,901468589,818708620,134926267,706341189,802702181,744329735,120875953,394134213,1220829,165997480,813043796,110596394,909381367,346186533,226978882,423400634,382444431,193911642,530040922,3429572,889647892,115394606,674402932,945117480,756267752,21607309,497616904,925201538,121873545,111998928,212816175,84796435,758959669,472287655,755312060,727986642,735904979,109348496,674602788,213609740,76191148,540137573,766551212,242870752,752541986,628336627,581994480,128184519,844845468,974810213,629368683,935647455,229442433,247473990,657776420,461609802,709173289,466155443,75143385,45122747,581048938,392757362,394848752,414233698,164910849,832821072,897460474,80707993,897514057,132865267,132443837,172108590,170123460,981629327,277436073,695247376,689696316,759379083,349110209,243162288,792568309,371938648,240927045,401582576,55752878,701557429,351033174,967353378,274211529,420789575,504963559,370601691,537793506,237324728,325825625,875626887,930644012,809324723,17318128,346520214,535902322,925626301,858667748,680715385,258428980,337642443,206837308,745898593,507806434,767735644,689056689,613357548,776205364,832203231,836959356,582091728,901965585,142733692,961287133,514971221,85603799,663331353,646967974,28868234,716958877,609980104,468872303,939908803,879325981,248376869,353186732,700631076,820831114,876337703,513788568,903857823,503783675,554275113,392687538,933998459,249338048,68317118,953402641,253685396,149865346,685508900,924809046,622636,347674969,976445853,346968436,551931564,629281116,203043478,26808555,182785591,478378383,157331959,777336342,488075947,647685713,156255613,666621260,413767969,18012189,104375269,533938385,277243355,59760942,181509652,49612152,275108965,52380907,990162862,244418680,811915148,168714740,981310954,391830595,971036383,355965255,452778523,59692999,202205265,54822057,467692570,482163456,111357512,622812666,737753020,423977417,88944902,47691439,586389836,886157487,120153352,121655534,368107229,970627168,925638435,26869282,436764732,172888337,73209796,394238941,565762154,431717432,83387323,636292411,224119177,43017194,127010211,49114408,694507232,259281157,327468517,470362711,253339545,444240273,306386742,361658087,628307425,134781164,358237065,677952693,529178507,632238158,707681610,876823715,473145090,620611258,185798536,652647085,227010451,719280124,287966216,61110182,462089918,103342891,337887606,881581997,122992145,823745886,395644464,500370714,990262404,775912660,67341397,595466060,478032439,416945767,240928222,686416495,860992735,843107773,869623087,586463063,922631194,528800818,636349891,394659195,360904419,966338370,612717822,400594269,362065528,655404247,697497797,145333150,851455155,538273863,445989256,732386644,858553010,12296034,580979854,695823147,665930226,788319208,303865234,35757887,72382757,419706123,487311381,481250465,719968317,173084480,963474517,276865157,147314377,187855086,240423445,339947136,687598650,122500257,772681618,946405250,36187645,593149012,767383887,745895772,678160490,387726182,803524942,737784161,580375368,270799357,815916868,107305270,384998202,803854436,568145926,981688384,421379783,510838628,985530141,2887273,462389442,672005937,85050695,531394256,500813310,867503121,335489057,837890021,450748596,572618161,200557419,176502950,621862140,213026623,444748631,211354006,995109576,851620710,932185084,300754880,284407836,510311179,683698918,96582478,874076682,317152588,790624350,807176912,640366437,694030070,635188426,507601760,615274558,175697663,723952750,730870377,571687568,124632984,170879595,375503445,670889878,628922097,698110250,134203529,506786733,739026,911098386,890378890,908082164,358050952,13715524,562872247,872963196,422195219,159593699,291320927,956868762,284535304,529480467,960255371,105053778,817790679,594759872,83544462,833809548,134480281,613836601,304459550,160286974,400597829,536457767,837823039,301857208,266336663,410609193,466938602,564649440,911075521,620574727,762785604,342075670,566109595,524931551,71979956,660645356,773756151,330277860,940779721,170470567,16128848,951751269,386436988,324018414,816081970,972392101,731641583,290024411,761529742,571267597,745178688,13824395,363479778,48690587,614004988,209358331,280424895,100062123,107809354,786910025,231810555,572467061,737734948,445586518,429434205,405553621,141772962,812206185,979201066,851618431,216840703,481372990,310570102,557614296,211652890,239974706,890986758,715710925,148705094,899085753,426671180,279769424,324588724,728100745,377953476,492879324,399152441,477964413,530556130,743417552,705769908,899886315,468716588,410004344,2683227,118858107,1816957,148622729,522751979,445084125,588826663,439867864,421038055,657157898,635525956,192253314,16067083,887433606,595582571,493010497,541183435,500967359,320115812,822839571,565984820,441953415,837804843,828112098,248475862,752632215,993379783,183472616,914598040,314207896,70029098,4748769,947633579,247805259,296362316,924761646,312923842,617951788,639800818,492228492,218466915,486743700,905581299,884319954,392995874,247882356,238632085,192007346,691555543,980913072,658264342,25811208,633937295,59586089,948076658,36360773,612543466,19443763,793349084,654002718,281651714,546611465,398310225,33128497,368983360,367597918,274814995,513143808,613204637,16345672,352221215,108952091,928703532,636931477,242327010,538540959,776414349,963118769,815605677,602091945,224876157,986865744,780685183,402514474,144444003,311136053,478000919,567642961,134656238,581506008,746831355,497178621,36978716,280844169,302628826,748379411,881139084,496191525,567237573,775841765,606926864,394805863,373098206,121921057,229549,648650520,210601657,357880080,570902408,713829103,344805182,969939327,127272948,940268234,788382929,739836755,636689762,147539983,928416106,524983713,502438514,864294134,144238318,433797723,393750436,73492535,251439000,191998130,959356670,720016418,529636304,336213482,797701790,521710485,774156540,151666882,444435780,536147581,650083316,859728775,949367003,523966817,381830674,586894949,302601990,404897882,413287414,963006237,302518313,689876544,849454043,528133631,604302534,576080268,507259464,878030432,390420624,940060996,149895397,989622231,720038575,111794154,30990750,209542723,538023737,389541891,299607450,860107077,882578804,825268421,384973658,231918776,18489195,263912663,751196439,522552057,714665083,111165583,843001036,603392268,183317062,636737912,251782409,641248313,12272806,790073758,289260617,127840952,846561132,888305274,820225783,903953655,43027658,555413925,34672010,445087839,81343293,4186252,711543240,996674830,274088081,587236424,35230891,674753677,290173636,673116132,639122265,691840589,513863239,340920488,261318726,303735697,255717655,777781410,586344035,904078698,332573822,989481681,908033945,161248835,330686949,813625106,443687912,644386179,430222493,528560754,542201913,507913072,885354546,495907748,35098193,843682525,546194358,162177149,333423797,221646017,927727963,281528628,459694816,338729320,415191712,94174912,461830162,643544234,946232910,8269338,175252064,958888852,941293767,473139096,46851007,973805230,6654468,833639180,858401458,16546994,291903021,933070408,861325875,71940671,588460054,787693807,211635378,280696002,913627041,189837629,791124697,37850959,969526236,445683090,293674814,241148482,915350113,449564302,62406542,187322826,98358961,824827468,638823274,810816703,923312841,589169369,750707134,604414263,50745666,966572552,645185027,916781113,696483407,351739534,858733649,881664473,483167893,862002523,366981174,964158020,978871191,903077644,783364599,103221314,32043233,107083526,73194314,188686342,19870537,14775567,964118237,843456538,228486962,408006052,922089417,62912901,131470784,53807988,907818253,38454847,270976171,654570028,466783645,848633021,35951244,498734281,104637413,705339618,220379637,34917818,371483002,586270061,79823855,240193835,803101816,63123460,809112027,489167735,815206838,739201974,553662425,685103996,629995876,534511316,342252972,824979093,754578965,445112395,964231368,559440353,369799062,727625146,283630703,484187492,656650604,224147271,972242135,467407491,647856699,886501672,19659928,51821063,898623356,163546976,237290224,433331078,128665004,109361473,96374818,91924008,990548813,878574550,101083513,787302006,661544374,872743560,920437483,760086241,931862531,429758278,747284133,2227983,946882710,286168414,121109287,900481316,451098263,355047225,934873792,850046534,19881970,38778855,79373215,214917873,177056206,398478261,854827705,478587527,664029588,545256334,556781971,662678982,101145619,277904352,823014772,32392684,961115440,153098313,928801837,101102247,18230706,138122573,31464006,765941338,218133774,109803901,343985125,864036422,521637896,180883942,500998122,908570421,376774883,142984349,431606773,390932697,577866981,10034308,543732114,914639050,959927339,816180358,427361851,946200544,273090458,425377507,883889720,549763744,813815205,53160877,1434011,755588139,756638338,699614641,684373193,330345548,112577107,92104407,749338691,850724850,749584265,737143677,78430652,155550920,661496016,954592993,911020450,585769903,674646858,28708158,843434366,325293394,968239606,123277369,82986893,444591126,831887690,761380053,958873518,527019758,255541240,995585540,702651513,444213362,675320497,472768436,383297834,287405354,815782198,404106622,291512504,874467926,420477755,110520249,787802665,991682021,794547185,199889391,268944188,42853366,355489942,870172830,790801299,530788814,161534011,479288196,171300170,462056391,291668006,776445263,639362166,861523385,906739881,10343970,768082796,606179627,741142669,450643868,136660518,252032487,799339097,427118966,918454808,208186447,564276779,901441539,65009536,32130340,752111718,376461785,223022536,642796492,418916111,58304326,318787546,350795058,49713033,465445366,943790387,655898787,741286576,801999758,146939738,981938041,669478852,522125170,387827106,15520773,416461344,830954423,864048044,901527115,657324337,800250558,452565983,660879071,746043766,851583522,189110915,353741006,139299653,987619316,888786381,414778142,711492693,452784787,420405727,504513861,389225586,157471464,477637863,631977710,10101563,58169412,964474851,509701937,421877351,523588340,198452000,425235643,62515030,404710129,801700574,641198768,761801188,99992095,858833638,230877945,282922643,820850711,800130266,828011543,218788918,937735633,431503087,765792740,89079580,831459443,575012798,578502127,881267707,682066562,389772154,367438645,837522407,242946677,82502081,340328318,611572635,1399022,103866621,274450596,739673994,71145515,735134335,57217092,429117833,689202914,583716028,73713874,85283690,658515353,232544714,185042337,930962505,126107303,51123386,471675173,411784140,96441147,350105855,895001028,180796298,7456946,596613401,684481676,58191531,984125434,460616323,882017102,144679940,155905798,721946984,399371980,967570796,869287620,769084702,390205642,570574615,871909029,83617293,553980213,956822449,934596092,116958534,687198105,245752202,487925656,383131174,390946880,160487344,505116877,518298165,321104857,502051084,207781220,360534834,862296307,333605746,103667756,694665966,231083024,375614352,520701610,843443810,358975230,253146405,252010800,299031929,930438411,392642782,648043088,669811107,403097325,641768595,846364809,602643637,782299411,782668759,889701616,782047983,32016237,965762056,849010281,769192605,84756369,571060980,809684196,274743689,545811024,662478313,908826887,785089171,291540570,576292532,772179053,927196914,263760119,859044997,848676761,812429988,704113753,51285560,662226547,519866544,210136333,896946605,614669733,358850212,664952886,932118990,364873157,588142983,451327775,893726384,896656820,509965931,359398966,46704139,33606857,958651915,398847272,592786404,133892544,330194358,676824862,705493553,638211297,277415531,25278590,660398183,291187270,698038618,857543967,10156331,54148475,883806657,783472589,104805551,365429824,55266072,367987503,409027858,458286572,598394528,399666366,587207795,596474597,400498180,41555770,399170123,697448991,833388979,144809483,621518946,201920608,739166826,983585865,615246201,501381452,202034889,565354154,636883469,376137530,479241684,653584658,537712565,697278247,439918696,983315198,805481603,396525399,97234300,612417348,23980680,237852542,14869849,918737292,561083251,999059825,966629853,339767442,629841629,477968454,573670129,931296721,349552847,494618746,613485028,402831190,794100535,154756332,112798510,243746524,294921764,958216389,224497843,927681644,596243981,418605853,708573129,245456594,103771139,171651329,811641498,664998278,10353266,380011935,360014494,639379668,399391113,499223968,207989762,85756242,719448360,823165966,904417439,680060068,780594083,321865674,181499090,184293265,424542378,780423122,731474970,966817148,645050638,876213567,479302305,329549936,105785451,420796347,778491376,702893287,687508759,887224614,294613450,651334883,429023175,836845103,454848419,270681731,981009200,984302925,968374506,494086191,55818071,995394860,736932238,477130020,536325611,790501866,602784592,359129183,299557579,218800368,700380227,132799491,625111455,926009481,860490893,978323269,723607330,417011475,303036029,651156526,286091312,47895872,617560353,583226550,151862599,860230663,535632741,645185546,32293017,239699180,675412979,637368772,560708854,297116270,26001509,511141371,818252748,668840321,146440358,664071277,238561716,347636019,94335187,933893168,424661029,986356551,57994162,405497787,675703909,540489425,352678841,760128073,222642053,652820571,171066232,119106581,101874843,798256107,484105140,112396048,486580460,886117237,103804219,655469407,302040581,732868435,805094825,180344188,765640325,886238145,255047148,697685708,303282985,195402664,311032398,841103955,299597353,705971988,496952566,888550896,90919205,190385880,769831856,357577748,435802563,591079381,5570576,578760407,312961779,666119090,612314250,777455145,810475487,190143874,886384971,701828777,121432841,893623869,198418252,220302405,964491016,325681424,349614882,970335653,734218508,72687518,112427652,268524498,644280262,580304304,487953086,586437702,260425827,807784974,506077884,522590461,862994644,532025190,159599435,309493228,162262190,754148745,960032233,516206668,779617213,267549536,914459342,789780568,757628790,344620033,945771277,227289645,406042899,124584681,738216211,571124433,250357237,730318784,569536538,133056371,437402007,335125095,116573961,78035492,346837917,731892746,845063646,718420532,20124291,328861195,923158295,55237852,945509718,867738323,241736144,66797745,757585321,644190287,656899948,672696388,439332862,331274960,676595738,288361463,653392076,452885957,292551474,204914150,741377424,140655096,424661599,311859296,181258834,781960165,211597888,17940949,537695469,798409053,653677462,37825845,411598775,304078471,312603792,203085612,439628868,515209282,368591201,659679139,613168289,416355586,140303395,433897753,321152581,448768082,802796410,975164352,721120880,435750872,820413818,484382005,101061643,649003569,36606807,569603002,651434989,338407193,419454273,24063868,728680114,970225606,941915838,518141934,358131209,111347523,457865291,158755118,164533518,745574399,52722813,872831561,440941828,742108822,693470545,63846615,728100118,234624590,806742448,923208516,115715767,411123552,274652301,81363518,559423500,645977825,458235286,896812229,500157248,262351107,21893066,632968220,754196080,411727222,282872657,320614432,863529715,516133658,990889207,161531118,846871768,656895080,407848616,465128819,954505065,621148373,633041955,457780428,746532721,967872968,230286403,554434854,885595760,74408767,872952643,367183853,296626752,208818093,466258975,34687165,943787883,751744694,603830028,86635438,841871779,818086952,223409952,509090788,310420428,63717520,622343192,513682248,888065085,304516726,956683708,500331431,140601045,549857066,462496494,617525105,475565651,178394122,707383615,552744091,636670208,87478169,526297356,632866649,635090757,879205515,377713561,893040705,729562809,578787624,868683482,652353486,119048267,64936433,42729622,823682330,430976384,115445873,211366774,996027885,324067717,124898319,24176916,304286311,550119927,497255378,208513292,512076800,116962974,714379996,609327226,137468021,793130508,918837909,44868734,989956934,57155068,71258146,40000069,750757867,562855577,868628559,891776378,471624778,323706569,840988400,673660246,40149927,298462862,669425667,984780134,410373518,521760364,736294475,846148314,226563804,958451302,541285998,5467090,727549707,849765839,561902699,436048168,409502230,318680574,840692963,258965731,237479193,371722022,262652843,283646798,320338418,995785005,688702093,347356181,840921054,73513580,882035411,726727223,628554945,366302016,850162656,493579365,288354435,453439088,623613325,177002788,232392756,703144468,221619736,119064124,757987180,585207633,890761621,177911895,881871821,933652574,855010578,601320121,222560067,911114740,565491866,821406790,164559949,979439758,137354219,630084108,845348363,33678327,348229478,761548673,290337198,154507993,54796072,4764834,581936239,248082060,218804851,654824318,573268552,189604356,721776904,386323919,268511901,426797259,754872977,817103465,626969148,310002320,521981036,660033235,108962346,288952360,549857333,378305748,808112463,409422374,155189292,183238869,475949204,957070545,789334502,636744709,775638210,624233149,491532911,371684001,272654556,300136021,679450388,72657169,647446211,884381311,247668091,411827907,736307637,863898461,338475919,87899291,728813098,556649532,691053618,991272044,22567138,996799244,99882111,250814128,656406227,365008382,546407803,556851449,323564373,273297461,693637612,109957076,663913740,5636748,309145683,762482848,631137734,132236162,980831073,199418032,647546051,956812777,82952619,849579860,285891223,233900110,355676787,865441153,804712639,132182279,790937430,329363287,176049589,62665936,54299173,885837229,475915337,480994903,986233220,978189985,487149603,101059030,575425190,635120734,429713076,551380038,189895353,967864171,849078041,768407921,800682818,50092629,772284577,634304024,708286699,335884180,474170239,509473453,885514382,440049483,441342693,122715899,552194804,590885689,218128753,844764296,290142175,422275700,395251455,428945924,244786498,596362115,413071265,363362858,655598621,349642532,859184197,255822440,22157072,734254163,799295578,390449348,655581506,812966640,154945837,712307577,409999377,888539695,501802229,211379643,972186001,647819948,321039855,754378571,323927111,209748212,304393388,416463213,544883837,705744878,233052637,623745297,975204241,927018392,750507441,18319660,414474010,655298557,174919172,679321026,562266797,519358676,462415771,215160295,12372494,99643020,339108112,866897370,123928484,495903236,123722768,445426845,376926763,396265894,131430261,462239829,328085057,665331767,302595510,962728232,889660670,848886416,787838497,719864974,577462060,664654722,949698265,837938282,460089703,571836516,943272305,508565540,522603244,451869610,600774240,391528173,292732084,69135668,56433973,291208213,138996635,920841075,112555602,537172599,293812109,945080477,151003519,492532104,736510035,108200482,163496379,156851606,703138607,576634932,618469574,445168543,40298315,58568456,64679779,819744363,120337233,623338494,199126679,488946320,395754108,819149654,320733217,818677526,137455539,674092183,120308566,928925667,595073284,136550851,161625551,7392237,353705007,936429594,273458183,248812218,639654469,678969858,833564067,468941840,49811114,967864424,488356009,762777053,992105597,412688892,616249303,57449528,299690204,713071266,767169471,878490810,83184935,797220348,796755334,901989930,712353461,916992024,547015829,542769137,575989049,615250052,369319632,415944259,570200665,941587935,134202738,871433295,247413392,542049956,221785942,116278630,899196328,576857494,595776815,490149822,966854440,784862712,561051768,839516939,181050575,106396123,453666356,860700342,85508146,72809388,590818745,589398108,690144131,374727684,155261602,929667255,184224656,551398485,770558441,163337712,627862633,923824862,461697587,102293577,870649600,517175493,959030242,898738122,41729506,102901041,388438088,841955782,382066189,187060044,448520742,71656877,426850890,829521069,592427295,638913128,402699615,796504755,12785425,483047791,78252497,857227377,873602182,814054908,978580261,293555710,649734965,463465095,379472527,548615331,158707640,500282700,579722810,640320333,940414501,946974467,339832391,918639749,20539079,963104427,24293342,897697936,201443854,480324890,663655104,786744269,169230015,801441101,645294910,14031008,389285154,990936062,96247643,394043735,811840298,367162855,721186856,912222057,319098615,977202097,373142538,423178295,556017116,524258448,682711168,672987661,976197460,283520399,568653129,302530970,330649258,208947850,648105705,490541638,669868564,434654955,921034446,953368341,153160724,516993038,854398446,478216386,372359047,386158363,861506747,937478550,619906975,120633573,350793581,223049192,150899005,569873465,814394035,950465657,100547522,312709152,272424944,698336015,588833535,149914725,944304567,283181953,855976340,697431114,971801431,333832137,667697459,156649071,693346492,252801716,219401943,512661591,650061037,125009754,215990884,395749089,21344063,408143521,658667152,133130943,801594830,536960310,9384784,45097863,972997775,888638448,557145567,700640716,20502094,24359792,599870947,998533508,909005053,486186431,799655415,849911513,439719099,414681450,90202010,837263065,183371894,51080532,1642388,965755384,964756044,597828202,640450862,616869527,431641774,929903260,916860252,237826207,14530444,831455298,521340981,197398299,657960654,886842073,851992495,884306919,438193962,919355758,462620132,312855328,150083285,194640569,600282624,758056930,727872893,446541068,21535359,585930420,820674785,742520289,158564878,520609852,170266903,12670888,598425498,144434601,906894947,345519832,679702963,295530791,242672781,514532501,200736311,997943549,917488034,573463227,833061341,762871867,548157893,46703650,766886439,523181373,833234211,418874478,111240945,987567004,769982117,83734688,798718415,496222003,86707998,795861247,682916121,339952817,450533813,346081701,289647523,755178844,227714430,504683145,94861964,958675571,734581013,888879505,205567800,226701804,684756878,56814592,75583981,55138638,685042862,986015810,519949863,885830523,517440051,269214847,167657039,801702362,56482479,482551648,102761305,920018111,461935592,271440636,913909739,249027612,668109514,788512837,302622850,380742619,988988228,725770182,406597719,987676845,761087053,648944531,547770267,364637451,757113750,369812693,60479928,97406120,409952022,839144140,979682775,155312995,643581685,235692905,516174547,21346886,821159631,210071016,199487551,167800882,957124830,997352099,858746321,771724908,78386814,604455830,522196427,788470984,100425088,56416683,192296625,765495237,96108286,248208025,359528919,260239737,683999210,749036939,702402940,358484918,946109773,732715044,604404871,945772467,316158256,503136682,992923053,757989964,186198481,334758561,732891190,481447608,210896136,573001420,94243291,402681225,315925191,217045246,246001061,917668793,395978879,729933098,934119158,840793897,172274530,151268505,226511051,646012103,228431215,788704455,914091523,285781295,292304025,838889655,348301265,388729559,25505226,823211991,713663904,723269316,890610314,986082859,105539667,36076810,988826031,831787477,344056750,435674728,153435183,322236232,875235106,790992650,26164790,32861803,809766559,120718516,559965210,862446000,161151433,27151030,59924957,421123552,63940816,564479085,315564853,761501195,453376955,683263836,799932028,813928674,715329940,356842103,721564871,425898953,372297497,644513888,713176399,940632597,566688714,436082459,888230416,524607673,649968705,115692097,596245416,245254927,710540087,419362541,961553829,276685006,668131680,812362193,103992945,234851612,355740928,241059857,664481780,23140064,191263847,968374372,351808275,10978707,144764510,348384702,117316873,851046810,807597901,709027591,261560269,787588118,182165566,581502752,631105226,197955136,896975219,808460607,451995191,683774978,116595283,991419943,313737096,165391466,142179510,800725677,233575460,854613284,184007820,503513779,731413720,523095984,118397084,735881993,664327692,810522410,15403011,339843760,958616522,61614738,765856430,986561755,162747958,722372976,356044448,536515248,564560586,460900161,283437784,395878710,267055673,15288388,931366660,357437018,3964316,397094648,403936031,990256394,655510249,769010880,779529080,600886251,828332974,119192915,362035329,821509441,691441240,819274162,163039599,490825161,42176448,139763668,489773579,954870401,957586924,3433552,225067789,508708345,190828100,78378622,596652991,702977856,128725925,507877785,477553624,931384359,362190054,870540582,176290510,717869779,652732501,247939893,644726156,621818867,580640066,592099770,264189983,411078083,942913954,48874102,917872312,756683660,818323577,696043289,297157948,394875854,406784446,114279128,923016637,378123006,805629511,488532468,346493322,333372881,520070776,270388966,589764170,408043569,339213032,88247903,684494808,793820313,567301955,869642112,94843676,819057852,823973865,547505565,891831938,814302444,712189608,962231778,204136392,488670424,26848891,505821475,702194741,720859571,387337732,672403319,181363402,319353186,544514258,934656683,579410119,980647629,384059097,106777446,893249681,322760918,786370984,426181277,258487629,798092327,829191601,150992785,941873753,301919752,207939149,268302918,901612175,666175455,978128820,253447503,372774354,868235000,934568789,451794354,139740562,642252205,562764837,247311815,509607490,82176905,206180060,843082897,709969090,926470434,860990512,693155592,391225208,447732998,355658595,911180994,571915770,263735581,65494295,269403268,254295446,155790343,154016863,608936263,305822579,142615127,232938463,826292609,523271918,349276466,30144836,282207667,174052902,506721944,590554912,399326574,93670726,389125871,220487324,334008877,673169534,473123532,182036714,882931825,257628865,381713926,9904360,798062288,196535163,588012776,824005464,679004567,454012742,655315687,350706187,547157171,461136209,615411020,478079803,451621471,68707528,330458236,960582245,206152798,455937985,412256712,263305051,929557190,345378160,196403244,239209926,596627375,118003633,304998584,758775801,250936383,419031687,988343606,297521485,299351741,832196092,69538740,343826219,178448535,137014850,879206757,169101252,59482992,209568933,180942945,753194524,290573616,893997638,830721781,504807714,175895319,227343640,379097623,156124407,578376000,973975884,40368308,670431344,853555,983481371,529464731,648700650,933486182,224711083,920695709,805657106,184259724,791935322,962676730,311265367,843230092,669612637,211842938,666104108,755018739,123259151,161979304,784525026,170945410,179584345,372808060,581775360,354551275,972037523,642288183,701901099,425898291,557822117,34449569,809930918,88812662,638964638,710769640,426063583,340430013,447905253,243188025,483103276,905848508,888373339,660958178,57852731,253868080,33933829,705875919,829811396,959044444,788275327,777359653,17586402,587893648,356249372,259023176,181560668,466620754,218853435,221141427,326052722,650976132,510362109,711978313,695099779,132514640,86506238,234881623,509278924,503744683,952550654,756906863,564653679,91355875,988950971,112014722,372085011,180276451,885202103,875180119,897876707,110790514,865062581,34457872,232517495,115872284,780740856,76175344,858938476,481499898,684215533,849244943,278789623,426174123,19581015,698040599,465575052,589294432,18602336,647935678,180321564,146200674,966742848,936409575,543959837,767028558,35671516,391000449,781446792,483324142,308034620,391876598,621881118,473331636,604160245,962835533,842684625,668085543,67530165,267979827,100473880,390367720,283199988,194530616,878867287,657501916,911261318,425870642,527648586,532926822,64261885,674950954,228391695,621840502,601719329,889889713,395657003,834471326,364957826,745399650,37215210,757477924,942510891,984063019,215357589,952160576,943592875,892594685,630556125,90658712,789022806,62341754,81024019,929417417,19557412,724838547,509145688,219480545,882449634,217420886,902498396,321652822,167813387,514820527,909137861,485696528,542196133,71990745,787482218,491097665,763190195,820257073,605456672,122786396,915971359,216662698,933080583,547471938,948091784,898010975,972273385,995579993,631849075,638517835,265256305,870266254,291608701,273241786,932872768,164218724,89233041,253327017,646311003,979893851,981852481,235938734,357552826,734206414,914754990,772439566,505173796,361606932,685254068,666990359,682547349,926185144,992586545,356382788,646576853,792188968,594925355,227305137,96634804,66646943,714006135,115234040,683149776,659160105,152821441,89953534,5637036,746348986,396842807,367393988,774518285,327470658,367298787,769696008,663086773,461409669,185860372,105942688,567114984,432659273,346217801,351661882,750100856,591579069,925259436,567316904,173062103,548849428,687691481,107000032,835420045,781416528,339729203,525188507,52896295,743175832,960257011,765484798,742107950,330937955,939005188,7527126,486462222,339958933,7322291,566921474,723565660,244635873,331202081,645370742,928872099,470621767,49680756,606194759,521341108,285075233,385694785,466976366,642555099,532658741,185686300,288617557,264151936,590220781,855804972,463351106,867951469,690866417,680785563,697344783,149517960,623624436,324773996,592191480,472948359,354449006,240015634,465773576,267499889,528035074,161736263,394064102,977517862,191225440,651534909,99154057,601121798,288007315,365853841,360100502,824075262,629827443,391627907,363054502,565127564,306300487,701248867,828924610,559494771,92065713,350379917,168493900,965639095,435414616,318298424,698058396,918895731,88921508,530931833,748706497,144003819,962081427,873032156,290946734,661377669,725049023,712945802,643313484,953810699,633855606,964225386,58662307,676853170,603704627,250156100,250289636,325587016,171794256,289244940,529106503,183636310,317620124,777165338,387052368,319938368,198294764,535408999,893840779,938313620,843706139,970416289,159675933,365553574,214045410,121603003,748288933,927060353,151207893,61280836,244942226,951869145,969358846,982857161,829450901,295292136,186660177,769692806,401513274,129609059,189032256,10853354,236197021,221963332,402698105,606679315,765819125,863325441,443835224,444070489,270103397,61836031,506610537,835150173,393702578,237610842,338682626,710394067,89160550,190376387,174785441,844587871,747601972,275219098,420182721,66656927,651192535,995367161,39635961,481669094,801548582,445364114,190165298,285860497,580308007,63021038,245682652,277396050,269947038,253344804,428151692,133246909,902505290,454096183,322006309,60309316,927438348,585965652,12467836,612542516,273528286,441039390,432205164,411232260,139207073,874668359,794323625,309829222,449889132,28629853,445200801,863841521,21212593,877841043,440603159,932720896,642071114,316003213,788376862,758829269,904650906,533758889,172467302,578920348,913618796,411300174,46991951,542351918,723747467,608866691,177472201,952311190,52476027,848514431,622496222,749506571,503998918,444466830,584578551,455849247,40121359,280672907,325154816,918666621,736973559,734170434,35678517,403395330,620641304,44052704,716579664,381257296,285037843,598833698,515786316,333246241,434561517,925406359,26038671,983248393,157252670,19337863,681305957,922276906,301661300,305457347,36298410,118051405,533741248,36502130,682240138,180725643,540432326,920817333,206988262,598931468,278751066,778808890,164418889,424074684,924085489,304276992,584949716,49290281,894722321,981240886,887546651,578842904,780050606,428098846,93074143,824284671,61417295,16879818,357237153,692190843,121574931,721085387,148078657,861083551,12538008,586095084,470806040,391760128,19013860,281245,920795625,597914359,247021428,600521097,228701541,327622852,616921858,437812977,578749302,279756306,689353978,933667954,475672595,868112036,563930618,955447185,386492865,244154659,58009789,329045734,733191331,444985875,977395023,476027350,777416958,699178874,35149566,142393520,87484739,998642117,570949421,85276877,700484831,646689511,192273846,76242752,305127685,418345135,22538935,382302271,73959554,618320828,800000646,767912132,7777631,573889575,908821761,170944170,294821783,288210723,951663332,612976934,153424790,567004290,799800725,9058465,525317778,164795538,11503589,806388974,62704950,331273150,453721985,381161858,760863407,916362491,511414932,661901609,788832637,712143706,866661776,174512602,847284922,705879404,509725397,338406632,716050684,460724861,353169369,86975538,198225847,112818996,34382042,473916212,542251330,474528199,604416118,807515013,797599063,264432824,150182071,80286802,672435465,152991604,525042674,993504537,153550538,510733161,632307484,297908489,992583507,28985672,189141860,248858660,640964213,361123941,368649441,925069036,915384704,803627835,5049580,339553201,930833558,294501555,734604955,795245702,1677375,676797059,11094537,977832048,190933986,147323265,103498928,827871501,726512297,126234681,483484837,825040722,651681531,104896848,206653720,829508549,316539963,411733545,970752432,707775729,556857890,422579916,426344222,598730761,396642926,871736556,392825001,423681478,530946985,582883081,549858330,845987075,883730703,246547373,82073250,742595375,450588602,455423123,652477572,171221850,640603804,921041425,42535532,479196184,946340996,292331222,517297919,429679601,860642492,632489807,549040822,526112314,404736182,805932997,672308186,726668104,62323767,673915469,321517920,109386976,481261867,729986766,954691482,801715135,141862390,736267544,365098749,413738523,971749575,134603990,171385602,438508764,902813345,661962495,140122116,705362473,55729322,481167725,817872143,307017401,58468807,83482032,836105920,258274490,350311677,994373311,671761071,1878924,921775435,420112816,193414704,150755485,651390454,103625775,697814366,763035455,9662862,704106493,430520595,309607827,934712193,124507626,404695178,55254222,921553196,672728584,792770801,994650899,7381490,92635944,243447729,438003795,629090229,268144749,845190758,785200493,520643989,591541111,789857745,976122358,460701075,99614953,459494796,481578134,922454911,547635755,567740253,411210126,83081197,29240720,88128610,346372400,696338034,219076598,97209035,959805030,497066978,424027887,819627743,425510116,360731241,522854801,142004368,614004625,895689071,534781453,483192857,477410540,274926600,325383837,921676375,143415598,927098269,829600042,899748055,18519335,96742037,760610379,51516249,419677182,543500280,472179750,32996536,32538616,376439793,347170906,799434881,850025560,868424476,149432754,779198692,89462220,432771013,275523449,535220447,659308501,466161507,511306924,42515831,497301497,749280226,890783335,497143769,890084967,520521723,89418624,341612696,926520230,650501473,228864179,139645198,843039495,279429875,457060473,51317344,54978841,389378158,855397889,50936911,404823940,25755971,614822709,906712967,15336243,274748581,446103002,126798901,472033839,769269654,818356878,993643327,21415809,269858878,360818726,933359639,682597956,247339452,552045175,815226682,741954957,934630955,571087523,458419719,629563951,918120655,298311389,37357166,570180180,92406768,781657536,164230186,912157384,695619768,34786440,948292342,81164706,131935917,361810580,330613137,149391187,354021715,20622923,570586629,454433024,649526977,145172080,395462576,270850633,374366601,573460455,796575775,936080855,554697791,778658044,868270578,975937201,543706233,806803798,249309225,7832989,937952640,49656987,904974119,984284773,882639806,324627231,991376062,172851090,931284035,476479167,54933202,350542136,598757942,312506808,382192883,571096994,762666420,498040068,809692041,725576092,636253170,908853477,737628705,592101937,682683547,810851692,80954539,92267417,15693970,760498377,151963273,345397981,238010451,806629103,250076436,506711737,729164527,242428371,931968329,384740038,671244791,603340249,384244608,946567588,320287842,362112103,754349024,557589257,496594415,777269476,900701249,796467671,268772166,222999883,637647020,270237963,181205365,171070044,554081040,220581364,65722194,693401814,225226041,567829256,681296896,776016568,329880940,397559521,670990044,981611348,871698628,234009706,473899327,485121049,309662361,781231076,65071461,804396417,407107000,719654290,797582728,653628504,585644405,882371099,440637501,601530976,737103516,632405926,623056894,660348801,824672524,92486570,897199746,153149390,911418021,988506893,251587605,107890176,730933788,870929834,478764746,413817292,559728149,524285472,641339845,896727948,660575041,182781973,804750180,773229198,851440461,948317209,665574788,19263195,408898853,188195158,133276546,1998126,459298570,71126665,169564929,450756354,473121017,463519966,805444556,951901756,482337674,657826747,213554375,711786100,968935035,707056807,338671960,401481892,786268335,447653795,216928947,623041871,478525566,109159103,803882963,841358068,82803543,252087071,593832328,86853207,183757571,327989464,107217394,304296748,606693711,396233028,112079247,377241368,792697805,40530104,163547407,668864381,572625349,886271204,284410043,672527749,138911680,57179523,355490785,596266232,776829897,327928718,108103133,377495095,193676620,79213042,820526778,157518636,416087635,22457938,487042206,892612594,622478172,200432791,519488423,47341267,795898427,255730550,901033072,261834459,476422914,548462566,302934735,612602630,759027731,401836477,960772230,834234315,493040600,645390022,399968108,215006942,222334605,189494525,545066644,668524733,62293210,926926813,992728081,889267186,28095357,71730236,445322205,391276644,526268090,767183511,261662088,150875881,810978166,140459088,134484386,985177362,616668878,390320773,364573032,904319540,8283534,96972897,560176037,876397561,912655083,134347762,212848322,206046239,869614760,389452793,237479639,973374967,940916631,851576935,222072151,143857671,956729331,348304596,337570479,862757016,974456675,730504357,398148063,57242342,289048017,583099554,838662565,582570445,162781479,956093775,3008375,46490800,608511542,394605864,87695553,268587616,866035644,776662696,791288563,699063504,783499246,58648708,361010326,274242936,944764418,419477840,337766793,773168675,6171756,485869409,680480568,281925250,568499672,338310058,613422699,638064256,309565019,780452923,967199556,73240704,507566836,48354564,114292719,203137695,380109459,201318647,975852393,652063008,674171283,854267747,347362266,558758352,913228679,520402394,31884068,122533539,711335829,46273444,663934211,655987472,319466178,156584518,302271713,386928264,468226389,741899859,173940743,968018174,535924512,221937222,467069207,833705542,579754408,357834217,260214491,576914921,143362823,28897584,917165155,962736720,913982761,308510675,150869341,880419580,55436211,643486574,920460281,827081302,822187083,787757804,536699304,422665348,960264444,905521148,584148608,169651371,414988473,801329115,822746221,939630416,919516404,411255485,188246562,985020753,489595602,755902018,745962438,758586320,838848826,584027284,150277666,243356349,763176780,990282571,863350289,360897363,81867464,686299430,52659901,96526801,54669142,665365705,644055768,361575158,185715501,122381477,346966568,215709424,563190204,540437953,196734263,774968445,303061867,659588274,635933336,307593296,505984654,431459058,50526834,863376197,421928012,557030023,734642760,496999049,554499386,325721184,574950100,666151024,146989800,587350333,840976004,617797939,64052561,926566964,393113898,730341315,21827422,890044153,581006395,901040403,144926552,329284060,753968189,509267878,479751952,92463007,989265893,769692919,620152332,771720204,382964425,871763543,635440838,884546996,699832328,911537939,414889359,223650569,480163692,724314835,85191979,589646432,911774713,626855450,55718937,129397796,402086687,784460352,124586469,657482955,978695954,603184090,911003446,169970954,91692226,994897870,617202375,147579272,316505757,239458716,39292677,571609169,232911039,680635571,996441336,152979214,994409291,807670840,581618826,52385481,976245447,875646638,323074476,597312250,822777398,53902010,425190661,895465934,587404180,664929688,728042773,643850540,398322045,341617702,223851840,925023768,352040847,909904001,258494392,424300639,492512675,492913053,587382859,321776665,286589928,520588817,12770459,825991293,992012749,183455768,546544766,895054470,183495440,792684209,61921037,690582518,50546619,457262638,516167149,218824661,215929408,360912926,567350808,500510307,989876353,597066554,648012513,828257172,948255434,556729839,285605753,751476636,866237757,315623867,54569661,128527692,856311351,820321549,454864521,836444120,35158997,494974935,588089723,644069086,511405828,469979923,280027251,201528500,274327565,619795547,563123046,863916563,845215595,437462502,414937373,547982025,702822500,632269932,782983736,587898622,677646446,531648330,270057821,755213096,385468550,68685801,595520796,553787850,495880243,196986448,310818340,238685568,143954814,427429192,575946842,23036104,240752015,962636031,271059248,356852113,588840921,689898186,966356476,147661190,403071107,701688994,542434210,568794036,73393119,126980521,328363496,235688151,346677755,438660863,160477832,945978175,604487169,561683470,55118178,679298364,696607921,112111059,285654569,706473294,425081432,166214052,965288454,734790186,978212124,976167351,150187024,222729130,269409357,442375375,42177806,263556982,184521148,840428629,240851858,703410953,646008832,991812026,19720021,186948224,61599980,941139458,201541540,140696669,410238624,106416973,291907134,202257351,850833554,73536466,284865618,227942091,645526902,435033342,11990478,553473812,253168012,660411455,731537549,970121319,832510011,926443215,709418505,824108098,181739862,253872981,751511101,14087326,810439428,869993727,180228532,155193424,845249102,850779335,439304517,830159781,200032958,294902883,56744360,786008189,273840166,368139929,187269513,451033617,984333497,945658115,948794531,665743732,36300229,446514590,323005137,266266902,526908076,118470351,983116427,559054300,227002795,539349043,161065118,354593854,333380522,82389292,253227772,815591005,701290380,648330110,103802728,131039196,337555036,823263599,459116660,530546479,816919519,394864780,880798820,895078751,656421146,381338080,175710703,508880620,947192412,436999794,306777896,268676998,427882730,574065785,335065920,954784168,462136312,995465896,985782435,906517535,17123201,710483252,763231095,99676889,232490020,869297354,876373899,258917339,824668267,679444267,622912064,426209125,217866680,836128396,742942672,853916306,556565135,38915132,948392291,806624899,563439560,204745893,550620101,496454621,328974405,596377600,666678413,57460605,141700181,364350888,926949907,768810613,926694222,114014290,120255055,989534780,360376767,380677229,621594215,353927162,197166323,849829887,628335609,573499335,34738904,683248802,361898159,718847592,518141773,184921254,475180732,843851175,632439568,481174030,522013241,81585399,475140680,921090067,983355570,219788006,37828541,24025666,623347995,374406812,219817371,792100549,303631736,774245828,239997730,85674123,478093306,371405733,833918570,504902175,704776040,803410148,267006997,42810080,354567574,409954007,773415908,617752742,401516587,638573403,938258477,598686319,380449049,618921958,569406628,712874644,797969292,284289088,26415256,406769763,147743408,47630883,705091017,77187781,999166799,535150185,727039425,10026817,834050133,634165190,889467787,431104750,379815275,281305137,73379980,557660991,632100065,299504982,367171994,576957030,86711813,378791756,833747172,434463854,33530488,35399628,276161643,31362026,918115170,118152313,970563577,685834256,280841287,345730006,344327172,489190174,213838696,754338736,86817495,379496260,660099680,305403167,434953255,644412264,709182153,27807455,583105523,3256893,33742144,625239228,760868259,756140347,413829487,98934637,696851336,176961139,363291341,556738648,629553807,481742560,873340307,983135985,755532501,779083192,971712912,190422157,234409965,865373811,35531755,673983654,463303349,739635011,173563074,15110923,41321971,202524548,16500114,487775655,385886747,434805993,408799070,154338635,290337159,939669573,836062224,19852696,135468999,887013494,322178873,626142391,207817547,112829900,164564074,802904884,613581699,459852377,523022522,540962882,789088046,259343527,486274519,373262400,181339772,286701368,702309600,117154145,780125235,988171712,583982962,410260131,827837247,86331983,766783194,241179513,566433183,107208328,777386661,253032991,365250298,128811872,74594458,66912338,636021101,975229626,716561508,381502802,537653670,112337855,637638898,133112633,629949838,681119469,11356607,504599932,916300791,594538805,973950076,797457278,953759782,120418256,744728812,658449328,389052006,755365871,800358450,875922393,918996337,55481180,768558299,556958920,890886950,409082647,234750367,186720392,545738096,76418333,798507319,585650152,10503098,268773303,847269875,697235853,249418385,668807264,537781808,10540504,618652587,589055482,446859455,760980212,345395343,471102347,114760784,170028561,978089536,912143598,390336094,769656247,585629668,792119727,492447118,662018357,830000253,161370017,132673766,316614630,948029393,348815308,585996892,49160881,919432031,632889802,231012282,808128852,78602110,743722422,775485745,779448269,201732335,169953734,856003391,358839146,260580797,763688057,979502403,504970812,414336038,604937539,162136614,507691138,37673599,434450194,121532312,143179729,575876792,199297495,166514526,754292182,113848750,128750374,140670537,376465633,445233312,740021013,898305081,272667170,180645115,532577176,746376697,503716051,702373966,491773667,119804721,629366293,819135971,766064782,523615630,384222867,723219195,703779202,892040140,102773874,388008585,801939839,319118724,656985577,713049512,706095687,419653983,13124813,752744028,934864985,455583941,872873158,90232259,820159334,137268743,289944606,225565966,632022202,848088813,838478372,672105082,781761934,982723436,886500110,426827485,173347050,909074817,638437152,129625665,401168967,802659420,797835846,702408309,91742058,71944034,759910076,288827877,109946001,515536390,976097288,614820766,237557356,689275795,30976280,405148284,741446988,424191508,356223072,365029813,786940254,126413101,316618105,863922869,820350012,658279327,92008332,142435299,917232724,67639874,160361608,413172695,318204313,384143942,847922100,429615257,276635114,565628469,127104316,470947317,988376121,454523103,953258411,837609270,990777961,771144308,743687717,75787048,855041076,928571547,317893262,648008637,438420862,970068739,272099443,883982936,52622181,201845508,743283853,485758342,741794894,678100131,308347350,44224702,317100605,204918412,38958648,382757670,36393117,990109937,175962815,978796423,896165559,108570881,716137367,118499870,95141142,590662357,865362170,969977733,232216895,274851217,843151921,611023228,814173174,495527980,383242790,121364300,831929150,763364346,993125279,669381256,710142668,374171779,21930182,201361557,293374996,415511360,84106504,610045248,702523733,245031991,462341859,663188724,431894950,562198559,746927160,150855134,46888383,973818359,187897535,668259336,302817314,669882086,623554124,925730305,433070071,653925727,899566482,21543825,677487108,255271488,134572868,848782088,147631793,936395592,904767852,347678936,268863789,815731559,770620063,205548336,764128177,926883808,895805297,247355584,836652216,308691959,435190436,896920986,232523043,785219738,709075509,472639410,104984560,984780002,227585882,373830464,421109278,480151149,220753867,108932942,308195833,602174553,478926534,587323557,239238959,854505755,286746001,542547983,663018807,170935959,652807419,107365913,361761440,806568579,500982429,844715197,556435367,144704426,586718133,50116435,447252504,233914776,502593634,771697554,272601401,77103279,76841744,93220790,463052435,407114590,43901851,440866617,536928560,349517741,765598760,117402339,328495739,34829899,619010910,74742707,859752166,477801934,777106411,825181118,508309232,154238273,470631683,874755847,114484298,196000981,434751438,684334511,235188030,963264785,890116896,938543294,384675823,51774810,86142767,151535325,831802481,900555933,618895734,721412418,785607717,556856120,231084882,893676109,852111808,365934964,655837659,791106932,5520717,341691252,364647305,368692388,73371489,455890055,837745251,126824422,918451673,831438368,127491274,721545813,973001819,565221710,936836554,404193907,863142982,210084875,599196719,702561495,199207140,619275610,474414841,40259673,134182883,791726853,806400521,368710612,138867646,388310720,936059536,920398111,973010989,99514831,409352432,228619262,492313407,451383801,829715365,614116095,497837099,38590498,335953372,419005115,438559054,161634304,946497903,675973331,975694305,424241747,81884981,964995235,463710606,109973442,439168930,349316646,586617837,866568031,135056222,671309830,251460610,719226596,155182405,35517019,610730859,430946065,507954208,842536038,70270957,41997061,846182556,290175116,435506898,307902442,782540376,211600750,202091237,42895867,835281142,261665334,342403253,74923753,212714167,637686867,893740716,329081170,710282325,288657024,773695194,406588859,652274190,453091928,774945400,764377525,394969566,617332154,76424860,418058160,573052686,205507134,535002468,680049212,229230831,782629436,541249445,371730462,154133325,306961964,546710454,281713980,702276936,392340470,480625039,152842584,698744320,171514470,718720132,85695530,740383841,457030604,893378,218830487,5526225,373224481,489308031,605013928,743264069,867123642,886155023,570747509,472015881,921226602,629700266,747343410,476728893,884753629,839431305,327073437,957672211,878929571,402036344,146402690,50503006,898732371,93344857,262585767,803804866,770838737,502958426,970221464,694674268,447740445,259875078,478434007,242238694,397015214,627624483,230585267,3359089,447611401,592854815,513255138,80525600,733730249,956795525,481362418,963029883,954699051,712956607,187260430,675974776,254635226,486436723,847135515,741412713,780671558,953945600,106308090,887053009,428875159,334152781,641261241,780318954,914453596,318134474,540308192,444903790,932060931,475742135,296579404,906494077,224216533,969857332,500900233,615880011,34151790,77749658,563754910,79122810,715195451,996385567,846073776,449401239,946996719,16338537,718356667,973833907,891810508,898142030,667344213,288781686,341760497,424171395,841131133,214055673,37546464,351910779,761384596,707377895,412967786,780946639,701153819,435418024,100999083,452049848,121234116,745985834,972030848,757440973,750407807,424020166,170491858,318328014,439579446,582302285,634676937,774951393,327664444,387210190,936456507,121059982,28395112,466508317,382906446,528486970,333120755,950460176,905531192,462405406,452329135,84146728,490248109,748227610,252065618,396354539,294671526,13241568,357206015,170860015,274497284,441805149,163613699,16230599,277189990,790883585,62955371,7684523,661278716,323962790,640182301,733281594,669064268,524562328,163470722,870780184,311965687,925387896,201861193,712232910,616120168,277316575,461764804,840751210,502584370,990724113,856950858,61127505,328716289,802447064,90746002,827095826,657751708,468127435,4787085,691796267,705482636,673767625,455642833,527060230,664653398,483401828,552456752,582248348,871335843,352959319,267051964,373765890,18342055,523895558,904214132,826366726,978215816,27292540,240576692,796739072,520556255,756125529,314203121,570508395,7185233,478987663,217991699,920756363,241634257,855750047,345602664,248962048,575431235,608602242,138080358,148156158,700713237,799999302,214451210,644045617,599951378,475828412,483422351,800337273,872361954,662196750,54943479,106195485,811367538,51956689,892384456,295689671,672980066,987525643,33437798,999629434,524351241,982637973,436609737,764830488,417058192,740612650,526477529,832682650,922912604,388224677,140690528,449900338,322209292,724006374,725251550,296165567,27730751,583847129,22365905,183799357,113018749,173666682,978739722,590773480,319112804,856679563,388016373,742179024,960682635,508828641,639765391,271012227,722983913,589052838,12942693,519552825,332026330,637085418,475033097,446720098,192420491,466173548,506897267,488955182,858677196,375333992,262997389,659507175,887183099,894821760,149425412,740991846,615734337,693606957,159625744,823590575,950837227,543191240,534258494,386242602,170510516,418944502,534086234,373100680,417513074,43368662,168392192,942354748,424779859,662656638,27826532,90504845,831319027,381629265,58878906,397952468,94706903,846397273,99303342,222763124,855539534,730728027,899868080,711071876,544836812,882776323,415996121,43353680,755858712,975947430,852799172,102782017,477481949,456298870,353244802,81803724,794471857,926038244,120679788,130634869,96890086,535470732,541401365,426707781,55347323,969199024,921540587,59457149,652775418,526659637,283017806,222052139,11607293,337120227,984826243,285935909,673085889,212942548,804421895,732508895,221837141,931897415,192554576,506304907,838515053,730414755,976014430,177897840,336573587,961167885,316676608,660399057,459286974,927061184,4060793,400925472,440617218,832275915,206061872,212707227,927606745,132801911,45644482,233337607,392850088,742314192,46381852,880609199,179769673,938819680,153875962,951975112,844139280,756069937,471952491,47480232,973680793,648180042,429049156,771677964,880735944,107856545,747013344,152164918,661699174,410096225,330302849,621595310,878553205,897479031,600999268,514196070,10781812,448467665,243636543,962866279,739034567,31576250,362788592,197430524,165648501,700489650,391662139,451921792,632926077,177459627,86217866,944437354,525438546,717209862,255340782,147299689,162578690,275783401,173555559,567684068,864160042,756879505,365792931,822528259,183065846,632603471,918619920,478714470,575563588,994816114,300907020,275197989,624329690,880276300,903742112,377844076,972180222,817723789,138299751,20427869,166846308,754911159,541610196,388321269,978891043,834737591,586377435,359975972,351608027,556175593,505726938,500151100,924104204,866939691,126873823,495371275,985216860,445543757,618367972,878056033,11376807,617285708,494289364,268682741,702831197,803302803,984069710,485318134,324264021,987935976,498923169,545747479,555656495,125705917,98367947,683204242,966893276,590656027,226660365,165985864,895339745,147770585,786513257,171360549,202681942,707272950,818406296,664330913,574208472,601222953,724805850,664415784,190146998,223253362,344853357,791372008,796136186,102833228,153804069,748330675,633519201,692236044,930648292,161811322,589694539,938250486,39334386,515141001,471238576,307228701,729084604,31871452,634924759,157129098,404819187,46092318,287007829,918930486,31231367,645351176,873166177,762468200,653392367,983108558,815301538,603264869,302768586,519460683,836382079,679738535,721927487,898516100,102964192,474813848,120372511,266791285,86799555,632050977,295183462,496080168,493541457,285058408,375541505,931474695,220412771,634498945,298911329,89133707,604006211,340442206,864534553,912611095,191686636,64577213,627068824,592235889,41781976,716644865,71260425,837495628,928521272,503888745,225615961,477546770,223572901,48417756,178529844,8869001,375623437,181457217,358961456,732672755,855613972,853894629,549773033,473798013,33924915,703322801,130376322,813963247,932072089,828283142,324637022,133689955,872694433,367441971,783036843,601930541,830819344,62168347,755698058,137527897,871609203,540314223,268169712,814962284,83820855,818404278,125096148,98052113,44157268,494113267,629895491,336123400,291855244,955346826,418871993,827906805,560003054,87117430,387420320,927809994,151524250,502637338,88543636,297004669,985436715,607660222,155008999,454632874,752805628,199163763,498857374,952142248,255767891,835531748,84083035,710922310,624283627,304567617,262868199,960531047,833190353,271031461,839402101,905422073,90529576,424561543,513968644,519198318,651893779,290525442,633702502,551433215,912635891,21842183,616305671,727553958,24866633,347416136,661350540,513807224,966640151,648642367,437447155,682773921,387308806,67799706,866682469,996595693,68821018,523490115,714747686,532320954,8508031,829089364,174024009,575338685,111386923,623615959,807798931,128634478,873682149,764942258,239937149,846818523,458148762,599086508,796950412,886198732,69945493,398494779,972802600,65466205,854223119,639114563,27613398,457537063,699231589,788631421,431072139,573340026,222080068,38122824,797215111,521857922,750908661,890494498,551280935,775842655,607573386,437159382,685019780,244521112,495636703,583627109,747067224,7642473,514482616,296255098,830659430,771413893,402379350,957111336,29635636,314139217,570982961,370085704,459425184,387392612,282581051,816620112,2811284,443185969,84010691,261979743,898475012,837692422,734726127,183451466,537774209,986395481,292935672,580891399,79419664,640530791,298103803,239532919,882574824,39245979,935406300,484737326,665359834,131800110,487345053,790923912,7722137,853037809,338306684,830180424,391517369,471425612,171700941,297505245,118950739,962888199,734254851,179914796,823910185,202082081,123574517,397382847,97203437,252119259,719830765,561231836,319609409,36729794,821309821,186536028,14923350,677425535,335805703,793300557,472502342,788505493,901162376,756152460,72343807,348085154,967693525,279730224,416997792,154157919,148748685,20087364,423461053,198635169,589398737,630224685,708483286,728011112,545466751,348359854,67743987,863236710,460487184,969716021,932033078,820281842,950291436,844742517,580290622,90244478,611659394,28812179,726372166,930402295,756641249,28346677,833603105,841803975,652770534,32015026,412256109,846650952,779644311,886259074,13488147,353899409,199683413,176738987,265424957,436303366,418066249,953928955,931206151,411322561,405036298,426519302,870744528,623427678,784346011,153561259,40384634,10705426,651678965,840293108,443584454,924051965,609515420,956568506,519914872,451474464,819060825,812346470,89352508,26246042,291087790,975819495,804023121,626186748,552706087,490012267,582209324,121332942,905225990,15276035,449707876,322897938,797039164,977982406,243798804,995139421,819695170,853790721,594065401,904327944,280029249,713863319,655937693,833217395,218439475,743069081,303807845,387709779,966764166,330176918,688333852,419233913,115630960,464161092,798791330,265247350,703424153,339582337,442272459,215663403,72576547,969212503,996158015,473044335,814003207,382835101,953036536,117038544,495750522,353480581,790644983,797245333,950961483,757767665,378092696,971924535,910619811,761368862,540769729,991388934,226622280,823230384,326395488,237071221,531431385,975626415,210010745,169272534,640358863,817289359,387306653,760308272,88286994,214793622,366297516,640850676,399293862,703405236,665237085,46745409,230603628,435064019,721393552,702557507,702652977,827344796,770191365,503304584,650733380,171676557,504421679,434045576,746914150,536573387,535202519,630117410,55454111,576222025,337614131,213222489,356597457,474810635,991906389,997492343,896220902,885133822,388718757,886819840,650463667,972598633,108005480,444923184,120218914,200436406,759123349,818436581,991057562,214315288,960740766,428066550,805623910,12191237,4075116,105989785,455139863,94010734,25397440,489708499,456938200,317519239,131895916,300739202,79315478,264660678,77274168,458477734,387960170,353052114,626366710,444551252,464650947,494516127,784310526,576229628,160865277,521562200,283304104,71760938,916853763,50271522,84239102,562973185,316642215,421329264,272254931,113143270,352055411,796410986,415073530,26766593,980008435,477163735,496403630,562759440,20838638,916332651,238575625,807108059,162009714,576946669,573274720,467579066,16222348,169618532,841108795,312530259,990845294,824607374,710959804,824513033,471382799,914446964,303844267,388939927,856224579,12407100,409247504,45998687,239241566,498678456,43600361,115993420,268371104,920229282,621538767,184659438,473459557,507104358,428863423,797086439,620441545,593845844,947996473,583834575,536366786,238963668,48945316,126628060,427098401,318608048,699527052,8670920,436015164,59985875,164014303,351915694,949161400,148406786,993443520,36243701,790515217,744388446,333877939,339002609,830128134,782408552,440522545,562517984,1928466,250798926,508717613,378734049,811356048,62223382,632004006,746796738,469929054,236549139,103109302,406081509,161668686,156225291,919154950,870522967,118116277,454423210,282098647,894067569,681531805,381232369,885297167,91397657,340765624,847193178,56828799,366358905,556104226,443523605,388963622,34450825,275228573,843937020,366062047,568857764,577875779,861171518,478223028,752487315,367753553,440309333,126528732,805797080,595824550,527169423,146604738,90594978,843455075,123807,252663591,585319427,627110354,426609168,60639860,168556996,382203073,720165238,619812908,167191026,203334549,503329799,51331920,659046150,168192133,17428813,639782841,854484423,384135902,329199695,254981568,672563592,168082756,584609549,776541923,556691802,119479342,367370657,38593977,972843642,648318760,539103793,311048545,172382122,720254938,511278112,969838364,781424580,591299821,179295366,227206566,238071785,320637350,103815409,163627547,442431645,767102348,280500531,46984248,69112189,166552433,809524614,501100390,137968872,660140224,641923995,870116548,838790604,994345484,675343467,65486177,8630755,900180603,658220096,755681909,931709587,609009714,689694512,960259871,338470225,549762389,744220807,800507640,800684178,798689705,154609342,513975915,852144524,513184778,929318362,395864011,13426090,698490244,227570586,439946951,447891756,901523370,994473509,634895427,451053898,58283149,565087902,755190597,620952917,562041876,544417876,803750152,656771517,606580507,786057722,838243274,812089079,90820802,777758728,698318728,747371006,26006940,942267451,746841316,1314344,168647876,203907581,62293624,724029973,741063966,376606720,915245278,626071306,164351577,839653016,245987140,809745889,649892393,546274058,523548022,825103438,594307206,221005720,402215064,940642999,84640038,588086513,385683263,240704618,803087332,14090536,675147465,251903753,819289299,800906246,129400218,388379498,93403877,381143158,776105278,130719997,652656322,296916922,831575405,630055409,65711425,282896246,876788315,940159393,339890613,698402628,711218059,547598571,40344645,591177739,703843906,298231600,924724523,278003707,935016754,849408112,145191882,240490337,805853131,801797318,727193291,55461632,674465687,918623322,391751672,829839670,634153825,928023856,597711200,131366747,547627326,249010336,323943833,176250878,678155605,982714671,605814711,980467518,952108392,171365687,150746902,78674272,492955557,548773184,386798505,239232837,352022548,963776448,738593662,170656242,906988263,137739986,524978215,640514275,585879626,918170435,432626117,346181049,831408395,47562786,458485594,539076006,992741864,388079318,483360584,188568167,150570723,203153202,813735884,251833685,342603568,881465933,197907018,652503086,649952190,890196240,488873291,796522121,217344683,613608493,491518028,108383597,969058394,598552524,851760488,917782154,938131592,498680306,238739745,73794022,185729689,739507919,50914066,571871991,882310990,531291902,327100170,405453679,212974315,145580571,218270268,668961992,100581604,795840554,994483804,449572077,873217860,457338740,855059991,53072288,717373070,485834476,506752092,193122260,465305474,49657869,784433029,142382512,309314978,870220283,721270173,543983017,237962594,309727370,389531281,43094071,521445574,140679776,975006712,10805434,901021649,906926485,915483527,321379921,531747027,869174853,543568729,688814091,594875663,704589462,876074645,868388955,794042199,14721044,539828817,812888655,245916063,546720866,68628808,120983942,374408116,554717609,317829426,574363459,450746687,38501130,303045725,727461206,281961988,122180462,80168395,530306607,915660944,560176796,622503591,699166560,694653805,838907739,559754300,762544920,768187712,33814284,962268864,494319195,763642458,744777207,235184294,850682861,139357,561604798,912467008,663554762,626853895,214010999,361659139,966001733,859348759,808618600,15351813,390890042,512188902,443810902,42504678,867584201,618921180,272865122,976432705,28576951,768734648,493879151,860114235,785382184,915617809,809272646,196597421,913660035,535525934,872709650,254965871,858960024,373373428,339159644,143081837,959462127,994708139,442448866,705091817,878130460,915972204,426593541,545697052,835697274,933485889,110913246,215617392,193342023,113109790,702965800,859347174,838107281,727753204,393091439,10959410,130526377,873994966,551306493,416827372,816479956,792073923,497753915,664754178,317460304,960129417,350184704,967515161,920254892,609946081,646149736,65624018,715103718,151077191,900374711,781621984,752465668,822957805,190756030,992431383,992400404,389331556,91466064,769642659,585588274,443826702,30983168,56495826,755739184,892702341,710836516,853766478,737254006,808899780,513410714,91197868,866842464,603314400,753729172,574604378,696950899,558544264,851446776,948537388,441504244,480576372,100325280,69211974,540212042,852301278,675725366,954661373,443851357,398259411,427469603,368774936,421858914,396144893,811003304,154911704,745320000,897208521,248591309,78908267,884813951,42671636,429682286,673062061,76963185,187037879,535651517,770969782,415026709,306158059,447441612,217047202,144881852,926314335,92663141,174747450,306967651,408207740,699818292,325946517,670760341,533449034,118486223,521392080,182636007,283389407,391715593,321172790,600417482,499681534,745432919,426745549,639239782,199462940,877232285,644968030,344770016,246947779,456436114,42956029,718143909,300211782,417292388,921607942,445842986,542067542,948699501,283178238,530461986,871354230,799055245,36770781,361802218,406454097,517071678,155813982,350163344,360536996,275071911,545146596,420187424,550619604,459568648,501421470,896434831,360391154,249437667,827084620,450595182,353852914,468319034,242885209,348254515,782289452,642928518,984146895,55560996,626508050,736760399,720008088,533256541,583294163,456446524,398474751,296943471,565058411,211241666,877738575,212995363,20592552,761034659,347372471,833455106,775438296,655537839,924164658,21338356,110357560,859902176,833899774,918932808,566695156,79607083,40193508,570042522,277476816,490718548,249706808,669529974,110408224,915517324,539319326,24285103,860277223,88190000,822381691,431597620,19103397,789834360,723772292,899155065,849483732,274378903,35646736,843875556,481744920,597120922,686260920,733670154,47243860,55702584,823659094,168155221,596789640,307353698,308742645,995869736,673923876,33937657,801643549,730369911,432033586,422019735,804016037,253730292,872305914,589443555,486554658,679492604,957871566,639893317,692121664,448817331,505483441,603406470,942228182,181302110,914740795,736607772,120286459,311573382,465248611,436766049,437109713,808775574,863065933,661726225,593380791,60539454,246909507,529983856,560563391,508422419,57029871,855837064,58233107,266647866,430574197,54601512,33603773,495179853,117428837,700517580,610071026,373954605,935398884,633069435,974941209,95508367,812870937,79704426,10479399,192722947,864757184,508962002,664274269,738701929,609960146,519440299,103167694,23735960,682600986,698986663,752839698,431885375,41031660,254073494,155953692,5848390,489091519,511674914,199646145,296583478,171368844,783983238,273676331,233427871,563910235,778837916,216912593,47416924,850926480,833958364,340681513,989383891,969537799,448971089,272481214,555214466,789296489,501506511,569588087,591858348,22727395,794242233,290059020,901028995,111115802,172917095,486515186,620587745,57920484,373860003,851896951,540440014,415011389,699388100,265120530,599723179,188706290,67932348,541882289,220004111,817600390,328157216,316588898,644975509,927042740,77992849,777276340,553899022,579250461,782626096,993866368,446854606,229924537,562086435,7166524,861184295,706530750,558763937,674687674,798619602,864386494,488902643,978003848,4768385,208320508,310802798,300778443,823569545,913050989,64969893,405702618,937171565,230774053,151389793,705982009,307488527,375609030,555430503,120487392,320467853,318885104,99875459,991584784,551885714,453915256,619115474,774504376,631437378,850662805,840333862,570389935,439142533,353358891,436332049,298459962,549077641,322410402,275945778,237873648,309493695,315663302,412175029,326928029,493843188,216769911,80669139,948207438,454420968,304257200,593847973,626590839,849560447,306529033,627386844,153443519,26802212,561655754,786452746,454828566,441608373,359810948,680892337,894645362,335681319,501152384,82679569,251575490,383260316,154159209,693434178,913039381,484996857,818489592,500809746,343893669,295094657,948195037,15319351,283590540,29365350,473770473,60661899,292982360,258185524,635350301,267868525,920380737,840328699,328674038,137877574,696265380,5961735,351283542,727556454,999942289,520837824,230816639,332691011,719689458,369130493,610024762,597469414,357776280,662870981,106962593,54231894,26960416,723122436,659506661,72438532,760867452,589121508,631129471,7510598,908309676,926480271,432675893,460457998,941494263,883270480,333078533,784923715,378247281,216653369,462629579,40595621,251613332,527367191,274175953,695586417,539768787,418579999,414745246,254046996,57820596,204947827,830468652,445963316,710893450,51897726,987460070,675603865,9394344,449680059,32699731,55385315,486276017,297092813,838706548,859141713,871295042,904792006,747998603,760801750,247490731,842488083,556657737,347356395,629041458,723383994,872294665,757931341,245141675,370068929,133118395,974278633,273081599,755117621,958959054,814947643,847003212,274191368,228868727,509892581,167973289,305680807,241082264,593701747,969948170,709746730,298882898,323335652,568953350,140447373,840061225,344612196,772824881,485636840,72788826,763234582,644509681,246522964,104251133,459872254,204315171,514653729,303997077,266781426,714993908,952719560,683369814,713985458,805995337,121986790,533031544,612196956,735841223,642460553,95587483,6398002,885269210,203863613,231074286,228279426,668254866,526231856,787084436,903306719,979809325,932250218,676441239,267699448,625053176,348182628,642356330,870241660,190608908,227567112,612379427,809177300,799986086,597199821,57385272,715064328,279687093,491969567,319279366,566015877,499684841,70412288,475085989,650302933,185636449,552791788,566662794,728701675,875434189,231989664,436061764,946150946,857724275,597531441,807767078,643762162,626115238,782161298,436448649,339307594,419175554,976463087,579431134,139759596,987875540,390948778,540853307,252661187,973829008,907641032,419829924,121068988,330607909,463070817,529462653,479750812,787046230,926258153,762613836,999422325,423697389,57076945,462341200,189102975,804420961,869997471,465359869,920720319,299124663,631652843,719254251,367486237,356983981,763587761,591843779,850184030,939433603,139608043,260083182,911923247,123096404,834053533,633606617,69309283,702373012,116702485,505085589,767428802,82194924,750405615,198056350,188630229,164388639,556130113,41003250,641357563,577149447,454383497,234397847,141073062,651476373,700043278,317335996,673751300,700666402,878879380,436776621,384532969,656713953,732721585,337274950,163369256,535351553,668105543,74482797,60297639,359708208,5403228,854489554,157993851,142048951,651189281,849861481,176318883,737816275,866390285,391611899,41365088,90291609,845712260,406964207,116913442,997992847,240880772,236165097,507987735,934385312,815906478,372488384,298097798,374257022,349655405,496649711,655169120,689305142,814007678,720301902,937455042,955353914,135175379,581130812,548764688,663703691,996295473,258249237,977115074,275117853,440441819,488563676,774629325,368725114,782039235,684665725,644043489,194656923,416998766,85249062,821405962,651080437,366647155,782462550,539854507,284159799,420107216,324312181,373336642,116565450,682745564,275705277,882391553,778880459,607131792,400245753,681585665,864930329,464017280,955868667,926872205,515952191,373822796,795186708,297130370,877778934,286600981,494592532,347157541,252650302,768214058,433193383,329870794,537087368,874805717,970636168,291907386,199942280,227550497,803409271,918121831,582790908,493143130,92225375,766799311,604611079,735160780,549295631,711433184,794577619,209146944,987099461,342582658,510862077,171818887,21627190,91496050,705184213,459604541,432017353,42396815,288594899,269199917,210933804,543892922,227403777,833460599,355490415,488106740,763345895,965477571,361746325,16701993,21613851,847709703,468742077,985173559,101399506,597621869,949141464,765932725,311507403,949619843,482478620,879061694,961148098,442217739,394585088,18930504,763949938,395223442,641552466,629772443,816025268,988118724,944010385,67105267,385877326,627302129,441521670,92307113,682910251,958912462,536476122,234551370,561900819,768441858,879499411,267637499,622609581,515726068,61646784,666210505,731736263,626406476,151567912,539620635,197897249,494379651,44187367,975498614,515835762,391575310,346764830,88990108,370292215,627689749,700537138,385520034,431388050,67250563,985267054,600389650,471581092,782905477,226571013,431945316,961857346,492596849,609702491,3312515,250352176,119135518,263883983,532524279,169390776,98948724,246929389,318844896,20238776,618440623,764103911,359279218,431565493,687952456,389391883,12378228,333779149,849108277,505023598,758635061,384023539,405731660,834182390,327238303,580076363,737601665,909596670,22871165,869873373,282532666,707070157,479361327,494509203,49894326,641796961,780692448,837512812,86234152,657143761,430997148,706080763,824842792,214621198,988118301,66118782,649162368,714617451,675849902,521343061,570776869,930742696,250934930,828432613,311466368,365369979,280612462,512644317,589132376,762308197,106839235,149136405,536342511,639163529,91655933,69318171,205601047,273071038,944538587,257106309,99034991,868983156,799945933,65161334,932386734,385901583,183345408,870473525,2490087,149677570,753936718,36939514,228437828,771339402,476557673,773424334,714048819,747324579,398449090,496095648,777747549,221956585,958265624,313396748,631014686,359037175,690602584,587710752,926281453,617256582,27667990,297794349,710300758,203168888,30205700,791242927,235230065,847789732,225436996,718710171,320339651,229778560,60011532,882652622,314508824,846775818,45281926,575249840,113681324,10840241,868283431,834098637,675533539,731432922,615791920,213592627,657662944,679106426,254147352,791272927,556572108,983856744,144744733,212502985,183897991,431232611,523640158,318809351,820256517,705973441,33762883,415678801,202814672,190137712,563951497,288714162,395137315,793732350,608459635,453952529,775629243,946699104,672247316,423024171,365422990,560981098,879913604,450367513,270960809,964578747,408391085,430946230,180579310,538506646,116843759,913331641,350384516,75195247,309355795,966157635,431377861,514236238,659115760,453622961,609017320,764900796,650091021,761525536,216494378,150756202,205590428,449245307,758243969,880973522,957388591,510311441,816553534,687589373,51117415,261955911,809977943,768956694,679251025,799431979,843744546,155125820,699285330,65811043,970939228,22031386,949709314,525174579,727256201,726016567,766937111,396106925,173743763,365603414,726241459,248849861,212445059,689246815,884819317,442431434,756742828,904033347,739985131,951602938,648580231,950980518,94818265,729624257,162844767,591506957,182432908,225540600,825948855,596622104,197943396,813076080,770520454,217007074,816256796,802426283,949600728,359950876,816962918,45778202,318683052,98618974,950806006,181949452,377235882,896908230,731234420,851789889,930429772,567768777,782624478,484752742,203106143,131557799,39818913,591418802,440373293,315091057,667015019,300147243,285963182,825295203,255905960,704608616,470731832,257051037,984213464,853781448,10574578,523255286,528632560,851914129,290089052,991334316,895722511,284401879,717862214,913587415,168794271,921955249,435578237,25803205,483326897,113548277,51712144,286444618,204257796,224834860,414581978,440084677,814687679,745473210,899512087,878878976,302667301,650924790,522094000,545582731,177929400,604235013,135575406,743968884,651247908,289858964,341052334,164084334,925398545,584239412,497580736,614383168,71062202,153897707,157380876,258499448,289502168,899062742,270613469,158615578,777336429,994839987,100724588,857244860,690733815,942500301,125849221,199727659,175200196,541470251,78946119,435397925,406505611,254781239,695928342,423489154,69786702,767944837,762690285,942827252,469788682,658546498,822342440,293091152,379961084,106590148,310681667,644596516,111876409,700003757,775989680,934878432,641860813,475323741,810332833,1275261,683225845,107606421,346210673,70124042,399663486,384706475,468610590,847017537,665901774,116048968,329615628,919435893,846109416,302824914,128556307,166153496,140476742,387948298,425570158,364369971,143680103,302009117,107263094,738769126,179975388,239015832,192679035,461630224,372599636,878889665,575422317,952796430,368788092,12193760,534249132,832252351,259729674,474070641,58872484,969836448,407880040,848985400,5070876,554579582,889472605,313227584,530132286,882507433,486519746,337592332,496130080,484726892,724367812,35416450,803216238,124072016,281339573,800835284,805603840,286129051,538120830,416372136,599177310,147061094,163865168,741528467,817756179,148508461,710623865,958344985,133463390,693268848,675265116,801447957,926586015,265279886,326944808,986139892,915234494,974524145,864908400,957851885,598194796,480051031,877546371,697446625,340542521,366142444,918608869,250446901,696434943,860655362,898594189,243873763,175747299,567734283,590817746,16821399,793501457,763627462,655506123,44109515,774984515,959896533,449903352,106426798,987725844,67081762,495697339,630871504,827263972,910972425,524654851,650299279,562417926,888229214,469677336,933995059,326939274,673957197,284359201,912151711,297174395,618370099,965844153,687708715,387159575,77844583,75633825,146806831,745625687,650445437,976402844,411052348,723037665,113469562,524391499,371669864,107597587,13444814,23122887,346576380,164390085,105251549,924512118,605139890,648110831,772313170,206149715,898117092,207347313,592387432,957792187,624477859,631012473,143553243,763790800,568950164,678999213,650173234,881017005,490855600,712152929,52815955,634568730,787592372,337256697,596554008,943039684,56565022,941322429,91385527,117939826,204584382,179605918,170541138,333828433,837823187,449592069,823271858,569123857,518707425,564111421,959639544,619701846,628948585,556893573,359456001,221611562,165800709,333177833,811986280,535294648,380230940,586399295,927352671,706936175,821731847,136574776,977289687,1039574,399362353,987881915,855941232,286021988,832702899,174511208,514381357,163311628,515392745,626015670,791676093,512010406,185899662,541304711,769523210,454980122,520742809,858429,874253015,967636158,982546249,155689459,88784458,169736562,589570169,699391183,917012397,775969001,603397923,393711535,659962528,477594400,390856045,275724811,165244296,907188919,51690749,396681671,568717365,626009683,220628172,720118117,294222331,973635545,860759507,596809094,901866375,667247271,288583982,886421193,168137276,632630495,104820108,355978179,873864872,686713573,253707829,204894782,839368997,493756316,761988073,978779556,151618424,965389413,214081440,534101805,333411574,73833637,212410554,735194097,239949694,742442270,77726098,212966457,517535868,882389119,969585696,614288907,791050629,833526472,365397673,373224830,679575264,881060053,612705588,515689931,692765264,663395976,981670862,807733804,31670580,125139073,411475798,385010331,221208904,35703942,762605430,637900106,284863434,443420538,279615830,595484846,882734422,446935418,239820803,851360587,9600618,924187754,31468999,690373024,516485047,48100116,695855725,989483141,776540909,315789621,29316660,551367767,159597313,257497262,834087132,819407652,414745303,444175723,285688175,317059946,794488537,593566762,878696174,595846252,22760643,24042234,887964578,233950422,475965019,398653771,526037080,25229408,646888955,553390597,469782417,798899460,723014274,653640649,236246281,267412659,163452462,30499221,52120112,914278054,82903167,555237023,481379225,699050571,123349396,282957796,746475695,299408060,492234952,881979872,636235044,399410435,416663704,2014977,415262301,831615223,88770550,399606849,188354488,283790119,564012395,30360006,867491069,246818215,67155475,290799257,335430094,676884470,73304128,527758692,454784672,89354897,79247742,951266187,568579017,919545031,512687976,477504761,864628176,391484965,601094581,466871615,498136940,688522562,62732516,768796586,981786216,78439981,794753258,99634197,602943797,171034421,198399970,539407798,217593277,254236837,61689246,357275202,130524729,69144307,514375516,317023639,258981612,896224812,107091150,402462760,678457157,492965250,926881684,938459666,494477274,464533333,183544750,327715304,399826834,771335186,710325700,929002357,270877916,835972933,471151330,837417741,714957505,313529539,153463739,388059392,738180099,175753162,379363082,921848422,311136382,343463618,890163690,11116976,256032385,120980205,932777590,635340223,707356524,165739636,781659694,6332611,387513973,190203334,464457461,805955503,10547461,847921308,873235252,802956936,748155186,618641785,295246938,487593856,832083930,770332222,540467936,326946886,394855674,38832752,104262448,933703261,352084173,941549790,994289299,257489263,370581783,787190100,34359199,897275828,795780430,754689739,866374877,406569148,886093569,469824456,269275291,577701015,257341311,900363499,813738376,359725401,473714136,309317698,954813286,563758593,781169676,675946404,690367359,181067455,947773925,797468576,11259142,143690017,832855144,492036626,502197317,646425663,875936860,1723721,863512381,726027011,771508007,554787448,205026258,706534052,744363283,970619813,571707416,86598999,630721644,317378224,108971515,430968657,709486196,160554892,218940903,55761652,876744038,464159484,405598620,367264387,612350863,971284418,5331915,274151444,959222210,373010336,710188224,154274529,479743587,160131114,393609694,133605669,980405040,101401120,580045254,467392231,452840487,353118367,332558535,758365853,715094017,264592773,980018161,220719191,431433587,472034541,233154402,352081523,724493209,835403919,155713790,303026929,955430300,330196890,437547761,172104660,370403972,459264589,381637385,867605749,968623357,543367400,875531776,632402134,346172838,139950795,853234354,745025188,832378380,365365846,546478636,999078626,985238787,88137038,14188278,235747480,103717893,723520829,136790089,603976114,779003561,351561070,625995772,340566102,824198081,731692627,843495311,489062166,325183858,994567391,63300326,461315928,481493093,119648126,103611196,235115092,589476686,486252680,862458014,686958541,946268881,563149146,767470607,687089442,413264610,760591984,90140949,547334805,964479266,188966915,258266694,587083493,64111321,157818380,7602092,827414645,497172355,564425841,92676540,540216110,950465871,548224500,484097418,169612089,265939816,102861044,910112477,899692013,5236834,51878046,62092276,688576083,280554593,443447775,844827268,261838241,351161666,474622168,858594073,957949465,264252755,222331367,150990275,998174325,158977816,145381048,600662588,57082977,587660645,23867135,338315545,203009727,79864535,237962171,146806912,703467691,311780762,198992625,759687602,788303584,644921423,479822157,962107181,5698088,921829534,656523034,928159856,474188893,129800136,13519483,949034019,988395920,136183102,917825213,279576583,218210603,754822016,266775163,658557527,451083507,750388957,371178441,560823284,110104127,465092279,482675587,917566939,391527087,101823809,839989575,854501148,928624942,897145323,471898538,772025058,935149033,582993336,698104181,196624097,819105635,635004373,187403249,438702333,977184758,751689069,482978393,449826034,304617425,564115264,311727803,945092806,717226332,374521853,777986149,905529382,771329430,858885955,724431076,148609508,645581896,869093559,29778384,537608685,194100362,176060480,89877301,968696597,547221929,697985984,626337889,42818945,111676949,387622314,544430999,62067808,532137376,726160582,408090326,962385470,283735434,459234524,43463159,566272249,121968050,331526664,239118461,32854616,314321005,284578182,486538996,911177883,558363792,472174516,277903991,579623880,557997228,685113253,305591104,647564985,608417746,746990630,28821524,806320313,235756582,992064921,94700956,524313580,230741628,389714164,506720175,28689450,463351006,16340084,801452144,95830795,448310847,803683459,995849244,264181434,449286128,109332448,966194382,137769919,548897413,135718922,656051803,109129275,710884276,154847469,456901667,974085846,160828109,26854353,520143852,459677867,899183015,89284880,641436441,921236718,660115147,360725240,537889306,655214130,46011722,121072355,685578563,618008352,883319727,645116531,700719960,136753501,23344087,464090632,226671187,113689153,595328139,563985633,439375840,806444316,71367965,760921905,668526992,782869908,724410715,600291595,811754403,975530159,386685434,799181748,89533653,471078056,31713095,976650793,898169122,837506302,870695597,892725123,926457530,587835784,671066255,43867451,829922696,665424769,781898350,173735461,764884052,464555460,790112067,81618608,354639641,277565000,475630813,345081142,67014832,651911727,857335977,97571253,223942145,729523495,720220825,179392212,120967741,785044767,835477602,5704877,908882815,296980210,519172824,531748033,622665576,729710070,622164112,968655563,388217430,113269384,935998626,567735439,581805225,870816138,572939087,520772832,249796767,500882515,887559354,199456958,540106200,204727745,129923053,676061149,740168874,945043616,203273631,165831385,421812772,68365355,625160829,401179158,402067057,301329933,766156461,254214324,600802189,832689578,943979130,944253122,619162782,337298363,613767967,724139148,363260309,338989398,430607413,990633228,400358617,198867397,884158547,842385608,410336972,271313819,535012593,902698939,227606066,358315010,626409860,132370210,708761237,675277244,227652058,767009008,610642449,181209497,39072864,720972922,104553688,949200362,237837312,828133005,368302544,350176869,124866546,232248605,165460616,626218617,559571190,89075773,977217667,809018618,701231479,798907067,228914741,752551932,454193475,230342620,490405608,418186676,470710972,950646808,325055800,188968435,3451155,644124721,955440156,142282632,447527427,964187960,231826661,236089186,541805506,671073611,922727948,525326368,816400252,961001848,155331360,759956101,195632378,449229147,501441794,470746496,702475583,916133051,237263530,714736800,934980044,303276778,858981709,795481975,125116028,33674863,370507208,973072989,920452819,922112700,270814660,784788573,951754128,107024709,179516012,340270843,465529945,102492217,189751949,256873723,598659601,971810812,510212663,240905218,361963409,833173435,768853645,38062596,275804885,996745124,488229839,407264050,649192106,607697149,601060213,602344370,543587101,540750962,874465691,400389416,255026174,50497042,860504470,314487327,534906103,101158152,157296668,666379138,120315762,152466072,966435351,323915552,485710097,737665524,545946639,261618008,93418338,47597936,772488326,255905,343123310,765272643,584756228,712874749,623992663,462644146,968897164,246952407,479240323,105318900,865825159,388005785,520144502,656828339,644280762,592969589,44630097,416397985,675827783,952222170,37831636,230204141,46446734,825387162,230550461,137278889,300031377,740777160,757675206,492502101,858128255,187278333,839553370,674333164,373719213,934156249,311058357,586716796,466465651,317661223,30834581,406745414,983641844,198139797,216052465,110914910,497665917,364423005,121784460,580530161,419292460,235370904,807841345,513938464,883210363,392253636,74876779,230361561,883718188,825701341,137592504,11989144,106234322,147486292,284395933,293141547,157366938,23837110,514878910,793654002,418354030,658055468,554490613,351862514,585004208,58160124,889364082,332914286,909593578,261717827,217453983,419092824,508392395,306848162,349022854,510831557,777136267,575662204,93914950,114232682,868764652,434837890,819309580,183077759,562326858,432304246,141199564,916226091,758528009,630744227,554186785,463790119,398096059,750598005,890558997,4497866,358609103,452360287,12065693,418444098,726706714,759850938,380064729,954523164,896122344,629524949,45531901,97635348,492751529,975225200,958564548,231431056,15703642,576169479,716646705,728556446,271025525,182365430,425757778,639445531,551731280,972423130,496439318,884418339,14979611,765906030,897756219,499197934,636165720,538968333,694823329,992661026,45516670,129838362,221402391,150629054,736417582,42238921,511711855,448964529,688209184,268716349,452451700,895231549,207331638,860168587,758869524,247909349,853560997,101703302,168346409,61387704,624896990,292693970,472176265,57174330,392662999,784934208,139121243,172157089,43507699,749335216,810807640,369944135,406449328,277362520,304151548,421497009,333780886,686986009,328080068,561744373,771728280,392558273,410536614,934907803,765396867,229081294,324762387,456336455,224405227,719456064,166590222,303510315,505540239,406654998,597802244,61396365,868277024,693347901,514908804,782133955,270914192,396991380,144397997,628855263,833811150,765418647,798197261,44906733,682813491,379863349,801777040,633173768,772239188,40548346,280715572,655717204,27897271,466915628,946872059,608570936,778739143,191348732,271009166,740327344,777495517,199847385,305414548,579979953,77545076,377573824,173264875,933729576,559030462,45406147,218605653,37570765,399862136,307931695,57278246,828483010,660998260,210260180,345091030,611758797,615595899,552808972,945320778,152532703,550933893,809861553,605751167,440297869,136012434,617117646,265117632,100758641,695915830,637041465,530558410,424209464,579687806,419344414,938989356,682962705,576650935,599138125,788103937,990488725,216615014,332173745,870552628,155617561,950985729,860566677,929648074,107348865,607875686,778861798,718683033,426351446,210928009,27243984,510471514,231800248,345010128,432155610,248063811,377207047,729758097,818821598,422590911,247966056,482392184,218310232,934084085,415498790,798207603,485272000,870638684,802938745,852623731,222027211,885362032,269265341,294285536,192845790,786657961,472771134,471897423,462080499,835633902,273751780,113630453,91017452,763984813,379742230,894885820,229326770,948149870,98802916,90838714,425430022,749312406,839401285,402546567,780121590,42574639,86991557,775795165,656910434,272238824,574800674,785419337,650659208,802255976,444831647,121102258,114086032,722505915,354582398,721805008,818406682,697122821,511803852,441389939,140937375,757762352,623753682,343618178,461722429,178600048,564120649,19923597,989524988,968894980,986247420,841132496,876301313,881929435,354750397,243128165,548405505,450422771,522340486,425842665,734194112,543980519,399171542,595998958,511981418,859504236,138068851,230399787,578502487,48645981,749623000,624032738,985334014,398528327,896016209,704264618,320346984,743295695,669043335,969555724,486550753,781494979,685816047,793477750,78713638,17877529,146481706,598924624,6227819,296647196,131650027,399950825,539262985,688323307,225501834,751528053,820085282,107977235,345805142,411363218,760620108,823149786,582240015,62462951,94466997,17300225,865356324,175759269,580795509,47709334,759249106,228402217,920451614,372446230,552985012,611407360,817349772,332348172,435682465,51677705,116023328,29199824,732314187,700512051,948069132,626372227,799062773,454755795,967719505,678795862,274073582,727189573,263894408,144560888,286681549,901144330,814557718,736938154,662140062,286427093,205364717,827899190,879518097,744227905,438431375,531311414,286244380,558992238,885791697,344748764,376245142,813655125,968318964,552919885,75769505,176163237,758884664,261559671,861164601,805872942,383860712,294956606,198067392,8652000,316050910,764130519,616124169,762412199,628594142,349010357,201152436,494595755,58947702,658630471,556555019,551747589,701779628,689292535,425729987,341775673,90525194,321223692,652831555,788182542,976717468,115839272,20891844,502500794,835502812,478340783,866194634,685632472,281862059,584737408,228705863,271462326,58236887,16753200,800557414,894072665,446350234,4058693,656412968,458431147,470209773,555006149,350956005,829104477,418199133,101983951,914455565,257770344,629814391,724204900,392619563,263015907,256153700,566568005,521024990,798352636,444274979,897550030,459454346,292382419,740308976,262369024,293894227,164119133,59654593,82877149,984888725,832674116,618401374,701210292,7184589,50915521,764185827,387536827,453768955,17521388,914962711,229230294,248116259,671791653,999376862,245502703,868893864,409896690,663439912,461658207,937327361,325224328,706545657,603323729,855982715,691996087,601625148,537551233,830956006,873663869,15660593,279342152,229880351,3932389,476855556,712145146,212020654,807223980,920116150,222757904,53895442,319835670,749079164,376596312,796211701,511626962,313446585,995629811,619134906,830469769,627302843,17323012,722654153,471967227,658384349,217753712,519934620,940257657,250336540,214689869,706606176,121590833,712333911,940071974,123481309,68838807,726165057,845142747,705940694,504408297,145579776,337063077,674663658,464155127,799790983,927977509,92092672,938567345,390341141,52875887,21930412,525864364,155714360,421243463,986395621,693744064,312597427,55830102,600568048,206341801,765924055,916417050,466837022,121574772,243141191,906826644,425558968,884198688,626626227,755358451,53059455,935576754,862687930,583043677,586155536,904388238,969444493,371182791,116252519,430242497,922465761,847753925,938443455,445366212,193031421,347817914,190844649,804810355,738125431,152987838,207377254,377270170,593328964,737983055,661966926,479829030,712275575,81087330,477267915,420327948,15673107,30686412,390024570,852887708,494416358,381767559,684885552,165773622,925920535,531203326,889457263,877079248,297665973,348138775,115498356,20754910,331333826,885405057,531256092,224951763,146362512,578081233,527232733,130767941,314846828,198235300,960217547,196040608,878460889,76855403,421634094,136211706,644010454,109382449,633038454,461514933,843914062,277979773,907752128,207593995,564139566,919753758,683053644,255967385,213702449,537383674,100654105,967572459,654769315,24169943,800033574,145232643,90496836,756317165,848853247,315143728,748011888,113796694,637749529,50512942,59290986,205675825,192689883,327283295,399211908,150162956,327047088,811453292,222110155,317813673,950827051,412591810,441513196,366138917,925997786,958861269,684354036,922657128,728843234,909817582,486521104,196088797,384495894,421329720,217598055,122714401,665692792,514257276,504868703,377331197,658610000,70810299,535347760,836851385,740898604,62545968,930296122,888777147,933647277,433816605,904167115,50111798,972155570,793567785,86731495,363222531,537835453,938885786,214220816,674564329,683874563,387332837,997436815,1051035,764057910,427144628,527052070,516613722,541795995,811406717,115219786,816126726,787658626,718611112,554280819,117869820,785950994,194158603,851076777,623356648,676439940,363148267,940232265,589568454,311032827,926444926,376989837,872285948,891747015,959878245,959536928,52106230,857016415,288498909,636915386,539044933,670855121,532251986,389630459,945936732,399618010,247230762,305805072,156313287,723495570,97275499,716159408,414474450,593411621,677092902,274723534,919110297,589341957,738907257,80223184,195435290,241367663,892609620,242121702,122530851,4085459,617612498,742685351,217033936,562903335,852678664,305122985,199780699,355295923,617359831,446275980,69005338,369459571,74336983,971531833,831586012,393028867,640360638,884405472,211166908,209015909,491500615,468887775,120997310,602636650,980239589,281373720,124249145,693219123,249883311,705486891,143678545,428207226,201976980,943676436,743733081,493781200,232017057,848196819,523460371,700816103,154834791,316258724,530711087,763906746,528065730,152431727,698468527,570939306,976747877,429905385,717227589,885226696,495974476,540666334,832503721,772565202,553716952,926495052,926826917,628519897,401786274,615879522,915377552,632651453,174007719,658023489,903085177,755873158,65355459,446961266,579113591,85453845,445814389,930075888,221382477,573746551,825368839,310189050,53557265,658513225,873581924,536698543,858836949,952240394,806458048,594492591,329187364,131242683,399909230,678086527,518353521,259750474,465490231,482879949,305819469,255551467,547501216,13371212,313118679,918938156,825327589,602794612,628653824,972741080,444960011,690914199,893896168,636779409,60545099,7976361,445562734,490984612,785064930,86508811,464417771,220426907,458138134,510380022,709069986,933468031,834528805,112295497,131544513,686551994,429216237,675244836,415641755,939847646,657008978,103354719,234197349,901966379,561418944,5192454,947007291,398050351,545780932,747738308,545716282,668315864,410887367,998984690,384205063,204453005,86484516,861375078,555293869,680959699,116466946,257402843,761883365,145681128,581718458,162554463,506046146,38156387,770468864,651921982,432289711,557917242,537285821,601269813,82573071,499265996,551775168,813380719,752459638,118075425,244504766,752060626,790251879,107864845,388998917,34605146,965311308,804236495,600236881,722884153,288571084,331625076,505605316,275344092,582776975,928424455,358709802,833145361,137457757,334076266,829812490,471435727,569092605,692941400,546187685,502235017,615608352,644535596,605588872,989693756,472414874,429810925,108212232,779247091,855025947,287571695,139159453,749790255,38179370,718414185,218217258,735843382,255911292,371838911,153504121,998102987,487793298,736526959,606415584,806844824,160328126,241919211,431318770,319178025,953225373,83572636,97922221,92182108,72307950,142771162,305570821,251712545,280395346,378454971,561105488,16960099,997357695,833026296,840254308,537089545,975550045,87730524,966085142,501810320,182817225,283969954,484068823,477850805,565202166,421205770,113977944,90619758,244245548,566676464,996855180,196242591,302892697,777713837,661100443,552939084,517468826,603019994,248200692,947206901,34053310,881505805,104780152,115531542,961963770,650336518,712930073,593753620,712145476,715755433,770395496,212503331,246136392,928981365,832201714,449566908,261171928,56680409,687144691,461061582,406088097,832364259,637991121,964262519,179830101,32118124,967342853,208864975,612821261,299938155,657476416,814985273,3830315,252144878,896988973,607278395,219297712,322817377,398975951,813900161,272775170,149522498,294675247,819120022,83899447,193764199,690393254,690595445,888791024,278320286,648001894,361674835,698072340,104459552,422103593,823015719,21918007,214269111,478500982,16056864,604183219,911836978,967217660,581450005,628964058,696106766,380373130,321424769,717447097,718970961,186011548,653439154,117902218,835287799,903847572,482131681,635847977,579928110,243718872,610487247,322262826,927393555,457687303,691398126,107294591,866541026,118536085,571655799,400762221,208315205,214515309,574715800,231994420,521875549,218081433,123089392,219725736,775669362,411728045,892983755,748086622,442806247,812073927,523495011,628971649,29827878,434959987,710580806,950644055,405392721,35505922,210187564,741265314,293198531,812404451,353426509,872617334,588384941,377448341,689310260,545762156,738304348,535573448,417091004,474857944,528426008,129808035,862033614,315738588,557738716,889104107,1082363,230610739,295607811,880970262,802167394,895244712,703550161,920556447,322274609,316819959,804019977,869882408,560919035,778689554,63101985,95629027,188065610,964018931,395074067,707652177,675762056,391674260,65934442,961732533,569948576,550171380,426166282,722898518,221440089,432841403,906644337,594603283,147151632,400802207,758531454,364266284,694330437,111195804,320753811,544024546,383239565,110524918,64013066,433671388,123447035,278482885,829800873,783506843,970592480,629557288,311669699,35965382,790574344,896333606,561228211,744742373,85804033,320655695,126540641,598151258,430372857,792318372,24677025,371306269,950864141,656243061,521097802,893817340,409639187,774942432,595630273,882719310,639220355,764642760,550128692,960362571,619761149,364925262,648864227,98112737,539011860,296592199,590352535,816678405,651751726,102728869,877920546,604506434,9028840,895305161,186047756,902629881,368692536,223512457,165519554,72545758,260112391,28781925,463095820,772151880,896799399,754266837,264857227,967764778,688499684,25029147,926116382,259594014,679901027,622209740,734306721,118778077,500404390,757069514,978312948,981135055,224154781,861725621,504884978,114421228,258900774,153536086,908951745,256958049,399697313,147824310,661916345,645482308,345288642,228808376,407048840,683741096,815974834,838169183,922364410,972630865,679438561,502740715,5561869,137633744,509836518,564031329,178796379,580171204,626912479,119552004,344998743,689584915,551797450,957255114,112954460,384618975,112607104,217668819,470507873,353618568,170908007,280940535,69024747,590271737,709681339,617537136,774486202,718610221,219388362,672041179,602830772,458439678,103374389,184279778,337411623,965217,138437582,760852141,796189204,714682152,877429404,818556188,835100039,164713939,875609733,708596278,572571641,722092782,339617374,906266015,537166134,608972494,469542484,755288715,144209495,799132147,696210357,588706679,980995699,905520026,470274237,491438585,864382562,213505806,299943160,423354158,254251354,64942214,677010418,101772081,871932866,756691346,854493035,247508376,103708930,755846410,375661813,706638069,816159807,902327494,216516273,428340900,507646906,651370435,274619075,870660637,708444870,290509416,776732847,846106412,500327977,270839650,581600288,804240048,972552054,573468303,986893148,295485895,689244787,221338652,856102476,352264781,616190657,825146388,277213349,179725355,127491087,507822330,613725504,94921037,834550270,317185844,106704303,642468696,803150431,412819061,446149879,252522598,290802893,349294903,222041317,819459436,848300847,732182583,890864103,813836828,285737800,850301737,68176644,925191566,556044880,716431250,853124718,608465002,401167757,433582476,162832359,862878910,382823629,461024733,626236089,363816207,327675849,378052606,34630462,802425145,29925645,316001033,837428692,568388653,991413586,400638458,564013153,536977370,35631777,325789392,771615174,502847205,814431842,542181268,773880717,697872640,565973423,234405807,536926499,913663615,115148653,253981560,674636690,364828747,117057959,646417389,655175692,96728313,115992009,694233802,451018886,36941353,772322653,672761888,115621672,198849085,797201555,680785845,124006808,60274229,236496559,331331592,361376069,406868469,226820824,874538711,468054632,700650016,966638378,137236940,706132700,794454396,435904298,211800850,942190708,179602697,167944784,963575910,505930011,260746531,612714465,573211422,311394406,632573241,461360733,531325954,153670524,795712812,124094600,742352338,950803932,927965038,978761184,429871083,193578488,22941655,604761468,256831404,138554530,462611643,289055790,840363093,171725253,294357808,719190050,422544636,769028366,833957893,363062278,937687296,214810826,380075989,374355541,18673711,356450828,710592208,117953105,2667775,235568351,158328758,418537245,587575467,877711359,664704419,633864270,843885315,743610097,460318527,103956247,935688509,197960780,557412302,809512931,602402725,596291694,819670624,640161798,238897826,581143793,192221690,707716987,784786674,534096244,693599152,210800943,661453676,565976568,665796651,494125047,595655636,215893217,283656211,965402896,49532048,853856296,230806398,690908523,464440735,165280015,835576167,448358571,392168693,581541819,614973782,859060435,299332417,298755981,268365045,557950966,747608473,974269687,442863413,927122125,956547443,986373561,358099696,479554784,227934053,642433997,304968034,348056476,490048394,267274746,725241970,646499915,656929443,139856547,822537339,821855139,483211231,405656284,56211051,535091768,22235195,483349496,217238656,423683126,107000404,468103424,547306923,586024700,1619654,391549793,406984989,710727938,497923763,392697654,912993650,254781080,129203269,606486313,911905198,614092523,438502430,749112705,9472539,794549641,84790061,273385549,146798617,686917412,895312106,385468680,18499520,755572652,542248770,392277384,510340370,630313316,441691269,948248998,931942523,96054988,415793346,259349413,903632556,873041138,311230630,830649900,44725853,638223390,376971642,540189522,416229120,769151327,714406582,855868791,312908285,280213538,179848604,152872463,638634061,359156672,335885719,834189657,134303228,476385232,567366225,375321688,276342084,417487875,270917825,104710446,260335984,525891171,174714789,990119061,252891807,956575148,406825921,213089301,83939419,815332271,615868007,553358520,52070459,506151142,878419755,768526425,443932195,663094527,318322887,840948532,5110414,744935538,360652990,381504820,154957212,465538476,447784099,999520294,314553315,569026754,883732389,649759290,369506553,690294418,877072101,358579477,911216657,982926693,495723033,896082151,435812747,12107187,200504814,457387322,632706775,880739799,822738424,805944275,832621094,549316832,240330177,215275358,592725614,933415039,726904778,609633556,137515741,591154956,893698633,260283738,651624519,17708301,636247358,437419885,501226344,660510547,828417402,823935334,915224580,460754999,845839107,495599707,709568287,474204745,325271693,685367033,388490755,197894546,530018801,548183696,240698342,292203844,772755840,599048891,272918131,461006701,736511218,3103036,429590818,368782283,236841296,985411597,400483016,521448719,164424999,767614614,370961316,172980994,606864671,556196681,155977986,569156723,455013253,489536515,83675382,380161840,515113309,52474117,339819450,124253952,137846902,886168533,550370962,607060614,606123690,591900356,68091583,9625330,652069914,816385746,909144565,667826384,490661228,532089280,218988980,415114900,427347959,182523047,439562421,460792262,68275949,828028758,19160681,836507722,995905963,64234672,881354026,819218805,492317069,825882694,386058687,827151184,440970774,108699096,350730451,951305274,137364337,28889291,752062370,289423791,369369897,964058956,506463964,37072979,505040093,986557798,586444385,283850709,313201629,679004501,378120200,647067800,362263965,152933625,438657754,212755847,970884851,202952452,498522045,163622921,967667058,41201692,949376366,20511327,960536204,986684678,556032950,828316655,813507112,531012796,431114930,593044994,157764514,482480446,720524420,944414708,331281578,926041788,469281857,555276709,624158881,236855186,281717897,205213804,344771437,301935393,166314945,193469431,78285731,947251585,56347928,739283826,198687273,958115145,939284413,96052462,918646845,314313948,55316618,751452997,380912787,867789716,698146882,679702871,142101114,143931102,600376867,764976518,925246039,656802354,59831458,948610025,399123464,7419561,401413724,594641432,978182925,274654023,739904290,511254938,354124603,78346310,269465787,251165262,288315611,795098877,146415381,281784102,258896220,10814060,826626371,255167915,304759024,929434471,144040194,786989866,201567496,309777539,749878133,568661913,780140740,160161521,232925767,344687437,51089288,537781532,514008402,480044729,71657805,752858176,536830920,104361948,844971060,450167829,269393810,758432539,85494275,250805335,544741659,76763743,347057280,695862734,567357588,84062720,589780253,182868683,897747810,671961414,696081460,140454667,292023617,876814465,597844803,998246887,994153456,469427213,550127906,416700671,977456573,874796988,476928576,408326464,122892650,278678629,406337060,938895061,625624201,880443443,844582666,504927652,2512182,872134753,325106746,716697306,590570220,143310393,682329324,464499722,483587853,305400487,237160398,449771082,68807294,618172177,599230924,189090997,848918545,749452273,539309513,295483146,681262996,917098654,337075076,130900302,165246672,474573936,610136866,336211066,108669496,802925507,48870947,912896948,9714594,712209362,65337791,750416576,868035231,711288645,273295866,100729766,495016564,747280268,549935890,518954900,246393785,220124609,150273733,766867425,682857794,913145152,507083344,209714507,376806463,222674635,799957527,585573549,139098131,784565888,759091747,425805382,911990005,141936169,73419055,434908898,905284411,153736145,975279148,651383590,731443878,945769738,674878596,659680113,740057725,748378576,778779766,330876126,567322454,117424586,589932923,523695036,60340925,176255513,905419762,912532517,511278653,666051557,235016807,56505960,721705070,254619834,583172634,436371717,777280744,671479761,736264284,223699142,709472961,744779838,717541756,65595997,401302813,471710440,974169211,66478030,468327556,506390255,292292105,492278032,339854325,548663332,397366801,830631,220207787,172100529,584344825,717637482,539865404,913829378,729130228,57991656,605100680,23683962,485762864,909046591,433078231,723744590,320475415,134008728,527330746,811233829,966237258,879364429,939828986,905185344,257305370,322024789,849764603,481106435,681008902,630499989,494074035,843754524,299898470,882290723,988007800,521907003,905816656,834946160,451965054,543603975,772236090,401702214,96995680,455218034,252362982,464671950,724440294,457637647,72953369,217462770,429362367,108529780,942798357,266086430,349311153,809243195,83714581,889387699,629020880,152341075,523521698,504310985,818903605,931812945,903522794,747543107,59540703,910310201,95869123,234825875,985041364,274821536,177424162,855234493,337588301,171741763,566206251,594647755,41364781,100671861,395697579,487941941,666463143,312178867,840232075,503085056,303116829,112354185,922213237,760403309,789602037,27827161,618445885,320614445,979329645,534823875,988037176,348796801,840081450,73398163,699009642,293001539,235332232,422804354,987704244,424107488,503843620,245796316,54271318,309071405,544026319,206912781,52145003,632821069,679047344,854861016,611310194,133598948,534835915,496484831,947367474,251847443,88142745,290415885,209683884,959220844,19010167,856968481,598301612,348051171,590206131,971587461,731817462,107558354,892274666,67609545,607019477,231755557,594386732,465314308,367915104,250549578,14125587,303059092,132152561,633381390,498194692,143021683,715534167,329095765,805052867,262881700,967667678,847571727,412916539,229163605,257634555,606685277,984472541,723274555,127155007,353780777,314594058,66937989,611835940,312460451,762690753,925885799,658739518,216387933,407433679,93141929,567542965,735704766,949892296,437805802,696959142,292201865,904957925,251048178,326011332,145149668,973679377,298692140,923369637,771481026,857288911,834885170,292867253,771229829,11349399,562169286,911385213,249195456,452380286,503870079,406545802,148083259,714684085,550392735,939218363,849458455,136163303,106707109,391481568,773711005,972170233,684459774,89519873,401413789,898639793,556896606,221935492,430854117,298094755,704168812,431701524,737995715,804281510,863154484,995657812,472119289,853408043,637961583,284000589,950111736,920311141,19035385,529770671,75168426,586494881,780765339,961227631,271390450,606878923,970841768,358725042,756976144,730488706,663383597,106107671,291049759,586283059,519095256,640768133,370148832,173989978,578210784,295182808,813345307,615947559,720067714,836815148,630370378,615949841,371253481,511329599,715928722,363238412,611404148,334980280,688567192,339606847,612052221,984951038,115383831,513343926,939328523,652495082,875151131,973958439,432124377,857448430,920681508,561790185,261224817,726471036,531979202,685508486,954199922,234360717,816023780,85436717,788438660,147046360,926778798,81573393,108085437,908746297,160399983,926904338,904376454,798981846,374064768,977841204,214307099,377064681,618508767,939428182,422493743,424214515,504730776,918034326,269076597,663635096,628407908,894749740,866638080,741391042,721105352,497577231,802231698,617707502,234245645,173208604,429808906,849043717,476143358,699977757,873123621,616087937,990121643,1826548,893013252,751929320,884677868,672632376,825981415,254205846,144622484,239019751,715985039,301896760,118666991,131959121,897551312,419645095,689947078,576689167,830844895,854040655,885338797,767591161,907886077,205294413,567609697,159437969,291626396,305729604,187182253,279206829,848269787,596297479,308977434,411600864,338993737,916951247,595230004,215996641,847798313,268585102,285890556,968022447,895191735,962091809,398559976,518816122,847940884,6820441,461990339,650005677,981197029,43406663,564696928,621335308,627588718,889497670,518459667,871546109,79554244,653335542,792627347,396704454,543797306,149337426,766542686,10162108,292329198,635526775,601857186,161184689,821684479,464134783,887315134,613756272,416985129,604068556,874620477,230562064,603440834,415784139,819417027,100711266,960979051,115121289,833210287,722355493,641364170,82986056,692182209,158914139,834789475,775282264,935888589,459918499,653822051,123479050,455224253,329335805,978465141,615554969,940564751,642591386,802469746,585279406,343563131,957987363,106263142,993130959,513717162,784814633,719737015,459413159,286731691,112814079,942879924,593609083,575662094,49558534,672746149,601205849,684412126,414672289,730953557,187523160,642946416,245847363,78396222,345833957,707628542,975724152,965786153,530651214,112620650,573800682,684333994,787491648,256383330,441093988,141211191,555770640,865714416,927376672,224695150,746368431,111291967,410417326,509061820,836291662,984561726,8235541,548255837,493086275,823931290,554862270,731437627,660958261,877448617,788901096,975947321,153879183,696864904,934467998,517726726,944722816,642461487,219038484,761723985,35159366,141603829,952644049,469982522,998211946,655944640,412855068,303317947,834889043,251974509,642058553,615477701,710567151,3795081,173106145,880531708,736592166,169537408,696778247,611366454,800096054,478436559,832691123,587161348,888731784,538928349,459208337,585207254,208988295,361959503,80973041,173693899,507597258,292449323,681708412,55883802,40868133,34428657,745922135,432630528,536906518,537564961,355254717,309375322,580476423,328611028,636875114,151519804,956625368,184944588,629312988,193003973,136675599,175772056,155643640,588510245,655789894,950323357,932956410,189979379,100714748,713795393,83088426,257228561,625840173,526039794,224290031,846017037,767244677,493613873,935329553,615762440,140447134,796399005,75528975,162002467,590059321,842476842,702454511,755026274,777052192,483879217,223994662,69310988,445279201,580517186,57800339,973771123,476546418,160588234,549980596,284720449,687319182,273054155,157517756,161691672,453072567,719319085,585905204,84064994,617218633,533759830,709088803,551412737,420952818,724389844,689941021,156634462,330078804,292454101,168971192,194605300,56532082,440180684,757923136,859099806,561315939,847555432,213513145,833601509,255309299,792582548,416251193,310765423,289330131,363388819,251344051,531323672,982465507,886474936,867841090,380530211,83232887,100466249,994869613,138617458,155183382,183292543,43036688,772287946,881577236,102878155,578338577,871042367,305023474,36584816,993023444,599205490,897863836,119388746,394655246,440473108,347111742,117295856,38753756,57457159,30308064,837277111,226500166,494690898,858265722,797931342,888056245,746504480,264395987,66793206,562871594,966451388,175338604,411670980,700263797,33272757,834187160,357819627,75632800,611505540,159226810,221664637,101364787,238245530,109842341,685553569,380915228,762047247,195596390,735834993,796451631,56250990,370854857,42893840,61177204,679814366,547796815,425371911,579488949,270545118,512708208,84845849,206380653,462780104,752756926,415019842,638528115,260575052,565353573,570872660,509393725,328382470,771753375,33730491,960609299,179482251,624897292,960585125,135696326,422433974,995348661,444192996,858864024,608999295,587925026,457727449,18816429,133725945,95078103,880622527,514188729,478788161,979105042,10543632,290107472,908081298,296580060,813760833,440680562,826166598,575284739,911633709,771804765,870546948,443869540,706542661,1303136,427907794,300869122,507273862,827953121,73084198,534133925,162494600,808301031,91670809,677278998,560498199,849710761,705246443,246768902,898761486,334445270,354238553,686603823,97667886,211227289,693717848,849474217,55401388,584246516,260708015,536128919,787596544,611482431,167009955,421301338,526741960,308146102,89437850,467564089,230578167,651208368,739533664,301129566,528316544,756472844,247392235,621985279,913089142,332200106,419227980,120990877,469144207,170919740,250140276,528956523,236018054,356805202,801212518,900558065,167301326,922371125,732583002,769277778,686395421,175892359,701242177,468231407,168924453,181295241,238760461,7827516,846111342,213275160,358157841,407473130,575768134,827585373,891119877,926302442,47674591,591350120,302347930,272498919,141716386,381557167,706208143,900193564,483946704,542045531,704203951,871073463,332629795,228735008,727012790,974099908,776759777,347922223,849704415,975182478,103940836,189060410,583377199,64287823,331638385,390877293,624479635,719101534,946100442,980503452,219397315,606435490,548573853,304448923,727130613,746602275,147244152,676870360,759986314,327938608,553177893,150875527,490267229,265894026,522114527,877602058,515736120,379176990,554934155,511256845,438743575,510894734,728397549,503061993,823949322,830785599,546608933,368329552,606899692,46910963,47183459,57794132,432536657,241856507,364403729,878394882,932195389,484715306,643225113,304270443,200206189,653883833,817455446,617282261,437108377,515855533,11459446,150124992,954686681,23944401,161078537,413628062,394110125,235878649,695179401,846334709,462931965,169562056,20522534,27928323,429673471,491275379,652253694,169250833,22757295,855832130,233533397,845325229,911675058,12012241,859156104,507859680,657063609,944250772,934030675,176203639,476665408,918210863,266302357,882746891,710543349,636757710,848659018,837341543,778612824,162173320,264303860,826251798,52104667,940198951,836516272,202757008,967668967,63414845,685897494,278644029,474214299,823463075,942378313,748417627,983516085,610405851,780423252,130109040,864532985,122073513,760259616,613746016,442975651,619424958,799795870,204755052,428610466,176275918,961481643,806703320,286839590,653288698,944409974,23985677,431596454,605937786,309845293,448293951,245610387,442035282,4953705,40871866,298804546,189821211,922560911,653798107,220270116,990384871,331336008,542824543,641891916,559904118,803003602,405700216,897101891,696448244,947849793,851941805,403975723,237375060,412412865,174157417,527215303,218068270,471707682,943596337,676980745,75081094,104078658,8013330,72137075,716550057,319056648,234381204,186912531,228083450,883473776,704841125,428159755,375473845,577590021,430084529,706029625,259795002,839117068,809722269,983224920,808290430,993642516,425888653,749798996,836094659,582260744,523780890,660085138,691291434,622969702,881917505,998673176,776971067,610363134,471380920,912439571,467404680,202931246,53372286,331326709,430404537,18694059,408485395,166324847,956587788,294149443,904996036,195481359,37190018,335487329,271164547,426234696,332811852,587376137,446617570,496581438,587575126,442899334,213134005,39616800,909316488,282178428,475796441,411460711,66549341,564190641,363340151,994043276,27938139,996765742,932614679,782348202,145753452,199270731,790960160,973935904,630599707,651124078,294794796,794421464,363015190,481295623,255127941,658976506,756816096,311294322,895313764,142930450,653425410,812119045,894901942,364597753,911202655,696579897,862931703,420727928,829279477,987223928,668549176,248905,8620437,365737173,955649920,972809126,40647416,323582658,869612502,75984122,949756072,428067511,17984537,866043330,488606926,466549642,433130445,560530369,557207654,939736028,584651756,672283991,427784467,697969182,456083215,839285225,636868314,529814870,207215793,527331281,871112042,685788552,270368054,344119728,852669366,735613339,535841595,566077938,947486816,282576512,982390047,495408323,440757058,181097338,380619013,206570966,405511716,732382285,202835890,679887318,594782080,986846581,445373237,965983967,175415013,683690534,26256246,145904358,651546928,805212674,306430869,402242498,826967745,341785239,134360385,10093281,398912656,235080340,765920414,352713406,10641550,670757516,144577499,232251712,597713101,696045056,710255859,266057292,544627287,189158965,382911405,377777799,454456356,523249891,450488047,208545842,671608631,145412550,857191652,371080255,760355305,64245526,215554014,775003598,176661142,446120403,474634816,564918484,343896339,617770796,880754829,667899173,402344994,900562937,64377501,571472323,835752103,56510307,673495322,847768892,356204764,978109948,893799804,400365525,734306427,418645371,241845589,299250263,424603070,835928293,872669228,690880202,449301315,905399880,429792236,840031665,25267393,829207424,415849428,596281370,974306447,400658179,71232949,116780158,248061185,699691517,551559149,495777527,21826266,766733461,825039553,106001492,345645467,997911672,940272543,266443469,880026346,494019319,697371221,316391550,830032984,178197006,255564630,139179047,293850852,258778093,514209636,666807235,634544798,952532527,63757803,86598465,319204536,420334445,749097466,922204663,506312346,942391167,416479426,612647872,396072753,874103070,522696083,440305571,62883221,963503880,280436140,30097899,76478972,266009417,187546057,420437094,168819545,361092972,3504273,706757459,516004016,635622566,836737720,947632021,13044764,69726426,466831925,503184932,89492376,234546037,227752185,878715114,901874443,802961653,746362270,355103722,164575235,589274772,84657462,608466410,538151358,133019513,47050396,840096451,56982583,466098592,440872101,177659676,877015140,742542369,853564134,796836913,612652476,310871036,597421337,173970498,482234461,689479249,722340417,325780291,183795513,931469474,467607990,507467380,204799194,654549055,232971953,580272680,556680783,713701930,144088866,697405702,949506393,413843950,21293661,211062924,575355195,568420216,716171250,349346301,22817135,169599371,834684890,449767472,122089018,693814755,991070871,805655446,466832352,989570359,65305481,908595453,175476588,375513822,899633781,597646494,442947289,114488567,210966618,115849297,157554322,400431277,661021130,217190310,296823652,968450074,10508620,295936205,85839178,676220335,72133597,952556470,535870954,193733500,313416516,606403932,772908701,212864925,156657412,888359356,621297755,638916083,191126241,399123379,497129912,840219325,363144378,403233957,288896502,508309933,351394109,43447902,493965010,588832834,370928809,173603529,73301538,999338644,131968359,323412124,486621126,306779604,771933963,275398373,120998091,673621996,387094642,417735654,156107237,355805673,782574798,831795057,235413004,367821210,505969380,11822228,476761410,510264800,124141716,443991742,95627083,233597842,392050715,138506199,652588610,452814232,468579258,118624983,54662934,977229143,977465467,284512110,610609213,450049320,701982022,298933242,67025145,665112517,184008124,220662587,952535439,965701608,631807402,177626038,306199062,329335555,809987824,808540919,520609031,321041687,104089085,577548532,524128535,555146551,148540715,350891624,706941556,878414393,126095141,571272237,674419878,961847003,224242566,606319021,791235955,250520056,323722233,824930677,989335377,545888411,117849049,883935180,693828891,385399392,196703087,637995977,984109845,979519895,818822391,220078936,862797622,320721161,902252659,588914945,94760273,570229595,798745578,507009388,123325689,218332396,959131600,53304869,401790001,837777515,519432123,385452535,171659099,298140064,976099485,854819603,538452463,161430862,390692118,949074908,769229418,766519789,126082598,126928138,753299463,25983355,210756916,918512084,938315428,791947886,37292628,661063309,909143809,295243304,9578377,183458929,183461510,35044104,258169202,114745891,434781403,710322249,720844530,948051317,899432123,430801216,69766840,498714195,220496129,535505781,345779494,59692415,434949497,102243135,35157868,393620169,72786184,507358376,81540701,924518933,180339132,365639151,613948404,59726986,311156467,464190237,387193642,203167458,409560664,836980745,648591257,652812348,772810710,650295376,323302783,325172476,78360939,176648627,115051577,114485096,37773763,821722643,825717861,16197956,551149251,540730943,883869081,713996981,283106803,677850545,549402294,378613502,878291728,153168221,232091777,417540455,677423784,382444062,859010427,250323448,216762309,894927400,763663333,799876940,47165020,142247164,89936763,202334215,944975498,849755631,559583313,622374179,643978615,913261022,319641351,775106189,450441193,249317396,17065625,974636354,547020805,429745755,757805828,884213295,532272425,547431167,503830076,504195606,183302475,883986531,440742773,686398738,299144266,391650378,45951434,969009806,819203235,147318317,818845967,248420895,650112495,876934869,542371460,691828839,647935651,374377858,840731779,746485122,567531888,245046566,196492761,206560771,502097176,952196891,418575709,60758391,163043430,32256809,890752231,793713294,186649995,534935521,391616132,268780944,998165525,820400195,212812470,956896543,677211661,178664295,841298972,315618695,14600926,956564567,759437763,869970597,951082994,483773090,519643380,32792344,214117893,238978598,585607307,794428761,627907902,111943095,278217902,655789675,402694428,663266612,462192029,412405076,927982733,349393476,177730458,64278265,305032476,717647182,652025465,55336776,202689301,133658763,404277310,492432908,375708994,453974256,667794580,228296099,557161457,51076839,581758748,323521667,694537098,699313523,654085269,31725387,295658207,876837473,66636813,214470356,542693876,286252156,977006771,100086770,406703921,476380785,338200741,980262228,92769949,583577938,978713419,136979262,734119970,383009227,75460171,69238327,464166881,841983508,798764770,776727338,704185465,132778464,627943487,460737731,504714517,404627282,693266436,723799954,13636324,472090881,749627815,502909394,852688959,949199776,562937745,294441954,326753121,154866413,444314968,44471283,22199644,862603356,463898582,588435518,364037288,826744277,619649146,535853858,260541609,471182422,11795041,281805265,392462061,457965114,885234165,903866793,721573676,605752078,281132836,604108891,365803420,494537765,652228874,576534894,448021209,202567270,666260621,434461805,169500187,900985624,86298966,382168941,236047946,76369654,911323538,899379950,408546484,684138311,817156953,392700464,834453961,972425748,769111746,228120602,873167161,924160230,575816723,153436048,373208700,677744907,914918950,6278117,881610395,844965606,7868937,124146497,615202087,599858999,125897223,816777174,186121585,71737887,957019403,197133695,740700648,660823270,818044841,880886698,243617288,667427247,620843131,487761485,876783837,211208878,988369935,296589421,129581903,148191223,440400708,772132988,487900770,196959856,183174751,596961561,650230375,646718243,908320314,74214816,14279134,609079511,153712062,339251176,510548633,725561002,608661665,755007192,28241030,687474749,670886126,510677486,415123881,700062525,377768578,649871827,511462695,985129158,613486100,392924424,605650073,631313745,378306850,458537647,587678895,827948077,828906408,920508918,25290304,704611494,278972625,65371289,337434363,917827626,253518940,221584333,988063051,247505101,108506235,96860354,756508204,313622264,119067780,144794553,120736584,267505460,325059932,225029454,12265510,104672789,945879148,759222872,519675329,54202102,92887584,617045725,889898685,235640463,720180551,495398268,584831639,109382029,599362754,258737685,413993970,271783745,389021568,295874163,869692473,212506686,912886124,42400663,572512973,306719719,430624245,615819147,501824421,947280810,506743958,782891031,405433506,820728835,888721908,149086467,618417095,546948451,252325197,376470419,93548855,665048472,291190840,130946467,584731307,681050546,641066148,690395796,652056954,25033711,182494022,684517094,81338008,823981803,558926937,792277821,43045625,757310695,966953224,282826236,28880208,403335509,47719812,27445772,331127492,704896283,446479674,393408641,956466641,628168419,272220070,817051286,609672733,992981849,165368812,346574357,320647466,584066667,133096172,721605883,472081547,321879653,997744666,194995426,405269128,337001002,794869315,569958659,437808280,42048943,787284899,68284526,167880708,193024085,691661004,684848882,491616865,903727613,442001859,445674284,8628530,311976480,961498245,493215010,511253643,231523675,483396444,360709641,243136124,923118759,541827318,61208707,857621807,412492215,556334884,83676038,273266678,893106127,925922052,773148282,480317392,412734013,738744954,983498218,678228218,8949573,486495135,163418615,682031246,767735897,472400651,746421923,708052470,315233495,412811409,746645121,200029382,381792753,277707953,511977946,945610069,297242609,55030465,75735737,596884631,705713940,995965727,983545496,575781166,249386721,169656689,101710331,575596136,896774826,255195724,242927495,765656821,709475535,468668803,551487630,350623051,863377225,382698436,809279405,893729742,200784814,767919962,968220008,259820739,115035724,841223256,732535325,29924234,163502376,68506914,293258811,331378411,673351632,324927952,184732611,449616852,3822493,916682028,900886633,114101324,439020423,593900730,458981767,890566604,782858614,196938423,232820216,868068867,376316325,623435856,282567651,22301579,480149926,806585638,616003143,739509536,409356395,33291049,647408268,931115734,15815485,700060041,347377562,922643645,374839939,329344940,848804539,969567271,351053533,65921101,850976395,449740988,292302291,33999363,803668068,495801157,938235280,289620754,742513776,463620022,279256243,570912477,235786263,769006866,597931632,139674751,275628541,734133488,730483851,201918681,60794392,186001568,79370337,975447897,892004860,651182150,213038065,456033156,594200827,787007232,278703878,367689918,58865667,282447439,98725040,782191280,821805273,17927579,319184851,642513648,388375875,823922165,654882414,445359936,429481014,416963207,921246328,645354800,349928317,263634678,306589523,462829808,111649320,971083689,344788426,210630682,450457333,252233296,85346973,360956242,179069035,612965401,37834442,399762074,44458936,921756703,584666835,956186640,543600268,109866042,630661328,810908749,544631074,252595670,1053935,749782450,159316949,896987529,950048887,17589294,503836584,550391293,671830417,401976372,442305364,954812459,766523501,160654858,43457925,914186900,47345566,259460118,584045021,775953525,643517163,503728897,865198520,362185145,639595131,829940213,582513943,540471864,449911119,600845522,588980638,752592711,804339892,140121299,110916671,389288886,747166809,800753751,789740615,118367360,820816294,409566390,785544708,941744818,447155970,904098323,500916988,573654164,474920288,985933940,797837927,106186028,307593128,536795673,645961248,99187308,331933452,790354151,399213100,837301393,706886513,297963035,875156037,633532239,957158248,838043008,923552440,506670623,557885585,261386774,365767218,688076784,998303561,391361051,671539979,668784898,161352125,664507487,941673566,128168133,479408779,478160189,73776159,424356517,389095514,498659182,982494198,409067945,872330572,717924819,768303869,223399898,419449336,873043050,665193685,934728180,665406382,701928458,313041005,557619269,694942122,452702282,18485831,373664478,953557924,479988313,765597134,425863630,718508798,620778926,678862052,910013153,716700776,825656310,257924619,748791211,168428956,628419842,796844407,177438392,107585940,197864597,447794658,368345777,136169329,939458154,877228731,410940828,882600762,449671509,301637491,732439439,280889046,393892716,8343049,720363960,357914170,547061233,638749154,918060183,484294067,540123632,149230330,242228209,726525502,328997734,711733131,390730664,425261001,840019128,738388310,291378958,246687887,93264603,667206990,760620228,340852921,3488975,771395492,223929653,481803554,669541097,391861566,378490014,632741232,515448139,895292876,324384061,662204076,996751660,231988550,219901083,956875577,454527791,145187027,225804072,46112619,885114672,405446210,74082088,625540682,227822618,208615525,211495815,935899132,797804663,463296683,167293775,443191069,716499091,868415280,260992195,48866817,981038629,868065919,423576307,200808574,152642884,796485504,970458597,462489430,346277250,157383601,312400232,273873507,105555690,71284311,414739325,352443205,350321657,788218049,771517879,259460623,497724447,152609459,273445435,926885023,573705828,129354199,30641770,311967071,371028670,803030606,191583619,734033106,16344373,272076747,534504489,60093199,908374732,359343139,523112511,88403147,422756270,290378132,397932713,145940070,398477764,340645301,571661751,935116679,750797902,307422902,55332333,741952136,106465175,452222229,880938197,81813304,544995562,583617741,866584092,729102209,855914745,935788068,972412914,374230098,771332442,689860304,330237094,47556855,180942569,43328099,890331940,605817736,667870181,939206735,499189996,145104521,26157725,854557072,322415743,475957924,556839790,532794800,235686805,568694146,508205309,253704279,537993103,355126031,117625282,615111674,357997144,186013604,302630286,600605210,334840506,447421007,123053679,386854841,500009040,381404587,200582462,449740012,75778903,753718506,595824290,316101751,796922432,679527551,179828284,35426580,163353932,595293292,981028926,805610907,528369860,674655646,816501867,907288736,116397762,317538006,665107537,270523325,984375833,663978032,139122590,836566998,238854243,830503276,837184294,290260804,221229144,618703010,41521918,935861063,840134804,850794027,317061042,155380905,504118342,87018449,756978873,815671652,855873807,625357853,786523736,178284044,30476510,582206344,35616102,752470291,125555016,756807632,3488648,22580202,227067006,228029461,818118251,563502325,704792689,307205227,591188234,351560041,186352246,944080807,946798326,204199518,299324635,109699284,186600590,656801947,495634713,924860439,416756944,526207573,766448257,251640392,434167458,645686597,97728089,946458892,409379749,246553752,515291985,666845354,126506696,77410407,621498139,510385579,811645937,579189310,818657717,904892551,188453584,675105284,168976668,852456769,888914175,879544153,859847382,370190907,295335687,886568524,538628995,562122713,830757176,925444827,746678717,332666610,969850280,425717593,50307065,737189847,864292349,623990719,305115047,353222024,241534554,831007486,903499689,241512551,732739680,898508905,339120022,640111616,421565236,803648350,626883015,585582660,876602985,879315360,189956066,261275390,949050282,607186546,173523815,732221694,288999121,707977691,955701995,47027592,467970218,307336267,919516662,796171181,272815287,299986325,353558028,362873223,590780105,181735397,771169162,585701782,410332748,294564239,602845671,388065114,546603516,424804472,249058005,760584440,821873782,776359515,44687291,693959690,427597117,266208538,138504933,10013101,202871862,165669969,456850010,351487752,133389529,460833025,325137620,68445431,778734082,994302133,925779017,694495708,3631248,805982333,430434584,233606336,390755691,816043385,510251920,494902821,812406695,195730359,402728870,477923850,409878621,218269000,125551531,645792478,947117474,225100113,56543833,432288435,948077606,222085953,189099664,750056277,923845780,658984862,876516300,854774976,259383236,699395015,588599802,675381227,773222845,339432889,600576869,22330273,956183461,545775405,362666623,967587552,162766280,2750771,165330287,108178095,824099795,18425519,740769938,640386447,784739348,6067433,79339344,995815529,389688543,44877284,176665570,544369425,963229344,584402176,60468979,16155965,839776631,383104196,790335833,154783593,67445631,506448796,98680821,593442416,570936989,462941686,488993377,734077970,518942073,597248001,778338467,723393411,166846261,536067682,699323554,105688917,716202824,254410308,767504210,990874462,78496947,218929850,731688760,933904660,993265676,596009649,842008338,210930133,999963620,339499085,447586102,782109555,957034088,828691193,365961473,721066818,88902300,917061804,727880222,342557107,618620693,316531831,332345786,990453029,69000500,834879776,485436702,711742318,562235902,111796493,827240395,12599560,911386938,906450810,741878964,246784941,284915868,232217659,447776623,635790504,913894151,929741335,416254455,469368502,352183131,507911715,749290599,708914561,131980870,330856200,429841592,256962011,861176562,633243544,327792106,933957138,912983163,461956451,131547807,463012461,870270437,43793503,714070453,809997701,597156085,590508792,748843435,587000100,477761614,866915459,881027801,298269762,354647653,238537089,267619719,590658595,496901791,89354690,900367642,810481861,230480221,677746798,403715721,556201562,273560377,93723353,754921611,917078150,528825065,374514319,713321989,759495731,814001597,963157862,880411561,534345988,356880812,52146308,382086134,76606779,628780751,162390087,71657824,28016474,3773974,155149258,310309120,105461699,377099053,857502586,543945207,443677668,671814275,321491220,713602269,804527274,350953048,863113395,88129281,490949788,994426500,565656484,999273262,186596634,559351280,856864729,586281416,797239315,146631439,976662044,600038531,450134317,87953121,966998297,350685916,695880532,228969609,497398276,535082421,645891575,71883172,455173803,682898973,593782101,135215094,47624849,606349396,76225834,197963991,301266459,850297004,614420372,416585672,111258401,930755226,614939771,874651191,160300714,350801212,803901448,173769726,177533172,484117312,407679643,765614316,250194908,465982433,751458156,744085526,305006472,159983226,383981949,680048922,257710264,388794617,661294741,4393039,674074131,456603176,292908433,434186077,276040049,940219058,863945342,245976482,649580863,427245699,889418029,916373794,221857934,89412147,423321418,736138277,855573890,672106973,187302154,250492789,796417302,375019243,911362026,274642228,61021752,851093052,675780618,964014176,938452068,14465405,547350400,689632692,944460054,470376403,845483638,818459555,985778163,387708948,174361440,979636780,317904784,808753050,468003317,681279847,224681453,350430936,229022458,304508094,797513128,606494070,997595200,394401095,356306594,190095895,366999267,22363436,133354528,828807131,996815502,107853720,990157842,791786111,141212431,951449319,103565636,690455958,383159150,898297280,305581242,409478853,190011008,187186927,728356715,894728712,887697413,516971936,157539295,635106801,405219264,593015250,5547863,427773055,424738645,844312332,160036327,441171602,86490066,707912947,468328857,928024588,729552404,946028779,403604130,784952273,917272175,144792333,7555983,46696130,596535703,938999131,383924192,696032094,126965052,358499640,446879274,915987192,123327205,661699943,856780717,275462123,680508212,694048244,677962248,945613100,897094491,509600700,728804014,806040469,958363210,726250565,443983849,801646791,351790197,32926639,482795784,365232815,917883453,424535055,85067625,952564125,608329929,43999974,645075605,281568659,519630098,368148939,550880006,917171123,222573822,341899312,342616584,986656540,591448344,206935327,897275890,199896749,469374112,832733584,166106597,966677161,486305781,895619917,432398708,80643432,204396174,854494891,667364708,235462740,492700555,55327012,819243859,69962240,733829022,865760227,735080532,61674441,300226138,424250770,156565157,135360271,51098650,982497598,47790576,458125193,567711074,613007552,602421870,817864792,845768174,775612945,212852644,824809273,446716628,534876195,1319500,418408976,353090562,966341355,302888318,284562562,428395050,458392448,55936235,535773128,869875264,340117132,407475972,397216438,900225220,306762627,456602020,939021507,47890639,851541451,209762495,4406612,398529777,342961277,80016369,664763769,877387156,343732489,776371925,901580924,690615300,427822323,571980717,479043454,887993876,10789255,731561989,957282197,553691103,708916302,538707734,853506163,759137474,219347391,199361909,358924166,688420122,355323213,239436202,383723577,855631564,368515657,12922466,813490067,155673523,45696671,75779933,538431037,550618317,903144438,980364935,159440671,108908406,287280341,545697891,440637179,18596839,623916804,721319834,612782840,603615611,805506941,643353745,669904026,545354930,76019317,900052494,402505755,419316254,452855735,506854532,304587002,536538411,519831574,86331938,714168646,751522956,883090564,319273879,731329460,689846501,582595694,434656097,401531258,714338117,378257406,319523870,802323672,6724133,866417929,381853315,619012783,772314402,335417553,638007396,643010179,440862500,497561294,398276432,277202292,122802157,38479879,17874109,790459386,542228944,170784223,554483732,524819736,586330490,597569129,224553704,694895218,18499108,471911386,871219654,670233473,868800791,137873457,693385992,804954572,987345238,287560812,613532272,738264019,36136091,200622940,159850396,94277625,325682523,975461182,48710815,879373944,99969943,948286063,158085386,142012697,201771818,940209897,191521323,679962047,957901060,772134035,892731642,815560174,624825219,697115418,74103071,707764634,169224859,363312020,90675762,661690409,376000588,167248306,892739859,817151227,189237571,297758362,541926922,407253018,671722882,841481946,778523729,370038809,704358087,765099814,165777532,916818456,226908464,893921097,126131600,883110978,796335500,641804263,753889928,769868463,896462926,726071486,167476017,355870825,532024846,91154872,64076136,213810420,329789673,416068789,215266278,641692791,370219472,725900605,307531087,8388431,704042194,437555628,601221206,536757170,342795941,931209181,983298252,492117669,735933627,819842934,996742495,810528439,533127842,199258933,180106390,56180617,441692048,27883020,586890734,941107216,915792244,868796372,890580673,699121158,639774833,341139709,683009658,923431104,387011661,948738099,996674778,40871036,603755899,916752631,940278388,213092835,580511806,201414417,426641109,590344416,424932777,473966954,873872429,219174440,790071036,856891024,662685936,955011498,127228685,218373933,264311249,249490556,936693181,491383142,78168252,255733275,958734681,325976458,656811389,685461077,43584168,2372567,305081147,303648541,219358208,940024897,738732160,871387213,336378140,261322929,965147262,747830749,402265408,925285526,181245548,681474771,804016633,951875946,401993755,468434132,639632285,843932494,240244612,889934095,568694220,670055298,654010578,992694603,817050549,131354975,538366121,461022867,624144351,708995626,831796389,921566340,411793215,136361506,924591080,534834494,361719912,873388977,653053449,338568509,846159410,279950896,686564254,15909764,752084019,283640687,847408903,676342737,435103859,1466016,589663658,291954011,139467326,537913328,504181674,607698073,931874083,414256933,22973303,171554146,922101092,446982738,184254336,177359244,529925175,950852054,741970294,74231948,12705900,994205565,533079435,49150231,510522129,520530788,450599301,151629463,2012973,975054782,741010890,919743220,943853093,263288765,149395412,924377885,264596450,666536341,527868378,992706526,39183250,188861222,56142131,99432265,587776807,245660135,381130267,58965614,300278988,66435446,44109844,898472576,55816452,481683903,513548482,111806504,63860674,258630053,392122475,713523548,630199923,713870706,867486049,719915737,927195399,737270793,722776525,186234870,500307332,173494665,153021667,278310011,568253305,224998534,722821881,128055511,135004854,393282924,535979670,549793178,410619428,14339235,435438913,622028147,754864122,834533360,582957628,243176213,557073914,500501997,543655955,739164389,252140865,268823138,826918707,667835912,108200685,706456244,204290520,916380914,530444570,122394058,584968152,562091914,102103158,883838944,33725560,299679289,397066444,704006630,57479325,705084755,98808259,56900641,70503774,650818785,958095694,150032521,254550423,289107643,442555946,506950538,965179348,178510402,242122604,975981808,543087346,161631085,780527195,581443937,54114848,28736894,966264642,110913211,348315169,117533452,176197523,282517033,167590055,49093669,800815175,543814924,820720854,307322835,155454251,490151448,910573185,87514867,203771102,862261008,36271759,946432983,209281280,218156462,162246314,810911970,969232277,828467577,410284267,697580769,53143116,935308556,869815762,317744832,806989825,906387618,609400123,438160013,896262722,33531141,529425712,350898144,90706242,475137081,378766898,65313108,761269498,392924952,238888558,850245208,419306145,564706451,833000427,543740478,516577128,783857159,3070389,982241901,94823502,550891626,871965028,678653468,298912737,430683226,335050861,510213894,222003809,259369237,410924480,55868335,47701564,569083695,988754098,56581230,914127078,870764347,306048443,786797298,793090883,384930227,976754778,572828298,625734148,996514172,818921947,915997726,698291891,73780519,883253438,702668950,227565187,332540665,34355957,742608015,116334517,391819780,440867128,512677433,408882023,718751239,848350033,697993942,4075947,517297903,343102373,243276344,815198865,904650990,726047906,440523670,64178583,704800411,71438416,14860143,488034280,883227847,489436893,678297740,690554897,293687053,121106080,127681067,368232819,684206478,455927807,799356204,837704155,109570088,154566058,265406723,289845900,98767585,408230512,718735114,517518073,65035114,106285678,896548079,863447905,32870300,934843175,173357361,391982385,891522565,708899048,984753393,497347557,378050720,918746247,739790911,321607597,886074461,506233052,481704838,363854082,61402363,334897148,887788390,389714831,387115029,976690753,900423345,866893701,799736106,919392070,276084936,776508882,823709008,938812765,604401816,487630344,916936480,228753730,301407993,553242583,314144751,67753030,514348242,745691564,420354630,830564747,328610973,553766097,306646058,485357505,33404172,374105388,600474415,44512745,495303773,222571960,588922407,221090912,785874600,712499634,457541971,870438873,343005151,666088238,787581113,244042662,988197443,503396874,994676969,381340993,511477845,274077676,580162709,566918030,440396678,638096761,573955654,920402202,645790189,283253782,693786691,68676997,654361404,633538741,447662886,2322380,514718851,327379445,20655273,56592171,93498464,956646828,87181695,671046449,136183005,187325848,659620325,374187556,467773749,933547712,948092152,273899611,826007251,672564164,677131262,932830306,845665902,629483939,862331345,404293671,875275197,995207099,699961160,182139831,682334326,193076575,25934677,158373219,854964041,728090843,181326998,400910025,18528436,674183740,758363236,427361671,498200088,910346193,124766024,610566673,635721611,679023951,807727855,899221619,71015875,415900692,199900436,223069240,981491768,783233476,857949329,690127292,575679235,768017382,668476850,37033100,837412724,790779629,848950690,827393653,49994281,537125499,673847588,863427742,598657124,339959322,34073517,767525429,322761612,831742976,154393761,134156289,328517851,919349414,311346964,85601650,405433502,697487678,469711576,772455807,166992140,282299598,38554845,651601513,552148092,948629864,179006487,870811091,406702671,845396671,357743855,541087635,253592975,143271774,610870368,615320469,440718023,629872109,614346483,469329482,20013188,325743498,436833088,984671581,15110558,74783272,76164057,119558190,526810422,977012869,782894116,795050471,132563005,14217165,609269495,374097320,915254601,544390695,174933989,931800046,759499345,582882905,328626267,116172860,881541133,12942745,350698230,960300999,445483681,920679308,53660114,546066569,481972554,545063295,891679746,219095108,601631567,880999380,454011959,695118532,898969128,61039274,633659359,719677599,954888040,151838541,209175964,891797097,263795659,836185997,666110996,616940853,230270447,763563391,189577450,420996504,886519559,187359437,74090089,831345976,442817339,310287445,498937925,882723383,969783196,728483504,697402863,79308632,89300168,683292694,95674741,127920570,760705754,311217756,768848367,839793726,858169765,849128004,488549769,866783138,341631551,930744458,601401712,480482838,817142993,332737117,434774206,388127667,351932831,566123899,52622551,251489399,538680695,164241415,594244754,846960184,928651100,633135838,968916237,760845055,297280090,557120787,41604229,335286515,246390491,888090465,8711629,245196431,833882828,805718739,424856562,733423128,210772310,957104660,635615001,133875377,93070874,220887255,893306759,973470521,624118219,441259914,505852166,651600339,842476583,507145383,178093976,323524408,994028347,912275646,493104805,383018598,504414021,148171868,130650270,1028921,614451746,191577036,685856717,812995161,383487829,243627019,291835068,494450891,813392854,381866992,482795271,379862234,862758821,857129192,135647297,474690221,80693504,673780909,3848072,366196062,615704948,780036115,538247327,183705468,216964404,22848713,73222866,571909017,74612967,231149418,505802956,446025485,995480299,286163080,365371242,806525637,188902073,941132820,759118337,515687446,716909288,614653886,149959333,906928433,691786638,461817768,454689469,266011655,930466335,994172038,589799976,440007144,818866743,350075929,77077177,821607456,494578245,185913507,435557679,950350676,609360167,220889233,61421944,847425904,308975251,72415232,708109285,347088095,355514838,106332644,528930298,647058760,726517592,518684591,912402412,764736997,245838309,134729545,326063542,98737307,503711760,317909186,92562513,492142714,440328761,121336359,875664130,752044177,233368826,599577152,547518029,366548414,211799216,695313111,468731223,746676276,818270440,22966306,181159918,501563322,16785651,540671291,998329384,591645045,648112277,377757632,870781505,476810006,944304770,824321265,991818734,510420554,419617976,110073188,809149885,287305495,528334849,990327731,892128992,200298029,713322378,730452539,368661878,235248133,532486030,275566284,318528048,962702828,67880577,638082437,994359169,887111770,2375812,674989781,417187831,400471021,188311866,415784546,426732066,227493240,505111475,119883227,341864976,647935923,58243113,647610804,94216850,709915665,623365922,752929354,11547919,516456575,394333491,73965809,915910069,437169203,432060007,306279300,490891380,963816431,200588566,195642186,524819763,507085088,628246217,955621618,9075503,335044540,486491430,124243327,687711326,731093356,500127929,293956064,584538346,343664343,239842611,252703455,622632227,121739871,700303465,467632873,252054397,492967272,560624182,446904661,858785949,986879737,35618254,276417285,451412381,203592659,556260464,347190879,997154247,537887313,657238553,632985854,970581656,998850089,964108056,381814933,623616512,220690801,422076433,417549849,414085555,709717039,159706249,725137001,937893865,867537992,85014582,310341520,962611623,779986202,928699051,707402963,738978564,712009092,900831304,692037737,87112229,190587391,514131262,134978416,935553090,916150405,704790000,693234444,366086926,54962731,985866658,868135710,59337706,759493152,816933414,714205950,505496202,746487513,515841239,617590332,536440555,849208278,740965759,47389218,261366808,206058146,897199357,612811828,507173957,867703668,772041014,214861266,894835741,145103204,319008409,417287789,384735960,785199256,434575750,194923559,304903466,350879058,598960071,615364651,686298072,562975890,324984042,695333545,470400735,753992592,797564250,545661434,867920972,173834917,952354479,558800163,90372852,437169847,40646275,435935560,268140852,288855523,603106481,817923760,950020114,349625329,764826548,650163521,841223549,336092570,998417630,103576763,131344082,472788602,623084400,408403081,300870435,43936011,324530131,681618644,576610897,617077628,978990569,497510767,277001805,70711010,183708416,705718039,370676120,571702362,836713649,436191567,516992175,229714668,310789875,404801140,413992866,644947216,844317487,326987043,761500918,525658682,399445102,51743951,46830704,276288736,600013618,472351576,824568081,523986992,339964079,19181294,958860898,916082564,714074917,487310742,103161461,670035325,40385094,561416976,337060663,742815381,749079870,130360049,738728119,903149639,417768978,857564171,554792674,500117437,968550686,639740385,378538507,248440472,853405386,932129739,255822385,196471744,823832602,796006818,26045985,336855144,962588290,254690682,735319667,70167326,447328487,183790161,356925251,560023520,856256783,942130878,94720335,308962986,908840001,714386427,762941534,420700116,66659330,108811001,524700955,49353861,203705837,380766224,164363331,264283620,408167519,91159591,197813849,963887965,668805256,768176818,853927196,118185242,222108598,758147328,757304919,284139251,269381484,614479479,779062370,548171603,617081257,243179484,677192901,31159304,64938905,227072273,752302527,245340618,295654307,79439116,78009285,906956005,329069291,926054037,142772071,96265890,657339425,588544168,503019899,732340769,324386166,691680368,425937407,419014400,838602272,4548441,415626494,606558253,862142404,121722976,837194583,865593014,400285675,745013491,257993573,342466750,977730844,422203177,348635399,217818222,495646444,558738279,187206252,603172886,695005698,460578128,176455402,102244878,911677880,986797988,469407613,397170634,389907868,517097050,816197789,525084086,770961991,282934879,583891519,592431727,251000285,201679044,872240373,770242431,631050987,364644950,240887024,187679009,985729801,494574819,636719802,444131588,716940251,153156215,678759125,715537362,121954306,481964946,765618982,352547304,609655109,112859232,354127926,532893192,265730621,944948407,538167717,859967676,197441338,87731849,841475397,871176598,58560660,443686301,748825287,646160631,72961434,189584772,883212095,921816224,31123176,851938508,826723483,666751122,894928735,122930365,859289744,755342193,47684586,169941353,51076615,887963814,962756890,763819021,881734387,508739237,169480921,152727449,931666299,573162451,905265722,84542526,450687677,258301510,966450693,972791005,600167156,902843188,740377346,660946755,350987216,808798430,119996353,787858122,744285201,586559034,955862867,675039467,55690746,640790840,166414949,770033058,495728706,426604113,922671897,296649427,634013022,93955667,988136392,275565561,166267694,289752167,462047406,53562317,428026924,973649371,406197266,275251867,573889112,460137282,907708176,822317738,564119184,474123164,561584072,759853400,846918144,302892449,927067123,709926048,290239122,521111480,256035953,162697181,624143042,41595390,177954977,614522510,979740622,521851640,491770026,324167227,148028392,5583635,453583083,162993829,275319451,644256168,837559820,800430643,430508677,408666522,510888506,500833243,200279595,967324924,176306438,68113874,887695125,733554297,962889148,562005675,484511667,820644211,481477430,468254890,111716295,121030784,875664346,965326339,794477792,690305032,515621949,493324069,95208468,241506746,508717836,940038175,47104017,907921177,650990622,740574954,410240791,380850863,316462611,315282572,527442454,746709585,539160210,631369306,735173393,554953978,398638745,568868919,214329561,981943710,126049111,598417737,462221091,702906710,26076500,926726002,789656815,556585131,999704235,802531853,764791604,170986288,101804301,929341294,129101895,30969151,12443287,887270619,58188986,222143379,931194708,539535060,107025262,898204370,949474716,132397727,977766187,806817578,353238464,84442386,520400535,256934070,754712064,569439079,630003191,470855094,476758942,27916196,625507370,751241224,922987918,374311130,696459998,675541930,707905940,291121991,440798096,211055269,661564598,771540056,446585898,678701563,534162433,108945610,424421467,440800572,977539809,233979459,681515310,100517675,714652681,999179918,935731527,611012967,604822129,683674146,246750857,255817383,422915641,19564946,553684471,512617429,328240719,902729807,888971030,994999213,578171775,125377866,221524129,331616594,958767787,390154422,522639683,533342813,666347646,871275975,102209874,453716690,829999822,193581807,578349946,765836554,187598238,401459355,74164577,485967515,768595529,213160475,95251897,639563875,395122789,492126338,824399441,407954641,999671046,678654860,352443384,863556389,184897466,100452979,310614615,880162439,700918193,663527822,785618010,285150264,731560723,607392402,188382097,914179389,763729604,336689740,964089945,296627743,533331252,836833262,103512180,857839332,177880634,636901295,732938476,557751220,501905852,675762966,511257047,776747639,788413615,687735920,692688874,548622399,168957530,715870117,451149218,361796251,385939811,783938785,197891916,868366543,201918113,85951431,632381736,651707220,476862597,249253989,834427923,190135135,667570180,420423527,730794511,926633760,813372117,255409138,838002919,197022550,388827950,714760229,252267397,227124523,226624450,211969974,268202379,748355963,765893991,123175009,935481032,31978456,658463629,396844995,421144539,141184271,888544695,617083743,692217355,340062793,312797453,680698908,625408116,340312776,289791705,976346182,939057714,296675526,474380744,597815095,160412321,399904314,254785272,723027352,188646565,607947991,646182289,423985645,794510024,267062364,325997419,409797141,397002052,396180109,545072658,472087119,829882175,315025807,564113436,445625538,424478235,651004640,720800937,395394702,646763304,811911435,50809052,556404030,243192690,11620409,946227637,635501384,510645934,50839933,888597297,833946467,639518696,274562136,578640716,469453803,286850361,109878755,974849594,271579268,464368070,751559708,535492957,448130544,640845578,780614082,259366157,984926194,965113524,594939055,190111418,380846865,561180638,127253370,28809083,508386772,965528521,793572594,982343705,234586254,391580178,360862308,632033680,128511546,127058770,408845990,185955673,983041436,658488528,911318699,374799587,792337251,475374198,830165063,75989824,465540863,276036238,131375382,904683963,145252245,698987879,324652406,640592368,597847502,232685369,301545545,266977803,297881045,945076060,361219138,842379697,87762712,593612894,998924960,416192447,416694192,764246966,981060826,938475423,608537401,423220581,562151541,577300638,667771511,872079614,445494593,398672511,655455692,651197081,341859496,780085403,25523222,982673929,89724096,828595258,179230,424996268,300348860,23562084,912189509,458720764,256355697,263412543,374842064,435189571,755015089,674069034,513452202,651630380,434105819,813195900,310088988,253205197,586379910,252848493,558811678,719157937,179844314,285767832,18286746,64706413,840953519,631969863,498738377,443828558,453015185,181355654,829487866,973833975,222346834,445904855,510587121,884802826,721694189,150318455,208844207,856274402,725584329,938648036,784567593,924550454,614183864,999062360,420922636,542995427,561414330,601930621,913776122,677355014,401453611,263435083,332042365,612069872,351081528,21349648,263662726,805794636,281856750,764146854,722264882,642662173,432235351,784467344,213094924,379122106,655887687,65717081,783832561,488687616,482997035,5469134,281562030,438377607,140912096,814469345,643791772,359247724,9476776,727260954,146144984,642151233,518782701,404950757,648074736,496935216,199937959,587872412,831438576,875600165,183589074,861715657,982636280,487454661,724727865,265193826,838941081,594875244,791845433,405760468,706886447,629195226,173975502,802333042,976652313,669747119,800744812,342338880,925457595,994019972,981105278,300208011,680675799,507903171,395464252,135240635,53024358,673345180,791606506,216607271,127205892,378836279,181805084,202369280,450123793,264956724,670959515,407675527,33300542,12668485,148540332,561051497,571761489,831428037,525659617,340221365,632410160,876043860,332304249,978635928,916392790,445257192,510875302,183055050,477856389,831175537,854694090,355611030,891645938,131647548,914188212,821547193,998989536,717094954,679431462,99088400,205220365,419958413,408806108,523456053,293849047,469226433,511569131,713908250,797888149,878274462,324940766,247693485,410154903,251491948,486765177,613012304,484198630,689998130,960082772,620725852,343245702,639682242,186281735,304936227,360304120,302458626,867273475,331178136,250098125,740324139,4939755,977581288,264205740,193033693,265310532,43630811,745677981,408213192,753820996,802265902,531981623,346950126,923804529,298364306,781334198,572589142,911655526,415165580,60297138,315120586,595442389,818972541,618195293,933080167,726707966,218225274,201094574,506368789,456828347,129172954,473298594,728881823,971449506,663518339,306086164,119711155,393166315,177317041,713004865,364113574,319340103,968569954,17290163,293606944,747110860,79146107,92321082,621972114,502403314,986581685,876087966,918462475,390728156,860174746,794005520,671612178,279760908,642935434,345619421,127403584,569167628,387409973,757377264,957249540,506183664,226354371,648459047,457849688,951250113,914739062,554791635,260201834,151563121,445483832,744741311,714818414,838748865,329489587,970508218,35639280,435353994,356710532,116523322,539357561,774240167,572112682,908436849,726017595,945784341,106136521,901381871,701437594,189278624,643891675,461252091,568129130,33502251,495800671,179972348,117027742,771380839,974682850,935627678,172744571,255834911,942291452,953476620,696026105,678688420,335397073,792846541,198099577,139664394,650553312,466190670,303812095,456021966,601320282,335849452,664127897,338979374,886123535,299441614,767767972,146990938,941248475,80710189,660314964,391546387,269571726,690658331,580220437,45289530,616168019,621011306,382108151,439511285,138049081,637965495,653577514,618308188,567016525,413902421,618364688,843137435,484415453,649870160,898967133,276172838,424461564,549089627,653752471,312641122,546496789,137936629,326203849,685778703,813475737,738972429,77749829,741192178,777680610,227652503,922516008,462708048,995808748,114157246,104601969,144740044,915604662,113082117,670374380,906996126,195045747,281997281,115499872,428266698,487196871,125909112,613591421,581485616,376376957,975334453,755558138,463999418,276819436,466981695,823792990,187583009,48957561,739180841,829090157,835580325,47090591,600150204,605425054,964469422,343844588,548333978,346943655,9169625,691183165,358371169,15614871,611267016,90276141,474695265,664251485,805303578,927295394,90731155,823727737,246333519,95461167,7901939,969203736,819008928,441277438,754934808,929626884,103384568,947646055,670099648,936095661,693989287,142788154,277792242,677934616,773081993,602386478,635636858,223069262,177022288,197926907,940502963,416634460,417001422,856865378,744963736,679491984,351601684,372559648,509691937,808044851,485794034,481792363,248014546,824114745,317437853,645053533,840351327,343975862,871365510,745039712,510606133,99378558,924065381,270850942,213810123,901868355,835482461,793458369,610732390,402087635,28859912,963115861,284491896,548494162,122509469,592304037,521710172,247970046,225668221,723764388,811784285,904694366,640548835,898904656,352629092,1435378,256337984,992152820,831192358,57926417,752803945,775776005,300119162,675375221,424147944,97866713,552708732,472130752,896499863,106782352,20678129,129100167,886905436,765691142,526420293,676450636,886147911,590852498,501119425,676515399,319334089,905098494,168378632,112018424,60100511,426015876,909705010,881039854,277915403,736783084,409724388,673946655,199054140,519410487,313851081,798551598,643458422,52906798,371952580,392905864,80430916,785592504,612801591,72394872,568308841,915524684,451620470,420196498,513282194,646823802,888005761,33867443,625598189,890950798,454676096,974898635,19142233,397323401,152896826,675322837,706445353,692476856,480200332,540148961,175137213,936706638,956471358,945518005,193193311,1163309,296931302,743461346,56192038,585057407,833145523,182758296,932664901,207534921,747376554,55824069,192870449,454248206,296046877,581979372,971119665,233493348,276632467,105574034,597342698,344686646,212333488,714473258,854268476,700183822,754882138,477408862,644060710,172303451,475038167,126396657,759600065,278930024,697774778,463755978,316969802,429064291,138623625,745277534,820417971,278601584,705832242,45283443,93120131,640661169,424660537,200945155,260876629,283023397,750498549,769464892,614083094,297536532,676111471,399229726,892958078,833204632,368675610,505364354,876542900,820320985,678204081,57390787,47164094,538332264,250223476,221043145,673264473,736533257,486697621,463621096,521274183,327295566,14463142,620250960,624669038,675876649,508465105,359458974,296732686,482635432,50740170,123257490,271473410,123437502,148871379,796803227,710221384,141003931,207957751,708947244,872939994,697658661,765725963,715535439,960137518,473897677,919338138,945231685,115036402,631081544,520134943,498515890,484902618,743410156,811500573,560708672,52563688,852916642,226196531,857518625,507147012,562989323,215371398,473709422,507727674,13097069,621360113,437927949,544804658,345585701,77214779,344566663,277309280,361510432,55730912,358743039,234859702,469000376,338106258,634905959,59678469,604910656,57590631,142644859,692411711,912499395,73269302,855066019,873642439,292642803,511325188,966388542,250365574,114441066,681176470,706905885,477648765,838050047,670512682,854415312,130074843,432331209,367942885,568808932,293342999,971245119,833187175,864672751,257567503,774773734,955630478,31824740,14412015,932777118,26632571,579376521,819157019,720034030,638114115,355509286,135182724,100095793,861938383,259354322,442908006,6602129,536720479,223261480,269746054,295117151,565854545,978120350,268390031,731776356,32809022,998114831,870472787,914195415,80477996,676336625,630269983,124757928,109010164,669062697,399810867,835104986,705849050,180600663,540732083,571598995,457592201,392730191,134002245,397161519,943697010,857260275,781455085,357719036,301026638,717566422,216741863,205216973,682027520,586809311,487608479,788357643,376970725,525075908,771921825,717167984,303427532,499237611,583267408,885790716,396083340,129792852,48358861,34817675,180923536,979045682,212413537,826687848,204450399,630886924,973029108,925241467,622911137,864049320,221557941,94745444,955388714,399985013,636565998,587229568,842221740,576918817,903189137,719066153,603466814,798324473,166919509,199351109,829248847,636905586,623964531,586266892,789501320,497405325,744661671,558415759,3488967,262773049,447512691,455833695,708713679,541950832,101419322,17652763,245698625,923995349,350618781,974876565,207343904,80756002,834389327,817039695,327202651,940062049,546044596,114927799,677709847,550815240,145207362,590155392,995762204,505330825,872950925,571813034,468377985,970678830,461676929,739294265,386357426,473060034,540503370,293049154,275417893,113425857,209787028,171823513,812929582,143300341,221967321,588645542,566546650,176696237,983967314,177218330,91113299,971534614,47063101,562989307,803615084,551103249,423878539,541892843,424646724,51643638,364584507,6722247,53851409,71658239,74568414,598252178,127555418,152721854,982841764,320148280,998261793,539883974,366037224,577693270,726969,644290642,245222831,271059140,906787993,308106249,750480709,249828562,116429036,636751892,248374810,431105799,558216871,683241772,770164320,509458096,725916456,24490726,885515459,160126466,240354476,74478402,354244182,150030735,11651472,49409342,369869542,75267343,488059950,254701003,680777905,609869599,771096057,632957278,596899903,539779302,892756768,711056778,761229119,710098009,560089277,483319601,355861001,202499738,163163884,294338036,295933214,503541091,863873231,962478527,347017522,47715655,542783246,424610942,952191277,71244709,797939761,949742138,978578903,696546716,262011820,638875303,981143948,445708214,262826852,460228476,847739952,983826323,868361329,180132553,245458953,651716229,8325348,510620231,242415690,238030537,25714359,734379798,879750916,421786554,694757263,601714974,89854172,473892079,404511894,51366813,283599365,793135982,181419620,493458238,962348456,598819536,401209655,783824630,895986090,549474241,47773942,197253283,979957950,631766878,155221592,76349391,14725076,698965608,421910031,303136023,767258377,72235801,84408027,958529898,939389641,996276665,210360063,774412457,726584121,276914657,678388660,359162943,762683898,495863413,610369455,527894692,28300095,167281895,480036656,869971722,81473028,818448948,138287724,358279641,396190999,110008272,335340462,948412249,262893506,539318381,431842621,595916136,32233046,935898337,56986178,278686725,781529328,383096698,185899655,889405601,111534803,70409372,501699894,698368821,256443700,933740676,803845217,869432803,55954468,196680387,937308569,604716853,360311332,492832249,446540144,948738757,771202690,635075906,139312441,96113462,503135437,990953332,333538948,960975423,189208544,405599375,945835087,673669802,941767439,762923809,62543117,818052564,486699500,816372505,452251231,413436184,378338452,667215068,93873032,55140497,237324110,319619519,96794472,448264826,210208046,401457884,845768031,404686406,731533189,73719673,955302361,235680684,589262915,259084931,896523673,34847243,625700754,100268149,404920665,851412246,219673161,369554252,982291833,258200876,871538322,475739922,611788881,101046233,560035625,430949101,172544433,502233554,775833923,586410787,43560506,215974945,365336962,142008515,39115969,724033190,98316445,717169720,772330886,661581693,138529017,405908560,888557139,351873161,147891809,54319263,401820612,958532709,453934752,540424133,809449715,145887681,34992633,113290234,300481808,76401570,508626362,874092383,184772069,134112657,767821613,568309475,390315158,510782781,126661980,937248048,528278028,448893215,339844438,763402028,35226236,438182368,931260617,228394842,972769645,948250379,929139025,323725732,763226224,165946988,288517389,123889293,402399600,625941534,155846410,984940257,418677713,458400659,395210586,15040637,883513729,821518750,410624051,20229131,764269768,499623145,135245755,650704728,383665011,394562620,779143952,328596582,750365584,383498448,684294259,601558355,975366895,968165771,178339957,835807431,525250991,664735746,930701341,398815754,70227449,615499331,564925643,617198684,611105609,93670360,909164940,177659521,911300587,906589678,318098261,718334442,446339265,797900740,729613167,371578797,913964286,146080043,964030723,838506992,306186198,902453763,272908946,41901313,990580901,825595533,982534547,672118391,461247156,270352912,393379455,917197360,869575569,43642119,282939083,258528942,989720950,85586112,441886343,274909749,194812330,88705025,254226320,79665498,511392272,14487941,586717515,421032637,818172731,819007877,687274506,258384,983349291,225310132,694523961,343275997,803860863,496353615,914977435,242701446,908913461,589714889,221052837,758352420,412493142,104379182,791812699,126175137,953854997,747478573,144091268,459235909,998277644,187802881,686886432,455146171,992663978,827200734,791355187,657409499,589771084,27094472,635369893,669708891,314231236,941487929,97724810,182694124,308432926,371182601,874918693,155027409,824241867,193525820,964460008,750729485,807611244,599639167,208730093,893285617,934578503,466366441,934617412,797281963,814536883,163822025,76508497,571019972,83384299,521671911,911749615,181537156,67693004,423376840,382248940,658379915,530868443,863626356,962089362,185032746,333990315,481687387,857696070,928391471,113306986,213796102,396863758,34222926,953470837,529203,128047449,909148186,318688067,26647225,763105482,538010487,208428315,436836523,642948408,36693428,761747870,738803895,828607812,90112718,933357183,78947250,309878951,373012226,724170798,497634350,373240676,583310500,21697387,681094530,173820265,196212951,236973552,381230831,928506683,42992916,553834945,225857169,778074674,868818132,446565802,104923560,310970338,925363065,590562302,449320007,69034493,200318461,791362109,603464030,270619147,204395066,752287701,307402578,826543885,182235247,465034195,25721235,143233621,821802698,608298348,590066709,407623197,609650237,702837553,100792351,438603833,946204268,222905753,27701944,442977235,534957638,784943840,324261389,430287525,231365734,331492235,738360435,936225627,507445710,869135177,406449199,15400013,216189888,482319032,255631895,806865320,446986979,284609102,96019313,217085918,836429214,808975288,507627433,500775113,633468017,30845907,692914458,641514049,317452766,624208579,705113678,438425741,751377085,517711396,332333640,450381216,260422515,428984949,184003369,28283151,75673125,370284747,714904793,848079649,363106438,108626724,43470251,901790342,612529740,840822153,176188787,803203456,323395926,934315138,662795628,784724883,641850797,939074507,427087558,978054522,351753666,955935566,256452400,746347240,443055399,173828081,7087909,7920500,887667013,602588467,214502673,437918130,202812861,298109057,382719155,643740021,306421129,803915713,336755079,105655702,840393570,10477968,775665467,559336580,716319407,979323718,13381902,692287255,597387703,487367927,973207990,758325373,59879861,21044813,606803418,358201826,11115348,927339270,39078212,459728383,2082128,325784420,275074055,399022763,834967540,446483685,110290865,138472593,536566504,840354764,245261112,641286076,875515156,875639490,565278488,382748888,454951812,520980250,263599718,454891863,922676235,502790109,818935928,431183008,943451546,337527622,215420556,20735066,459998387,986013778,720444811,427123609,564056625,665522751,116023241,435007782,537760111,125691434,409119863,682754764,645016471,995869357,913877943,838440079,122787469,242453786,194277128,492315911,600986708,393340410,693402103,92471400,32629135,815626369,110296039,717470791,143746335,976363483,360106190,751330555,367498040,737677454,455113430,347365780,15278413,767507340,376536815,930491447,146144092,404871514,485326182,377796009,216215053,61650478,329232353,217523907,491476828,934964949,467727584,565717075,409441920,367253757,274332255,476903142,716368643,55935898,799368041,521229131,63204210,199478044,185508367,699939079,167471142,202427286,281125372,155635886,272633528,855021487,469440640,796067900,77838902,97043058,946140763,379044646,309374258,847435658,531117040,653707356,161968009,725994716,302913220,534843845,216855151,659821100,469555134,633376633,668802898,589509092,662691104,180139313,863475707,374053859,13047787,431273370,274608667,5520333,585239104,4843797,542830641,625077650,512532665,223050872,633402268,841872146,446187115,193741130,203157393,775595970,829808319,173253109,71489076,888905163,520245066,357878788,871795129,408513669,46976562,552334403,704207574,426906149,287432662,266492223,421330342,920935608,988961688,461081901,663600436,618773101,901817151,110389844,219743886,258443732,586811175,764496441,634241473,258138605,984491762,396414316,614704188,574050202,205998042,229730822,119455358,107817801,454010408,132468293,459702336,968300245,487673133,561875252,443796956,997720253,899397283,570438623,684777793,652371303,826171427,775862151,110611142,894434674,347133446,60240228,444112868,274541201,218518162,647619798,95697769,754851143,81395214,2864053,627142328,813887216,813346439,30616036,619195366,654299179,517911411,331182679,129110551,881219551,849468079,160356073,211238540,913386979,762301246,828259738,140871453,162314318,223942670,694405900,290140691,389030343,742120327,682719147,535422792,349044405,878438113,114199172,547318399,687896206,658145568,545694666,800914919,214659532,762416089,325110792,305749618,943771328,916380313,612158300,520101890,894783724,442854472,354237016,878462389,486507588,58824137,207047035,149368364,925804805,602227501,193882598,914399470,911296137,928988071,745373355,512311108,138210856,150737795,301736060,910974287,958012419,959981664,77720822,705793489,380929330,457870948,38700464,74118967,732744150,713723744,979140426,110490924,157948159,632721556,621648001,391263692,906993080,829748828,902737966,857077783,105637771,942432664,791486782,319396526,34764173,338557467,117301271,689668896,467772348,729378569,673246822,141394385,83781876,140380506,948028403,756309953,751464926,587607594,965292117,306318911,737594652,586310810,412786205,624871330,435524939,567204985,112847175,68970779,231564261,707233500,894197357,239887600,71314588,19928626,918057031,915985731,564309430,901430097,75712731,617876770,109267499,510989663,71792854,153892235,77827342,849199043,694529206,289792750,556712050,341166267,859795557,435001444,872212061,72043006,603664272,620757800,652642414,758398847,823997805,364254282,223277298,513849909,999787748,774065645,867302151,944051081,609719063,981316962,239104588,661518012,801152019,834614427,531910099,595339443,602109129,555922477,731241874,854627410,264815294,583362291,69913690,164859855,125073979,622265042,394125487,601204602,600892499,980979849,638794284,432543683,855900831,588489443,234279274,192786087,805449578,151163315,494613195,384781606,936051467,282447142,365502739,415021196,458615999,420205546,601146182,933052044,794261630,779434416,214035089,935889058,26841046,436758160,346602242,275051312,742635528,885704164,153880336,500888079,273127483,402346183,987133486,408549271,461222952,541635439,802528010,774153432,339345214,371716879,945183405,480033157,28343280,442016285,214041360,289950931,794826176,378486426,919179202,884559663,639104864,198490737,272256594,479891801,798587279,151287116,990082951,547412218,24360495,632539656,920489754,103388337,940477347,407956992,769449639,20635089,949867628,745183218,670893520,995142227,467259816,262657630,289836327,596758230,422188405,347734530,193245431,285346348,251599749,949989896,246765254,788244783,982933706,159426039,131362176,39334583,580093956,777156655,790870288,921058623,29544043,443727793,936949414,804083308,119143635,617912180,930264833,847759535,774389303,114148829,524751539,316271522,216505619,31174550,754506224,401901163,590287874,95488496,225267044,243681546,329352689,735330442,177505496,630971469,340271357,979289665,385689129,203095799,16894592,950525849,476388997,244065578,570118969,229870282,393101588,898229836,461565944,315646874,41549663,218819186,768082473,202119491,651218428,413838980,674198382,952684218,767585905,228124338,22600911,304058639,886470692,286309846,903974709,739102959,582630760,157398895,734119576,793764774,807314969,138654911,91458693,483332966,406337684,282794950,510913606,293764333,302455827,801483287,225304926,336700538,757165333,236674049,201606482,982091939,665458125,59460514,637275010,695999274,875445789,236487132,820790202,80984631,712246307,552603926,933146544,658682785,402192180,602666273,777670877,219205496,405437981,14026194,891918902,32560989,138191648,27556481,665040965,609378772,555696878,733542416,580829364,660462121,643311061,68170900,933452197,362619244,392479076,323551728,118044644,551999041,421585666,403641427,287290003,214258394,853070933,541440112,489005693,359592822,144431711,38168014,260533552,993778331,12185337,120535327,290018150,394758830,742595732,754481437,248121613,60549203,925454796,206507391,126714077,638712852,370518616,169683502,630889966,835072292,17273844,919758046,203495156,948967887,614415088,541120256,153849346,752291323,364177119,443295506,116644066,40518510,774337606,32169621,322077331,981115237,783843860,253927957,349061947,158719993,817070716,762471008,535846829,687064923,369481023,347921368,630959334,916470433,401991503,711455036,221897506,378316325,870449312,594287533,76299068,216163615,540557726,990053537,453769219,669891395,936421243,73980395,395736639,348136065,198189325,960168325,707144028,667688687,257335317,968437089,662421619,726373834,948815597,667464064,670995203,766668431,441557093,452112254,92070992,52916157,948063777,876888579,543438781,708614616,483149790,540502547,25135330,138960996,113882440,620657971,903980919,279109697,523589472,626311098,706012041,715301195,649849329,980351481,907367234,799677726,713879109,845817359,497792915,404726392,47905447,204070550,476511840,23472416,243197144,77173565,609692676,722208563,182216506,125433223,851312261,886399829,463024894,571848856,903913693,33321904,790539331,594816529,598112941,733755988,247139078,563202357,628576705,87855947,214070295,413693492,131687093,655919103,256972455,627516145,479249249,512758670,884000103,711728036,501741401,225004765,849100707,706381023,957858480,204974683,872434795,581792736,66031618,691175528,197889384,267482574,408279893,113459732,108579578,236343137,879787568,289018021,458939226,764965575,297087577,717259026,11780982,334145951,153276166,879309784,200909815,596531442,989760226,30704615,236367271,605244339,616606421,740175442,499660157,74219197,538020575,563039966,262508994,758871247,752931863,183647577,53251635,92013299,594769669,881613276,886962312,974953037,296367034,620107259,407899865,95980146,955748583,80085303,901037319,763385770,179300317,671171926,75621601,188055472,164202289,584369284,463431681,265486168,387385282,795360723,61838486,404018926,280572493,493290026,945120092,725231128,392004080,44716305,315463823,742223683,479358905,906870385,458352519,325295770,689484027,126080267,482968834,812103154,134862764,359572656,813346988,308558104,80599723,529758005,879442636,323498444,675039381,166166038,263059930,759880991,5907414,22407368,838832858,236028114,913766601,87035818,320046693,960534423,435589947,271867476,723889337,709188432,657802893,842842213,110552305,967458419,830681054,889505189,340515072,263088901,89183353,874670403,612995931,414866649,181870706,784075351,862366347,192034494,676066053,551719309,588796929,254593231,948103130,763739450,825688558,444409215,35254728,949004436,372231261,902276389,477659264,359840779,851570178,477814525,374569412,304740686,343161521,231283054,25748997,382482576,792177033,248041597,291248611,17388281,303123258,869680249,141219697,388963861,660559464,397817300,602614548,913841748,484689804,958400612,66950669,652906757,785477242,707305801,898373745,215387915,908543650,226465395,199620421,950703011,723256466,499088776,530565202,234951164,717094350,695213350,755828181,673561644,489002302,924904384,996067753,537173411,346038559,62018992,569919737,840084791,858859476,463178363,100519279,132137945,589552220,838526768,174806502,501575335,481575529,201869880,920031438,501285865,917893902,407011204,180864763,24905589,32523829,26124555,947360029,240087460,195497627,514374172,942542578,397349328,884485077,521173268,237811176,12780071,417676551,168908470,186825065,232344204,110387262,115046379,511474778,700448860,387594616,92314653,245821218,629077818,759702845,410693218,877757333,342054196,219916427,994997370,265174751,150233540,179058384,49230653,782061818,281492027,612894468,4187740,682116961,249864609,889513624,421178396,160966037,84641006,829485531,99361076,449851301,146112602,870779009,618625675,194869893,962003272,944635648,747139325,561966871,182199971,172991929,974430334,528799969,515421850,530738779,627431080,741451234,968168126,286484614,902460372,322420067,556226845,693552698,927544606,581988192,523961909,840344625,180877576,301018367,919613660,88180580,853558747,170830241,71665,535380579,901769775,838739057,309311966,963704878,576337065,124597705,994635829,217108383,866587841,956578353,488106620,239318583,766218089,876273901,388115741,573422062,28930428,175197153,527991510,518007956,974229708,686941259,687453237,433903339,945605805,745900786,644291118,689156950,958153732,605798670,991326266,380377961,108125534,475883773,575923084,604805463,285419462,853293032,53464437,136180181,269287836,438378027,552429398,719329848,958329006,236208943,359756714,411796263,553591917,958097794,420360027,720690233,668406522,457744313,493855212,315163443,432016325,725274510,998124134,519555893,579277685,456828409,27563931,977924975,15718031,941719212,727498157,284895699,125098537,80457097,676515474,724999538,419378424,729607110,341977102,944912916,209519465,189154832,796479367,145513127,969657955,49626067,693309619,20594937,522113497,269022927,252108766,920368714,573549660,957880433,627330266,434153026,238028319,65866185,127306350,52065208,979212461,729885468,334255991,431425905,6583348,483363893,655505557,450967723,822317543,736005438,481220801,147358483,26940101,27533903,236681651,784794374,912460805,807516418,171588866,450046304,721034650,139672529,22795512,861791110,751305696,254723879,987287357,12423209,73989313,215442158,973825091,372328812,271745704,323859405,738909131,542356826,488887070,324230937,221202012,922650534,264661170,9328885,349018039,46189553,935443365,223411389,724116302,763157660,280362746,253743354,616570042,766031249,204260314,815245052,349132879,218405709,162364633,203135205,298016355,997261239,178210100,99178528,925465677,656461808,771739630,147963932,807000178,864211934,810240143,106120561,344417319,787357577,722237639,904263796,594715116,27853585,152326590,805159546,177093048,97621792,563531342,377300581,22940797,171759866,852181373,433180278,392103128,387125736,594742546,437350235,813683487,693565938,944428092,544724319,613953445,798153156,825295368,217452613,332406689,790395827,654625478,43385803,591793241,117857363,289375837,73866962,482425661,231317289,251277957,301175415,234797631,456922803,636644033,338560231,924740126,594717654,507220711,837245333,398809406,719107901,198947834,786834461,146019189,829155161,461989009,753369542,596937313,847406212,268267368,107296045,409680032,504510244,388655665,479127459,174066526,999550218,764929854,587535459,486284275,917258720,119443780,254637296,442553290,970097300,37879500,410761395,462610933,206889575,361343069,295641763,796872932,937450745,198583321,147041243,731739988,407078484,96059101,745932599,604490174,129298480,166099351,297370752,494204260,237423519,32935509,567272439,613782281,147959005,17196753,52491276,840262506,197275558,518416555,727695320,634549014,233615147,358477481,654973661,330768039,365159494,391358052,206345643,335180015,932827249,194573294,551179094,257213379,875993964,582772980,382148585,734584299,343454691,38380965,745068110,141954491,416683161,380621797,531623862,230935205,212604370,306485798,826403190,4743319,75766310,198438002,397732018,599963118,406839623,481026601,368224139,226517806,595626588,885912799,886755060,671171721,341033832,410302665,124855006,672145160,619778111,630908390,902771535,732520044,680281235,495981151,117317075,858567180,618609914,792057356,877368703,144310852,838400241,201665123,41148850,827561342,637773823,830927222,256639282,597600079,123714698,112825272,422806959,810074024,1397538,176372972,317344137,333203217,938255465,616796396,636275463,740452878,276105661,247179642,600980607,975383506,531365295,24826746,579163321,140136416,218326490,911412906,640738024,771723501,170195762,880445726,727857441,217377924,421018370,398557429,536639143,876241066,130258977,362624403,400557250,464253577,266324883,947771610,766540452,613986463,739729010,583774815,90488521,545607592,524905336,421690895,24244931,401210881,753738419,421824527,233356691,981414994,415167486,183960103,984302232,584282428,543076370,250311332,889476151,711373272,908525662,616223147,13041242,531518432,52275570,650091984,465827861,834155187,756989554,972301558,750055484,529671212,129862051,305747452,184164696,911756335,816371608,308086573,158829149,436671635,802048007,348280530,277704744,263295363,777739153,124528297,503545556,470989802,861790369,845267753,768724832,403862285,861716517,934284477,175905984,949478782,181360623,513529748,873085511,372589620,896361989,215487853,865731473,691779962,54818841,426061491,373085965,573802427,877479966,897274980,357995810,529770100,474658113,234037730,470549715,845572793,102355501,594711964,453902070,630800149,58407747,703638202,84054784,388439278,876639112,58668171,469504178,799407814,699694434,369069910,476336164,819427390,457917421,150120618,307390081,602528114,558012013,697150566,62925838,437292017,243762835,332345676,766495243,617045475,729275077,59217357,931436824,826034826,834451514,879655645,665032011,839602605,433718638,560498590,39305538,866852593,113974441,643678403,920864386,101989183,34957870,777494829,100464626,338037743,17951309,118865088,606823443,897418804,878490639,316484108,448465259,968336556,362310099,502705194,921919210,648468497,427314047,702059966,398788522,218602329,882759283,105427632,363428108,494519018,410714919,822571435,604825191,232377025,364383011,701859104,388510802,698543812,540652719,721032382,39422050,767542299,960748893,188644185,836536872,225701551,297865205,106277950,217499807,746545658,972789330,233374606,819864554,625717721,410641249,166919328,681288554,389253416,213333444,655770385,386553515,287353608,457248405,112484894,208167145,382063625,68330887,806700309,193683668,715402631,982112104,325496795,782352630,746982315,475758525,210800029,421532524,671064794,720044578,12533295,652977634,880272283,739124638,553056955,980158865,375573762,803743281,717053628,460637787,446130922,364863237,957652462,869270960,85895324,453437429,725128853,214856868,773300882,591070891,832383299,501531633,594825226,887744627,389028865,491959295,899728397,539087236,273354482,654414373,570989389,478399726,701763582,773185273,713375340,412721239,821284496,235611649,123572304,373382152,225921095,241971631,336030700,935379301,393701513,173667218,497161106,508673763,26605656,203430462,335115595,278889960,447976812,81169323,204565322,589063696,410919506,775989873,421640532,299592802,209385338,525633422,645847456,39090612,888556789,5367718,261083853,675027545,523906645,405983159,504165552,967669549,845395284,486794211,8129122,793989718,433371556,386361013,923127161,908138148,623099897,703891363,880197009,283843244,408281883,96043342,6796341,194216093,347713566,733625454,613793876,111799075,582926522,463853944,71185954,822000140,37664744,936106827,357145241,881156144,55028466,709111765,311071826,130165372,230381544,78052916,993071402,547297987,297459804,208474025,778495114,163147593,779584048,682564581,864313899,808184012,104636653,315989889,438763085,719351756,848666317,9349035,581634334,732932318,243763516,633713403,429966611,419623894,200451266,927688829,493729264,198844227,683184059,240489700,823235333,435497753,841415985,987237455,119132545,869870589,609385374,365380146,940839241,214641794,362703749,11796612,156324338,383243693,876240600,564212500,121572814,783164297,360762090,115195777,779676316,742633035,655290699,763847837,183073057,309109928,166084377,707710903,347915553,104065401,264973019,20473280,256017894,209150851,242793521,260451868,467580743,392135206,369560405,146451358,716468815,774496310,223920180,914309099,654768893,728890752,875946044,910697646,343269333,305256817,75200765,97576496,322757778,783207194,501667272,58964444,231752776,910989225,246616758,182549455,614747139,234648741,740036012,388046571,967202617,205827149,680664692,486357803,819816391,473662266,354058067,902123678,915426615,250213934,362687363,955751220,897228550,887318668,41293158,933635583,386050546,552939874,976146990,538936985,139515832,693894567,572315577,181711504,202553756,614218499,674422194,802989713,716689125,784140901,317630064,790551859,882930310,497595206,569228720,83670492,33244742,198902178,314495443,125058996,936144840,850973626,386436435,659894101,830339950,232429817,370714274,414730306,358635269,234587826,119343413,159580032,667912078,33349188,868124754,132759916,938835832,759059644,495059165,553792630,19615707,333032230,52038751,383529006,506134247,557852895,248958419,422541289,444891253,493247246,228719584,200960696,139364518,357369009,801708712,420476571,661548752,399521516,160362606,23573804,518079687,156726040,647201594,925304907,131487143,190744311,864045334,359977498,343142138,375922324,1206719,12396173,110389979,471709475,21186728,588700022,138338730,816318372,142323509,304576577,949474254,607779358,738260015,735913959,254212145,108195114,335925194,408624828,242764186,665536936,792656920,646077420,745348945,834271611,95815561,765610324,791444505,511854286,314093427,304367854,190463890,891567351,341185088,131177675,1914169,743915341,493701446,14122075,782935504,293904013,833044129,554084395,558020442,382470121,500755674,788053784,337596308,983415951,972248955,480797450,853903774,530067088,992022141,87360777,807407023,599126852,914097601,908101923,875216211,159650899,88325569,421136695,504917166,786040842,47080740,869160327,940824513,860582192,880374605,445972168,862594491,580481128,649705284,18748129,623623414,898048129,128453575,157655163,22191080,887920610,221683752,889122648,707482565,239040425,128779488,177321944,801461230,906919579,536195004,314638237,977965781,961846244,365678655,455941737,445297576,248329925,262233170,986479202,76345040,878495272,788653564,810003947,486375507,944045655,900315448,408908206,909580946,974336237,760811413,253217753,497862965,996708258,359182188,586159868,441181991,685844142,980109788,801677431,823515321,74369025,931267821,284467636,733792150,154202141,614477066,131268365,492815176,551900586,266348098,209189282,566057132,429482794,444925650,120814487,182831407,137969040,936930494,46079178,260189958,655517687,580774825,152607178,649664908,649975417,172174421,686248702,774192052,457265685,126884485,305095145,634944945,806387131,949143147,588706141,489450256,536250444,557405743,182634015,473112733,45305606,715353970,795713901,800585632,525208359,43918940,763286104,189463812,552629001,64526762,23192008,218628838,13041801,677950501,465813491,948148192,982123005,803347875,419532105,834737177,291377401,245197464,253573510,481503646,373534508,310352926,48336312,397206602,560690621,445151761,163834500,661107381,983889832,285117425,752317124,790968440,493331023,21639776,682522627,90196949,940712,679437549,860703187,75747935,727057337,480317426,464831782,235742284,461590979,567826398,984692506,296216724,93236906,331351437,224134165,352144226,343555567,668082644,599629024,176513568,93038341,232923199,922666154,342682877,957388980,782286659,985292800,329371198,333893975,946319305,764072509,510789970,345331891,623107465,213825543,236250590,656127333,341725131,457852588,72424112,128087623,870045281,245473590,511675612,844589511,935855562,214613934,302091361,444697763,26112930,601174055,776666705,259811363,897121899,449515720,861404251,508537205,575321841,268562806,540362608,79493135,851118617,460431730,117286020,235824583,52307123,455343887,662009722,708627862,388017664,208289404,938074345,698670768,431206055,438762696,754684766,687407119,141168733,692207574,52343027,185644794,664657089,345231021,500381546,623624886,467391130,747995642,710063778,570532413,825057726,840673375,321645043,901446119,724885716,597675219,227257943,554506529,531882158,564794529,529949584,640908627,990875835,732242452,492147614,273428937,289766128,741598314,847447490,718539114,37491583,933232788,539640729,934745017,5199647,271958768,781613873,919026268,261765580,473592494,308386190,564726446,813200905,611427819,832721482,376059764,877275114,464138230,156959839,910846386,527236632,789005384,238166062,584364084,815811023,362127508,405771870,857017923,317259948,638189045,400849312,797238107,154567831,129360224,475742030,980108131,593647294,99926917,66650004,949472089,56269160,740908434,679914722,328986827,224212928,985923972,609334553,743468857,324579395,782251601,731484413,414136262,239855367,661142651,491029284,816098416,884480638,161829124,908281554,494368285,569767783,580757749,998882028,993500994,48706271,812567998,595467749,625445130,191936657,154109410,295285872,387113709,520830281,616894442,956515999,590300008,974793632,350510966,110650130,646028696,701974505,931484985,14111643,966678467,728723037,824646429,210204805,908159406,885140090,680706332,308567296,873274177,660443158,734075141,489321210,109730725,222743712,813205154,452742304,645821882,467725307,109083269,400101033,277107075,979394259,624365044,308174436,337604085,415066406,80343206,453375233,426475750,930096640,105107875,834634443,178433884,487834396,6181757,557095055,586924134,409476467,781404674,117102363,122563353,962417196,548215191,58054814,445911322,439289235,981172510,27420902,36046239,491169286,289842339,528541845,282273579,532928551,832418892,746367364,874140933,56384270,242929232,719336393,136034149,20036422,735840345,19818202,678582374,377536214,162836230,86302481,820571263,164671568,37659530,653801493,131072014,905373032,980218276,711347596,234176197,786909542,502088767,767203596,797173872,160411577,334901906,126027827,339906795,895326389,87142968,936454524,135746023,610385163,173342687,889588581,826082296,116087660,320909420,926615219,70547185,899089851,319463800,510165932,172764729,718514094,272532653,32087028,820099746,847649037,441019040,677159333,661343672,332275582,526651390,586696324,153943919,520872863,845003279,612533420,99516575,282279117,65498664,212898967,881809482,795407777,304630413,378984109,456156109,366164752,427101304,291621995,736466740,870402968,625106542,163137402,250699903,898840320,981817955,988358214,791840488,125409546,355770627,604290914,72113718,753560560,410593745,532465030,964770637,546639050,177618196,112553293,931032893,670933113,968076817,266917847,267079523,486989001,876651268,854026129,439048148,574493836,475370888,964341232,584538604,891484031,98253637,368885206,356143879,846497238,74864334,116125762,210213733,949047819,409323922,433928867,990041044,945554980,114847220,278837623,559257645,342838392,521195191,298697640,96264568,697466219,813606191,448086401,460245595,408797181,92640449,462623431,755439644,620089588,657687050,735952670,981472830,977603658,145395476,695523827,931416467,808643910,262391779,924422112,718814624,849503636,226513322,83195923,734346718,727039169,301911777,154559055,461319062,800706552,18684932,910639035,436502078,621096206,195213935,166222142,642447113,96067609,474678758,83098592,97928284,925955383,554987283,603299959,261039521,800298572,278991733,986290337,708222300,409265026,893263351,192658992,626438342,202004008,369958169,556318642,282703671,743273850,435885454,793523679,30391986,795843419,288272530,446257822,574504311,230265486,855200461,1249734,371858732,676047248,53519098,557748057,821508450,76433643,55140623,76035900,203788050,450154642,838021398,527289277,677042953,105703009,987849582,359322047,632656179,85191966,678190724,856092,889908587,89996827,831396090,204909211,344076494,464753354,618652308,721712391,472687197,28955592,128767036,65283948,800445218,729762489,271798828,681090584,526323164,81626471,996293234,667987349,352294329,336908064,549067738,690902985,47453459,570997732,171056424,863347084,295654012,537137598,49666713,302704313,826208949,691829714,140752592,854116976,819477649,963550949,728710920,113084458,596757475,989608591,7858305,135060266,940205945,954091837,3127327,814099598,724329119,387991933,721395435,938470326,68064722,30951897,24044098,984075196,793456935,715610233,708960096,888266453,393051199,158210841,94821983,491461822,637024908,903773125,806714988,681693392,612413310,226064008,217611290,931802985,9309334,794853932,949842866,561688169,956735110,723992927,215186972,263098973,542886681,400679463,99414381,561485213,818164357,786553319,731562945,627808042,248026286,362786447,444773479,687988104,618761095,867593824,68788470,826096952,743758946,254504074,970786252,571789082,487180964,849633599,28778241,187602112,722636696,995576586,334813423,153285391,155743001,48057347,351723849,725919483,547254875,70033257,901864117,825257143,726113172,409812101,704356891,106709730,437408614,14336163,65963718,172733307,988998757,555265846,542197273,890284404,515026132,553450563,112158916,18317509,628262085,695938666,26742466,57676942,824216632,264010116,607296758,709236095,389865200,51224361,647407058,322052168,580126483,469344806,123478595,941189668,491851360,987274162,234139385,424985595,738228534,493000015,277417064,282262784,901451086,576799980,673251696,862989463,742873193,573597973,929421787,617998818,589236526,453541231,554720589,391895154,813375376,874061872,115713405,744114492,346288367,799102781,696320734,545378011,783033164,687776053,145351953,495577506,420165790,15525560,798908243,692653565,351683987,901473633,334902642,499187393,311804393,489294284,783540812,819505773,199760357,320581850,311535050,305029689,735244627,231220901,707349130,213650382,771763118,132171245,455460998,118914,488712230,480445122,64169009,323945324,775983413,673409206,626412504,193446597,894150580,656091248,716277277,57221879,354625044,598456150,653097751,61272821,987447737,782817677,480882476,895721461,588957952,592913152,442192527,496769106,25286925,510403754,317406418,383736881,44336576,480430455,296410278,43157977,392004191,358312724,295025075,713241898,52131880,864883581,961325587,477189129,304348479,763642759,868897521,696302594,871042292,225225782,748413782,906730851,642609807,394762437,338623349,21553020,462574629,271711336,958580072,178170077,543054884,692337298,344985528,342234380,252633180,186111595,247760024,619327399,482718748,844992318,381707507,51032996,7978600,158081445,166352513,907461079,11033607,500615943,238484496,216717128,467388296,360401043,437821505,230603253,958516696,320165184,450088963,546264212,127279628,441205143,167469904,266841357,279014438,960759080,920435749,229450872,626003022,807008090,967452785,137898364,591558542,613367884,720302279,190855784,716434375,623091407,214410161,812345807,131142086,225956765,569850909,507321000,999660356,54422306,317785527,960418286,580886160,461113591,513935470,722665413,426068305,207980328,518952104,358193799,184262168,357847860,721152081,638303575,475553871,857708401,396803680,936435956,136508790,534130844,918932281,175102334,560981026,336354949,362501820,266360254,145777042,903620897,960434321,184834166,876606757,545749577,218256261,709011591,766704979,784693155,706846821,801154918,807072942,67942395,232860722,597765720,99744424,961700017,298447062,593137006,207382685,289506625,572030824,871186382,708802922,833451615,121526047,612858402,570433791,249895184,359548889,494337494,112235647,485746013,939932303,44624755,294995287,931024536,201248811,1824234,357235570,540564057,901667388,538767136,827628130,908144095,736148273,763529893,888991941,456875185,655014715,416120950,347184768,957817564,247816397,622884813,348543416,591566340,830637889,39189078,291026494,825356434,368842146,66274050,7956897,207981241,391411424,255828746,554690901,474930863,841399930,46322545,768354382,770769022,795523669,860499675,841746207,340788198,975065068,722277675,28544430,90254079,107992862,140771898,217349689,170482906,983594282,953584262,290325144,561953100,122566443,271910274,791868474,578421220,713486506,738174226,577583204,416230806,933904834,974411064,296364190,306452932,880580610,306243420,314717319,657360253,500700250,365846198,477994979,41690296,675655022,253746379,333661402,431006314,118679613,891828847,756084544,221472896,957892759,40462727,229613035,332503965,761978550,736199801,780313157,582652828,286817320,424133095,504783597,360994188,59800761,162586505,295102754,694006330,846188657,575302129,948855905,782393319,974030727,35153145,674904909,67283282,711471130,101458486,730370763,961752476,723304202,965141402,985443134,326208281,131973775,900938005,58232820,759694505,926937668,178005197,981384895,274121293,139014822,336924447,272675573,509169462,869530331,22435533,777415408,92154430,729181672,881026781,301322072,909077744,476508415,618237752,465530168,533127570,624058898,762659065,117589254,393404621,320801526,205347912,345587726,444176173,339911451,170386617,755267198,463364741,391292701,170562921,920500980,122701779,212326512,121941175,188240390,661446257,426964506,826720941,128957988,257900587,881317771,358882771,335472952,982276324,131688115,95572078,684438723,400316729,148483780,186033646,392420889,78965245,476821139,408229470,253514614,659455021,676415855,449961667,428791546,970883047,335954163,808185361,224913543,140151188,724514378,769194928,667006300,377626092,476129846,419514695,711735423,49314728,258936221,365800366,696231957,13949505,656589608,101904727,844831218,598673949,752417952,73875414,604909209,50670309,671996262,366958840,798927072,897470326,66770025,789820041,258794885,947136434,392059740,119161647,18510619,457774627,765702634,973731001,890112821,580426458,476231607,26844963,493808550,685055838,868038183,725579477,843549903,888541015,91672175,9215943,101450713,483153357,220442701,93373070,855873981,840324475,614281123,152211234,899102532,745709851,588705326,52209863,440782940,601540682,27041964,800101351,168057600,363550132,2283003,735740209,788532924,118310676,570504411,38827466,138771248,88039854,183480186,826553213,726306842,383625886,447830759,772857247,594870888,480545977,571157994,250173385,903864335,374086551,896886733,773382915,518090172,199570659,878394082,466740926,322505340,24415032,290979115,436363338,131847228,144109960,475022324,342541940,743100216,184609300,868934889,170187170,381750094,358607866,832136451,125750973,737877435,160445766,335046464,505536230,749617302,534568106,284330187,959570272,664011545,3541253,929025409,678950096,209179796,777674758,692776835,162250406,250575311,172789704,514268333,802703247,313833166,234407773,57623625,631543684,419332935,440922493,204347503,512227415,364658837,662523447,232453152,7644022,328764916,987806657,979540070,343937227,120414536,515927279,969408580,899994666,803228072,403810874,968698975,52467177,719637135,269493841,425459557,642642278,560993736,534754993,880072704,945433179,486279790,948635315,114178486,821227941,761621530,60376226,43821938,991542343,125893782,942723105,894713800,228206773,138549920,255173166,497979944,152556789,364353115,725807383,654060808,723467156,406052511,714136808,348816028,716958121,808262565,187531371,303587999,843750174,683873799,269734972,697318950,684560647,49200576,342236089,562463361,555111029,853300703,437502620,932537500,609537796,969823115,708456441,612750033,243829681,282982921,635908157,392290103,476033904,949871589,692850628,597728526,464111983,627142231,809444839,763145572,791786550,229568327,316681291,373574472,420561153,395736886,594920242,701129220,159835858,232195278,326959870,109691133,274416855,257697125,301707968,82920602,930803172,368005712,328258763,663655673,457275860,797070785,43599100,647028888,568834005,179128861,648682244,636620972,407288529,46116146,913369645,276951306,453521976,422172082,6212649,605277583,582557437,763675652,750343448,93604095,966746396,653536459,975205880,257367282,831400470,464046565,665085411,727221718,773495619,573606600,848187330,708683042,183942159,456167763,272462834,971891488,443753174,474133977,163459914,277698755,516915005,118989903,182685179,983112494,673018066,709225040,866511509,127368616,400858110,826946476,48017137,200741014,486687589,317001305,968889489,3991935,250943173,343150176,721604565,614277930,860618471,900701986,143213312,654017561,937141347,564971740,3742439,263653755,346646833,865385641,803708839,647667215,395256908,729574206,801169872,619721354,141686757,434889723,337746568,399177840,163234717,99418705,726390704,3316466,36722707,693190595,74215720,280604550,734330503,197880091,24940155,184114188,510788546,687757960,438905995,318232351,594470971,404372953,553770988,802741329,661289041,254450898,236610217,524881417,156364574,317111409,131935811,200666894,848312385,916977235,473061257,20413484,664363793,419728427,850867141,216006085,58475396,111641754,492315805,610688286,806982917,682237817,235111150,337265615,854686092,215974003,353920270,222503914,132487471,51724818,64479251,433486463,570507056,999026741,944648695,960406427,22661382,532557249,703250529,382437651,208839734,669629023,937478581,570078185,947194293,458802452,699804706,865367837,720238049,862700298,231266418,271599641,832566650,974246277,844940196,362980599,174172981,343360138,531824958,141294383,159219603,551021628,521348449,970735547,216092598,830886879,149659997,999889796,567377838,148140082,194746739,179571328,929548030,964006641,961629699,597265300,466313196,712350190,444899847,477763249,199483557,15368243,307966565,106189622,617286690,146967917,21058337,52848590,254849127,757083842,340716271,264838944,600453364,182762320,668234390,37660729,155426576,467911359,629330400,161554861,974628883,697420094,937221905,852639737,312594314,270104024,90471186,891036106,728281875,181860383,825713843,86063205,949737011,822994691,130281252,38719647,275052834,271544044,446932542,457248302,164408492,660026548,709002293,87165085,439798102,376302545,465295889,135382454,303820586,20968695,298142800,811162273,410120869,140591477,648154771,638944570,437091677,883495122,13904197,772718069,592364635,711608791,352686437,803275257,507116154,199739817,610357688,19862310,451676633,906792827,987734906,186472235,428190427,824477279,571628408,25954958,482803499,259554951,272086761,537208739,79128749,72461571,587542754,888223854,163837963,246159476,723775405,690302967,742516660,519019804,679141122,453458672,752749381,40600243,165071833,458260341,664015430,630744790,810753810,348617253,237356040,326068845,691631588,34830200,961911784,990076717,305323437,710617766,753506876,519675072,918513131,232343688,294289191,764320741,930684772,336811307,771375452,634470537,441977050,247169769,804872739,508920868,566418771,727541535,548721672,849350791,702489277,42882735,916642761,601728997,846391870,110859668,63972754,643397490,594933856,306436219,589566573,45903353,408835315,531903031,213946347,64752891,837769506,850350296,539493471,34352060,626062430,113317306,809347826,744157215,140019362,654728475,113682779,888930182,142259784,154561194,439080190,251253290,963664519,804240929,189250527,525542560,311234760,375433059,639223400,660098749,330916268,370662802,107593041,112434013,881762189,887807738,277783629,184994230,706877487,945352075,119595302,385130884,718625817,802983304,485120708,896881342,923402059,614162091,371164351,528709614,416954691,483625562,268868324,927121105,693510369,768003319,384845668,737230907,256254704,866292266,460633431,466185005,103128271,38083307,960574677,483084663,796338939,341765577,970503025,774507101,84393927,750309176,356847381,552835415,211401394,472402591,549196940,205948353,545738550,102221752,838129434,546838600,265548084,865177065,896832427,834466056,956378064,250906786,420047030,109708992,454746008,192304311,48667001,922980564,118933469,595688740,829403696,394621522,703476658,708090088,721511969,722219548,398189347,528300221,772220015,462832647,671302233,33952842,182159945,223779367,213716328,349046133,726713277,382232867,500869056,125735586,405262115,375931956,881128488,855331088,978324214,176127148,953338009,593019864,790277843,512668563,956617931,111797967,235283819,994095324,878151127,123854191,319841718,74686845,863033104,700564175,180300177,229517635,98222640,729024033,574880388,666432494,430540490,595811337,474776895,437702012,418309294,969716236,796450079,570527605,833489757,543544254,674381310,438466591,900960777,791440989,80336194,314702675,561832426,449552359,990654435,967115822,174571817,405604805,557737569,927732914,151268087,511454772,562844811,640873993,681541171,886469260,889453812,966455992,357931872,972488119,956279879,155181231,377928979,151823499,436365966,974745387,767472819,732547566,721159019,164822959,33650054,453810170,421259979,276382761,295936415,14590079,822242655,135800085,532777328,404066851,811640441,847406218,116610185,48410240,130826823,433529156,340764660,285963873,581496228,855067290,543531403,205910346,934333733,733130839,972433547,546669043,369406132,910516762,641875456,86721207,524051672,764446577,437296527,779537019,495415311,442483635,414711229,742129364,304320412,793586299,781563394,465557305,383096079,679062748,360828695,590623810,267420418,611548111,193958475,823049594,697465856,974495034,888666718,8590928,352495904,730175720,84178456,402574501,500830842,406614760,393305710,768064083,468680376,708454903,636143126,159293658,956953450,454064758,394680726,568600361,827921076,952432658,305323188,721854715,281059308,264943246,962164936,905409793,204100159,748833261,375313786,746099107,818340478,317637971,955783918,374963087,878419847,876150998,331830858,5786895,829150294,534906737,300360311,564108442,291618115,217450636,501212404,998627956,628710626,297307901,26785313,669781016,375615554,50599726,274795957,415249806,746421952,374407972,754515859,733929996,497704826,54193455,952675137,404075466,318124731,62631001,613952222,810140000,681105665,524639303,859774756,439421724,923421934,704733269,747830816,345197616,112102695,663113311,312163416,76161481,519289772,546655434,883948621,184846144,861981817,391023279,674269044,225125472,898710230,858465012,148448987,140397075,869621862,796647657,113920386,324654639,112455591,454072289,859611730,254899947,491716681,79023409,184411324,922011303,37522981,65558357,453288998,881959830,821914608,56251755,484094130,132652665,36407320,503625027,312329999,901108369,694483167,479347224,218721717,824001845,775768233,912754955,852066323,717259892,335874953,175912312,112209588,790564677,62456276,135026381,916158156,913159213,319703220,570758400,311567678,389915190,258349138,644583261,940192836,534696373,79931747,990814166,478326833,596332447,362216465,537828807,367419851,550660957,192961143,731036626,689139221,660478988,591282005,345793399,463186915,385773365,200453553,180697738,899463139,382793137,395783381,930498470,429527676,214574730,703776722,782656557,60845640,829637379,180800556,258526380,817850117,528678395,719059849,163651753,498428250,630353712,948485848,865375425,735885838,793322308,830152450,817926748,486224668,992080537,340506965,989862645,23251250,237221637,749211513,595883873,539415699,258221716,281961695,871909457,542274717,297562260,864555200,453447585,778641292,839591414,537311504,732674649,207075709,772167613,468069597,834855904,344546187,496905778,860338005,406784628,901598702,883756988,564204474,513329576,558364753,193319279,586587047,981264117,307525722,658276806,821756604,836933366,524036291,581637362,270290104,980765761,713647520,247316665,279270305,562461724,479290609,377780932,999894289,373048249,413612039,633499290,166281735,319909871,982563874,950641996,309715810,643786428,197461430,781981547,689873847,841643195,111006026,852445345,167443451,966941452,433670862,534458216,146790818,113970630,404133663,976998341,429016702,801443534,89899091,883680791,107468272,296721536,285427947,500665674,673429558,894322739,805351226,383389244,578043440,143273838,132964046,875304292,233662311,180048309,653136008,498946818,292792362,320861267,374895519,147401627,640855835,507859850,363875907,571052881,656925773,911387290,184354515,295455243,484425400,931536846,904097262,907817849,112770347,442990717,531723820,853640477,353964621,199131161,305693545,701678345,230562529,24160831,388239346,502332590,812431218,869857555,25554122,56985742,658529320,898900236,383585560,240117682,103316672,255545253,412018252,435093171,445152365,507742939,324974053,38602656,942187856,963082818,827172722,764108669,591404008,38189918,664398318,774544853,65755351,760764439,333991186,127540832,241854,275886564,975248755,742552780,997913331,530553671,3925,981229587,825942932,12565013,884018204,65893488,77705810,242342608,383743474,755539187,667420572,312635720,59790116,92067642,284946162,161429183,610226676,649234665,967217070,724424451,698791046,642289181,964990586,761372656,880051322,13559311,777614371,657585149,47395414,933490929,318329256,647095623,352902575,799906045,548276358,64024718,426840086,222621118,187015644,763973663,662302426,58655325,564832754,353142784,274821552,365775027,598116892,206120203,602688176,240106503,26067195,842686815,187379449,341007944,666468695,881640469,875889430,301996213,1282628,963184981,234865296,989689795,268748602,100258422,340406405,857982502,732921428,393151756,159000499,362468194,571372833,466098927,939793247,755519169,623730872,512033341,51932314,760745562,368103763,734649228,98547102,701560338,447540842,155282013,134967943,507632282,241785348,239195100,672204407,527198273,547194084,174128416,800601141,580530054,778547544,910568832,573146563,453458911,998509037,90187429,838779761,186144061,407514568,203654932,910378816,493597622,79329321,513200944,692604122,351170088,576353668,724080298,909262710,774777669,654889875,90279289,628091537,414863962,620202857,784147751,825267159,307747961,494608787,491143711,381071806,844089386,916115394,786645058,738389840,533547143,87615223,581608804,984297740,97975874,170293990,966703442,54419066,291515381,404900969,343380751,441229452,967746265,809536386,486638220,180581356,650924926,772623958,979916764,416938837,869268115,495757935,147820542,325379837,77889288,887938575,939697702,232285507,913979536,592246166,86844243,771234875,57029731,519084998,741654279,881720105,501448232,568464567,702261119,979134256,773326588,923764273,794165036,679145823,594709655,980195139,811576968,673081824,647498915,631836398,208050768,260663351,205047197,612129988,189449068,257435731,180338138,627233536,38710218,788698296,100619197,521140196,982887970,644493532,362690362,996902864,756557353,974738767,269986833,603845384,763255410,20293014,54351206,472796142,160536111,246076341,607686341,267978464,129351837,741443054,424537528,660535863,677856769,154635808,314146634,469614433,941560051,227510577,610901573,673868389,943889362,698789079,495095556,374437674,774196940,114286520,173577095,209598524,176607060,153067308,806810946,320787243,372513770,619981138,989117410,630364910,496820838,731058762,736459315,589202211,995485912,321212383,458015033,46331247,921354546,18201860,400749438,47618676,169140826,647575644,198753179,675612053,778679031,133417918,554610739,103304644,27297349,485400718,231280910,353954223,836627916,762698765,187949099,643584919,209999238,202532194,721724485,725148312,866519902,233437284,657079826,198330417,364560325,670778776,197012931,428059978,531001683,367556220,488425252,709055125,310743262,608649182,203478492,852774943,702103538,379152666,952491315,670386716,969248762,584626945,450505435,41142732,219896241,930831642,320668140,734858627,873683803,210741632,333127002,109369815,887788969,493562178,633632997,53216400,940167085,570367901,58410482,203214730,679109069,856863945,578781720,651457871,471087719,854595610,39507562,35178719,56683117,83128427,552614874,653285027,17797912,198259292,562119770,841584775,413610737,23127307,5578625,17246473,922171379,384083219,981918523,97526375,202544856,502079899,934323552,610683599,345337723,670017659,4326498,724638767,231816213,467387718,719281545,910526160,498431171,611279566,801119800,399319862,830029666,516810516,898014490,546475233,271903652,182530295,37078946,474669211,802192104,302459726,961356813,782328836,326397741,563490782,610337849,165404962,29730060,1385377,800718070,542854420,622851492,711932719,605606337,604169697,773455808,381699058,929227560,190209514,655287426,70707160,260336899,654931090,428141662,236248922,669684944,290538765,458328998,835357476,103273159,673370696,846179473,398270312,763521704,549279428,588445034,517547930,616330941,618252663,179620933,258006169,78017456,138364957,665179322,709602910,765472087,212406089,160295169,284750292,734016994,855981101,750773540,250173056,438196418,114220746,915585058,636940170,175234898,726472776,598460373,174980472,494852943,745835976,655277864,223456457,784958488,65895963,738065287,767075140,323227510,595342058,837639614,305363685,365590635,878033603,825518107,773332207,163030012,494655508,307979143,305235216,607766997,228830675,392039909,416919522,584724401,351466982,986104396,839759588,950284814,19181242,758184602,593168179,342830384,909187595,23752613,203643333,555691975,279222154,440958212,35836144,485607740,722252286,959647926,500058362,190349159,589817986,638053147,338718849,551742594,761919835,400846007,284747113,735074467,50087117,19712371,827490540,640874963,530841370,836214165,633581786,737367378,87354815,649392718,771695339,151723097,429567778,96077685,746163102,129241163,957357646,431044604,614733492,682157251,916801448,574514195,697022169,112610882,897725755,720875868,572705951,697739316,435914617,317847605,971219469,864770650,13754416,930758189,946243644,964372824,425759797,827424138,957828952,896276001,351444964,520737664,485398381,601077455,336358098,399953252,202407386,322478538,718471194,705024266,57328113,839998182,75288611,724911749,477253535,736254072,678346643,193616462,679447187,515894321,399494018,653014785,160981342,242654968,803464344,871860838,717427202,948374547,975213024,640968742,249951106,708564659,235295270,988903794,775066700,540356662,790092906,548774923,990601720,622270675,849472487,467161055,43370198,206249964,742031808,753353084,460809219,776206844,791433802,556216264,68079723,781787702,99134506,451455560,446831051,901428512,429441166,79962626,246264117,629502794,711050708,242633989,911463528,191199691,802597376,754261975,357842032,622614302,782598693,476580268,318738049,167269176,614290558,204033623,271908831,497633622,982263266,593662300,261905343,913485273,129087600,612279308,6426952,784897948,284380694,40846821,126950692,942262282,858324624,269125020,217706868,43340954,687099773,153547466,779952448,5522497,332754299,492501944,287370288,495148927,641293267,144953705,381922873,389249398,281638003,31115527,888343278,651706398,807102917,177775462,107621770,174512140,207922461,985194920,492892437,889766870,983879619,834934839,519168223,827524481,299136175,98637870,259995752,281356488,345193834,523856381,972185370,503283559,910154838,371233932,324824739,894772335,285984383,479032982,331020214,293042171,454161085,317035681,750244778,697939662,822633870,173979769,237034700,731120794,245752659,553340304,603882797,70083042,366692072,729115316,365216072,696507202,683017158,567695191,787156494,668917094,937666243,945766612,865457666,358383312,456615980,632454452,946344447,250640389,233012829,884206713,431908591,763484276,525910497,689048855,920686173,742633166,477612977,947531782,977598393,729708795,205872393,671360830,480654274,609740104,749503759,356336332,566343338,424055780,322403463,738091724,716154753,550612232,312431997,978062360,102094777,933041119,352947204,525040048,979124974,638806146,263359129,316508108,458987695,496850820,482676667,592861424,842119905,657298232,478383280,925977353,728143220,168597355,85715437,186411215,46644022,474799881,349203578,935449388,938566021,70117904,737065228,879141153,851928148,743885171,864412802,871806740,865580893,232091888,739857858,973917404,853071929,397216486,931123941,150025705,631764834,157775848,989945176,223724083,857708419,804151438,978223829,228969643,49483864,368023835,760299229,730532780,605588935,320626563,691346539,756248570,562550136,818731673,99769090,944411313,733543702,202010337,967660834,680886768,241458786,888884146,937934370,990149293,367538851,949939428,881038630,792716039,411755192,535931539,571599097,669314054,943819683,635475799,208791679,379034571,519052658,573171318,566766603,760926774,86235031,138464358,277824511,933310296,663950934,618593963,794172324,613032627,437460133,67480186,183733563,477791074,441708913,287457630,434261119,256665692,134633518,561603249,719505414,469936903,881106836,127196412,916804115,566420051,787083812,453954977,587639976,184819215,472600144,175465786,875690656,24517080,479605660,464203028,449535504,515482285,656612522,348117302,281086141,315301909,416614236,269341212,198139275,672442907,967796870,505620760,515508967,671437922,829970002,726435643,566855291,207884469,599044304,565896858,123861861,144953215,122754478,467799025,823023211,919418237,836145827,196845312,512770460,364318421,638340331,632239044,601052658,411216402,554744905,760850842,608868368,736084046,23846704,261609475,101588197,123400856,721598684,311050628,170542733,685904962,449462761,742674866,711338038,729107192,700636679,34140174,234327567,185928971,86765933,9434752,143470851,874143381,923446678,830555976,852083886,437303483,987589839,879313351,691060007,802459574,979037066,129939171,44763833,925128996,422440960,430686889,604052398,636480720,515456783,684065929,934124852,219876681,143288687,562796295,976670825,291081531,818142429,951192500,235402474,100095384,421276663,997297453,495271225,51656055,612307512,947425950,733952478,761708594,51493501,374180147,207772541,458529008,900539679,101437513,597739471,18468323,72290574,757532952,972656914,500018212,619801451,159445512,970176237,984434668,475773388,6258706,134474508,633066998,253163507,483860663,428675021,345695630,449030185,465685775,597920615,91166047,843312486,690414872,351035760,819273260,662781289,729280154,662086127,12890821,389725188,798837539,851882086,356689591,777499779,432431126,972157524,835158805,340634708,729764830,464420203,353922630,194509580,124379261,433464820,232130501,840564940,441020548,116195713,146209507,989035224,490570932,334128840,212603193,674129359,995076909,947085497,960300088,182772448,584977948,279816720,545554094,583235486,446448353,792894076,770114807,637871626,454148412,832220486,760567159,929362614,694113553,652077027,954759470,424302679,355656888,352092630,979025803,968273686,635298427,513707787,29652956,288169612,945243896,281786848,370687193,857103415,182205637,148905999,901490981,22960216,238401806,956423919,642406204,943013330,500606736,138722950,745833987,769703800,502960965,283334319,509387178,654175626,78958599,359316619,477089880,341438941,44465937,799323922,804341655,861743922,839303984,389868570,640883424,343466960,672457693,629870881,571499301,901479295,760560287,433368826,809053346,816426742,610953735,918540449,368672115,752382754,426176063,244472863,638014383,485317007,356227158,828634345,334502208,551595712,373805398,437266696,212604132,15743835,402898573,937791096,917178877,325948574,712452402,475417465,730584957,455647922,604686483,922047442,759386908,521734037,512585510,578067483,495233701,198131305,241421416,411927282,663297798,84506331,191821057,497332590,167632574,951584737,509534058,626026435,849122510,89845573,416189232,684835690,120985507,881303656,731283072,873804916,601565793,241511345,134371440,625196665,674522895,523286358,434652731,316621981,64068196,253195867,461712209,587295857,151903571,152880778,626110307,548326592,357704272,778855701,808307431,78373581,993877769,628445295,226767608,857249917,744847592,523504570,852886856,354435297,250392598,209151961,405505670,838872597,907636791,108877724,58782929,260934999,841721621,232579154,950762479,557882148,337282104,54994758,508666684,482881718,42825233,599498592,960365888,361111253,222884137,712652454,600481825,390737501,840294905,925750533,765400799,638357477,410138713,207966328,976386740,144386036,814830696,133776866,427752705,64714458,802457299,963641603,486648807,160061430,600722219,7962402,835320552,678888993,33135440,162201559,558607516,724389757,294327705,138179682,508448183,66028410,742968796,706755522,269636816,396012332,539431641,76548291,900338342,118952024,833974125,661381830,67818895,65156752,62667613,877356624,173623581,654801874,805914132,796963618,351032820,733680755,247668787,261912457,766181480,927526295,636069119,99073279,126606959,962192116,877518007,600994465,6345080,136726123,62418225,77278976,6751515,597278901,586067,569418552,413152402,477504332,259954832,6957724,544913414,270122560,25312575,696263926,187046390,776015795,719504879,877663495,115377239,415968254,790730208,187327809,360204771,247050704,870174169,963690592,62215708,338309140,265910081,596190901,224099898,854296591,365437753,204309458,714325546,64943583,439106983,290941694,974859592,137769029,245786069,934041051,403908864,214370199,42751471,686818650,502085382,917709494,366779398,630611233,177263919,38282208,877949847,308172203,696234642,786356850,206900066,772399431,146333919,126070297,494079519,864511127,796376640,939314583,795871716,953436278,245563956,141303218,123462724,528374111,295275725,912583063,381949294,69061452,551178314,944702794,507987115,835229501,235056423,971787991,230325642,781887421,103965138,464731592,647869052,974638805,916390329,715960742,143734062,316346759,584172800,560443999,338442416,440138162,83194865,973643435,316461210,319985776,437991125,475774882,15718160,724181075,989095710,527643549,220971783,458546025,872997721,75715525,795963478,580944681,265886426,43941964,481802152,696886878,511334856,131819344,363334067,594504748,202854334,283560933,691117234,952285763,521046626,7983921,640345036,858395186,849398371,778297420,752968168,158289659,592459153,441076288,703450165,172779396,825257307,262601384,502319282,735913544,331050588,650530076,486670504,296567977,648681036,541031458,570132342,453312754,931799236,814164205,247358241,758457156,307373357,608392735,885259554,138455439,838877366,664969496,584716262,390356623,136521210,343190708,290685052,738772012,721432520,225808628,432754723,956055718,836507338,720553857,817766703,903629120,401939012,228086194,255406642,193776828,250452216,260982388,270141023,336793209,116000805,140561030,91402841,706511356,340499527,449930855,5024618,147914866,714707224,933713380,221062135,178162988,254725013,471411771,10292973,641116738,195258049,702404677,648772305,240968309,166983741,127244264,379562554,117038007,145483321,234387695,215154557,432057917,594625166,464792119,530516660,707450202,785650204,111304874,676228413,836638284,521556811,659517313,642070466,101598074,226650790,798953230,551825251,81535180,443499914,682319033,102848109,138075104,514530417,237597104,178926575,558744626,165746611,436101040,805962199,549025527,560933686,458084556,553368646,895291189,364042703,624696674,859390971,668791418,167202343,537530521,194327906,89516633,540321461,443398249,68122460,413147216,144638639,700890907,829674813,272767111,182676484,546897537,856767182,61069009,711503521,34148772,592025420,712398330,565034765,172714847,715476070,941961717,411651643,26783398,841986644,72919210,247217126,570350769,741814440,286763204,826980076,115365345,499871019,732774224,957786131,351785563,20781599,662854089,172935671,60426821,483370897,865912086,204069468,622581621,450178264,656928500,60284334,865543453,651385551,734281115,863853484,74818091,955489639,640407625,789309556,214472426,248039768,744907403,246233291,965611882,678207358,400781066,209245103,863717612,439492041,307331704,248428853,476950331,589111366,321784384,746073321,294684076,768341482,378560302,91042577,815447561,79060143,493369911,764484582,252952877,879019888,603687403,132230903,552781670,720143327,897653158,697442957,361043900,553000487,196773339,409924443,552379688,294104890,862951876,494377392,231698386,888513070,918165846,531788577,652622661,639780359,400104854,484953738,742263642,504444781,531682435,508409361,553050316,570119808,347833516,397611978,254996556,834330315,743031171,417677398,545152205,394650533,185306386,315699391,240577206,804052738,664173872,907506630,348964262,661820276,386036335,224530202,102183958,325202589,422983292,549906937,414013848,396166466,258106665,541135271,198025007,334438508,805325716,826183012,569018216,153879386,320235679,224003369,468297085,104069513,607357158,23723485,152843867,935935006,382095733,1398347,354997020,666696809,714326406,706764800,571680874,438566591,706059912,604467513,563517593,985507382,97839246,970239851,444571327,779727803,650951966,704162558,737784975,313401325,101967493,395358567,136858550,626108957,616678485,423552302,355669317,595432882,154662700,206619113,298318468,358944669,396114693,455069494,19966400,569527586,127242917,672881957,453487534,37618432,775418751,598086342,399157797,56688698,44002927,907217744,952761943,530750731,399390477,935886800,667214989,507224102,17462341,69788662,998624000,116505462,107661604,635873952,85259001,837425219,986300914,330107215,185591910,121840996,226941074,764090854,972448046,963489593,365957807,78919190,484905411,636570400,986936585,652591725,369851669,625196191,892583403,703807699,751769421,424283941,424901794,903100348,941943954,237136863,521077798,365291131,988607487,336636678,832463866,130671041,637502697,145973616,366051586,34237102,785858078,921471981,691751503,469784315,546279812,51002435,949076548,655129784,191193130,609059008,882515158,920216086,674883260,606578576,608922275,601646934,78745100,87428033,992141134,875351289,235543387,964207021,973944572,747269767,303922241,601051923,892236308,710071625,309445548,274235297,758222036,1451083,990377119,277489752,699586712,478343688,718000123,679421767,822738798,483284591,778084587,324295691,814259682,984820906,61615263,179563648,911355489,873212970,728128791,829590815,143249711,276858123,177249157,235978393,291285998,557430237,851053333,357590872,857967020,692127690,783394191,465865172,705365636,649036922,492896097,149737317,125564579,775969480,718447581,945340314,816110359,312154670,799388514,477197004,313269489,453221846,863539031,43586370,148478858,500238008,841242618,939712727,540503917,584804142,844000074,269141229,242804228,884642280,275804601,198457723,800693517,730296688,876061427,363794441,478732465,259207218,385919175,758839908,223101570,728146246,317412495,321040214,949401206,797620192,446334038,878846062,529420920,628320395,671903497,558244744,572952161,321653080,489543349,237496823,480837927,918448648,421190468,16382793,974699792,768633198,800706416,630091502,235361428,198246576,158383506,614602045,252234425,98431571,573884351,293955430,96577450,739508439,8867900,984645412,124160687,554837169,397862166,383975575,373233731,554945151,96320301,670209344,700949528,975987063,208739168,607547745,354456009,670419168,489131622,535570897,668292747,134116694,190511640,526938688,345765068,112345444,274778345,983017306,935691745,726547392,630908860,1412513,44701814,704460310,842089209,786634026,94684017,764956998,483271102,501959677,811107969,535900233,609156717,761424079,708432403,850361979,338331532,418316879,91260344,964101344,83394635,531495813,765503149,452207461,452957043,247243819,100711578,849649846,729026849,781593323,651608048,98233426,962452081,827429227,498289632,529253387,385121876,404528659,443229455,615491759,882237119,298707128,575245514,817803956,634240928,971911849,306025236,634746616,604342030,677460178,11232355,444411625,509792376,852086892,663877841,508157443,492072058,470483603,692058892,443631860,705822627,910135431,467160988,476403030,191528011,872523,450714939,114895405,669845647,289168241,992280153,882223629,898722298,514036383,461267589,70990106,139671801,954277233,137500116,492207901,38561957,708924151,241314547,902187090,856043069,549663579,704628192,692352992,262881943,459739628,780930663,824733324,561802408,702105432,202462056,771343307,168809504,890287800,978807216,637686552,184174352,452842215,809071494,634727636,710039456,260294184,773695679,95056679,614280271,475162988,457146892,510912582,275889236,340209964,952596718,728453796,692764680,993454486,409251223,472934916,641345529,562047080,888743151,777303061,194270543,423217423,444611861,944779775,503139456,444022309,846561569,476466126,724259309,460809645,364351488,974105026,586632662,941661566,170065244,223049845,322078181,994167652,767361860,365189876,912613013,464103717,786237150,549130933,655486354,107328811,84828708,766318250,409606594,891251495,188532312,978378554,215281410,415404340,379235826,554883606,750535916,313169159,54289391,424144052,175607644,551583371,825048987,224125657,721457757,831384594,58187480,709551847,163229312,849644807,685561192,563883060,844779701,58442445,132445870,157497506,210131612,459290812,714934424,428502977,522812327,569888287,206891636,911620322,52701630,312221368,991968506,129936088,166710481,787947382,86726534,832406306,880680972,406144035,803101752,791714803,83989596,91009372,7925095,199340826,778282060,532229442,910039832,669866888,453924641,72516249,50869606,294727395,741067625,556467216,546744809,477305893,377474793,901710245,469341641,510169766,237023238,462368747,939683321,588867138,792751551,378997421,289561480,64728707,587853552,497865085,133330846,921539950,176300654,977988138,227372731,868409087,248559212,603972188,958185211,103569721,771236827,522203508,948096529,404125226,614400811,346409374,223736930,300733332,518742069,859099542,608899049,252470614,910445510,834654688,714890094,326645742,576555943,106170654,196779462,68970740,160968241,73708319,455668061,430056650,543314169,677638620,839969463,782998280,714319523,185944174,110098747,218958332,385326416,578272438,732977640,191459981,418131396,783518603,629495587,854503431,75702696,516543801,70824961,300533351,419376390,618371298,100800893,18616991,570257266,358602078,684848920,373256665,385869402,2038854,78543055,298391605,879422101,793049383,142075212,939566067,753249628,236117716,177785579,349519975,448239671,825479620,922865491,500151430,610302546,519979107,505596775,425196686,218470045,355563057,685348757,532878976,218730098,184198151,627944494,600530533,655635571,29053448,10039369,280887348,222702489,168152428,775598508,887632746,329067736,436802454,529855468,23787608,797545949,650946808,34264868,612483331,471946340,670527813,791940349,457606976,271688393,627236815,371058530,939769628,993357898,120875824,235610134,814749331,865270011,55523010,835255202,875602579,348771624,101781166,213005774,984199902,190278888,370564805,633919181,997360634,799313485,812179325,651746920,465310820,968135281,738717167,23729966,415538801,724437017,668930909,518566200,807588089,565156701,246022414,195830641,131962142,983746125,40091336,228582807,968083732,701502052,365442271,386387763,142031961,763819839,358349830,593410746,266859882,315210995,1962248,70753952,919017301,649972360,587477165,444603871,278262102,659942441,23479717,995231073,873619013,52213135,577813691,568493771,256626095,216891172,653878867,579898959,834075320,566794610,352361453,423117844,505034659,360904451,298518032,352373226,339562714,69000790,895861612,255121667,370932137,168181436,898263710,307753006,764556731,823591551,225577503,680928025,510856154,118185595,343671986,165311609,624048706,915031393,816889617,869768095,773610698,972122556,112580040,242310533,828533161,855822410,426336260,118944715,560067774,102256757,316411028,579618102,730992272,182080121,972516053,378860993,151198397,697678082,992249845,418680505,368156860,550381361,637142283,882161712,259357527,533529347,213962240,847678199,831434346,322839588,117714974,987681553,7558454,344716443,383033359,370630448,704128657,460128500,301991137,806839035,308812688,422038342,72212735,377601808,781395940,729280954,234308938,745206601,731785458,269631354,552782441,786735941,333939476,382181377,365873736,629261222,30458178,633239595,753211788,31950013,53650793,795348031,979693832,846534958,529495234,237179038,100124890,59104918,996928549,496513686,437085519,350153665,41250774,719335743,619859031,557118747,171193994,827185698,296893370,106205113,211105395,396584530,940900715,419713138,39353133,497279336,120180240,762672017,743354011,806548413,479864409,271753131,979894958,883139972,998431156,180272815,865249362,680923915,519451434,450671898,254520324,29628258,958003378,793647801,43166823,747876125,447088723,773570014,339075160,203985421,597614334,337032837,880433400,546330920,806519721,69189111,850258684,677911851,68607899,947377893,179621821,32053191,475543630,510174972,343831809,471327759,793694603,84728017,501384151,295967047,899740325,154672224,708085822,438024730,489050277,380064913,549468995,191278335,931758534,630210425,624090332,547838418,548828338,719828126,684100237,699317310,719720889,202912880,751607600,950948292,413023301,647084446,346150935,524136993,486027474,216949955,310605796,572788615,101216867,575031390,461108777,748342239,666687276,800784607,540206243,435007734,9698841,382984366,982467555,228730687,839791729,780288510,53297850,778779325,838748535,696179654,365789436,938035116,434620329,76237083,123653581,567868209,114593613,521741204,760105576,653217943,832172078,639898478,266648250,796044855,795783707,339362414,121572381,136703310,970006523,123271835,781100602,241897322,693244478,662302425,137018773,772176009,904395851,973138590,437716654,155207868,579975447,107446824,987510370,619398246,961177704,847545814,856600235,178930812,809627240,544949545,712966973,551302931,861332261,509181418,460955350,184502013,190014235,631066014,604929537,738021689,906713540,30947330,128356358,879774347,930941527,250371200,804015274,8943125,449500353,961207123,41165007,53652100,133855228,928967201,935708575,483933435,535430684,109304259,121013421,552977248,347980841,387224888,991291327,751548784,910780067,363390207,12689577,179234066,430043563,132755729,111014446,367265848,3866419,684738478,93573264,682236998,542643453,175427953,182136266,923120586,133044755,115311649,51831097,343737067,811710120,574264507,783736876,659236805,543864479,443611749,301640114,457997570,984658088,457976061,391802747,557952904,180089134,760612340,521354347,987842748,909926376,422085948,740615999,113907871,881540595,784878330,481035682,700855232,809350995,530233839,818978889,488824566,86998384,8404796,288076948,26573482,357505357,772979042,157628516,208504789,5473244,383409175,275112660,88795425,97812055,64439056,184227828,323680425,452057601,931652151,392618254,587936945,584432160,82621081,354245479,10165235,480203062,588535904,98813289,178197962,231155345,935704986,504985975,13837971,788507024,723889231,832765808,209537917,390716045,741596131,838225388,336576385,948446680,355708988,305538944,559133833,252336584,561934091,553613245,516773781,565986130,818183126,138581608,287439794,223279925,818186178,6265888,836813299,982213262,959896345,148946260,305113497,651457041,573647408,284828326,988680879,726104387,506518866,754388759,114722904,988797176,983589299,1473662,427126585,35249609,646346319,485543833,430798677,83375198,887107015,638753004,249468554,243409174,39903537,875765156,568629942,907918341,938912500,458612948,221964248,571205592,189374574,476042778,677923913,274545109,703903003,994829240,891676854,253756291,441890932,857470962,914354961,594278753,957976203,414286522,242732773,85440262,765057731,303371715,709378115,489164871,695950739,866100957,856759072,540422284,504109308,906852775,164223004,575911856,298782515,588104371,129629495,244016741,346922047,779472144,829302342,951345723,881666846,843823242,820737790,671099624,845747084,25125264,144435657,27622564,980036034,58583101,863279353,633906684,281938090,261488327,227322723,587692221,352425529,396456592,182335812,647718305,337982016,61186223,906132967,314273252,10896917,269480459,859534701,604563466,332641237,331478727,500505290,730371504,281350388,953022197,948807570,981775938,716026356,871346991,939409459,529502003,270928092,782441380,899932696,829514954,410306715,769150981,268435637,578042534,846399681,44120770,785652215,774586511,601641930,871440395,859817659,240844685,543626381,184627088,691670878,448904315,810186378,482217660,271960526,495504158,926902990,333809618,889022081,865994268,578406021,331388560,628000168,635835920,339657533,25796372,952026256,911662959,421134231,693459972,357847361,600165852,120906656,330415762,557710854,801797237,164324562,121728448,82781978,360613507,417706562,730373835,164995239,834277875,350364269,83216496,170217890,750514182,85300411,432904320,46873439,874967740,759746783,93553379,759381070,899466852,608241294,972166080,452799190,159387683,449741143,466619163,808027978,678593537,730542773,9093646,723766681,254167141,641849439,350264608,160817512,765642289,585520898,480070450,857862996,874767129,853030262,393018167,442364380,24433014,768889811,34826430,727762402,783257636,113515035,900842086,915328895,889180699,275171067,799119501,330066011,920893712,805851670,147053278,517215938,658385817,239717391,801089443,529609795,649374625,649864471,151713553,644603595,457842659,419005635,204369298,912788145,746578672,858325119,433880823,589057777,802049801,70648633,969840821,358588804,817531603,320907576,730039413,555640637,755631138,391269654,561297726,652963519,719969296,268213244,334880585,428863768,566127401,881408931,8774639,88545891,220740994,356454894,256670933,268117949,123998954,428194707,266176593,875088130,369302968,146970854,326064670,60457962,477708500,483717953,301067286,13601183,665413678,601172774,540811606,746802789,803194483,222764642,341685828,293558606,972045561,164897513,333881416,131093885,782741719,840007740,860720938,320737685,572599137,937586134,402243863,145218100,971463019,715095540,826636403,719434066,9718641,774580775,155602513,914249150,619132005,567908246,30084092,505251972,105607447,908464703,253478319,25336312,140799838,186334774,235094961,896038197,30604273,27892817,162499760,401954333,39053623,634212932,434331474,952929640,317996665,148345091,185623319,835072008,591126890,85218001,400500901,125037357,549435212,645935692,402229654,22967916,106875468,118251726,612622605,807117554,117375731,236123255,388123544,702839531,747297539,85548065,346230753,869837487,914354650,32741975,147881848,855122265,899277601,872693408,938956963,799845611,989051150,839843009,522929952,953323119,867343730,576561226,776431232,581810904,264336401,540441335,424235847,232815169,348846603,688598017,376432813,903329657,152349302,207749020,576381548,42100859,82349788,967538276,681094570,29059953,763295409,636939675,135161429,602281663,259155401,497166480,859339959,716196021,513714796,25248,377001500,709755565,78324193,521052810,500399313,388920617,688176908,729517289,539586205,130635405,496084669,836806171,774422451,310611381,794583758,914426667,600499743,971320828,545414058,195255558,700669667,78000789,937845502,215314141,866390355,620655808,40455469,569457883,122144134,589159294,9262390,838356510,853762306,438383612,680759282,475363833,215582316,488695205,104808840,747047978,14830103,832345381,100982886,655096893,861773379,540037436,883516846,76874052,833581242,876639749,281148777,161366997,842970482,207736419,276949746,349679088,843962307,984305272,266402192,957863385,140658715,547197059,662659304,60081039,951667296,650212564,338333006,867499092,926360065,876806087,574899793,354556040,655340538,789599101,353729434,44461168,30884219,866627142,316396648,78445868,193673602,548358171,964169278,146241352,337660931,623922921,164630789,818589530,155077925,735512873,17350110,809483048,151298670,751687969,523119465,918269176,24513595,675397611,7384445,35196791,195066902,419480781,739392852,367385971,148863019,135413998,576089000,641922574,408443861,292923847,300052279,250315595,175626711,495000240,921011080,78191725,762969588,385169524,60993162,758983896,707093997,809868556,378887629,365592118,684519593,643349816,736327656,700000389,211098972,598028111,667155645,982604781,436246150,381591595,34730067,836632705,817254014,109822943,752333795,238764968,932945960,316296240,186107682,243076884,905907222,902016054,406416160,371769128,678404009,154770424,812601018,212608674,254952631,104854415,313232720,966432306,225131173,392939721,446684413,835766788,507604618,785429682,82088137,527838033,392925774,359494751,190699010,476507123,325223897,741936272,196206996,565004894,432322319,447279991,620127894,673748914,452287492,122675886,775152548,218484745,571750661,247266037,889632807,876981185,863479505,469768087,93971367,272107731,156449810,380918185,626073470,501933634,399303517,36356961,323068228,668863460,744991586,23045894,813717176,834172108,888968981,437831519,263406851,254471229,260310181,617518269,200453777,736009358,592849785,173142450,352687432,919196837,251111229,309306464,158332439,296048964,701329932,442071484,626294571,507896326,651535396,396024024,682708767,971273778,233166207,582364430,91266876,841199789,656404639,551600802,521071066,753538813,304408975,914497802,917605315,595552702,275352412,186833096,862767621,71768877,715865119,442351797,813605736,797157747,453888353,825909963,744501976,679687117,241872109,513983432,217554984,12574340,308848684,108836266,569909873,221764756,108387151,810524428,719409882,703026190,778094074,301160405,495383561,840738165,501024733,57237198,572822423,200778409,344466693,839149904,488992906,44250338,148113404,500807909,966107257,978174481,673799404,607785544,272117377,180043720,511964787,223214363,292101851,816705971,59146588,602124373,835800039,204693287,674880005,51785204,217564109,919708576,40833828,975861070,384812346,50069176,864572863,409986900,924198337,718154274,221291847,958493077,649513497,626726412,273448788,492807974,658441592,534496556,334301842,267058815,690246227,397938027,388100378,96911426,193395119,438418000,363075687,667356273,67922891,191772690,657618264,22318746,382184658,87674840,900710953,870315486,498073994,390277667,33754677,542799416,995334651,85600822,765094702,174115586,775035038,726741060,917324324,23227086,716931296,60494887,160322705,95308569,180783548,433594436,866057871,678008134,509631787,316537509,845245283,32664527,138936785,245352905,338985115,421418864,87121329,400974555,564655613,575150190,711204351,44242377,503560823,959803883,527188609,756283359,605569225,574265046,550724704,534262282,879347000,804857665,822470064,342051476,942221540,537227429,864517898,382523321,686182788,181785269,888316281,680381485,195083814,826798775,553439820,379977434,804198574,389973193,403896905,99234933,84436234,47979963,836190478,128239003,412862700,3670330,465174550,14782710,887410477,281278390,31882520,186564292,693887243,218820308,406362098,179283280,695602767,698459729,30958608,728855402,57302364,77869439,200064190,548771508,129069840,710947254,902386437,596091993,829027179,741365482,939886597,946458907,896776032,278202727,794584037,362285867,102227082,854265230,218857619,724801409,471476662,650766666,123733657,568984018,514918572,521816632,385398737,953609469,497451165,1174885,218179485,756875044,351200607,857006093,801247986,503212799,246258096,291283944,73516702,32883591,3110680,883977283,18041891,124324881,399451799,159892119,522956379,289521656,656862724,889210553,515051618,574804611,775092823,721183850,825024759,353905669,360864109,395451064,109731944,461569838,817484914,850002857,259222345,714982583,152025053,957525242,639044998,672457926,693835050,527942505,640586096,174395594,993406928,977503689,564145656,397198438,518074000,281498576,816920972,668930893,989209719,687366400,452707259,713390984,926038854,807550020,996025381,213456059,182321660,958706558,127437346,223543677,305954200,302505356,937353302,978585472,429475241,108358348,976821935,579262579,360743351,885240230,442217781,159038141,358948168,805468108,645707864,558257005,425145840,389080818,39336296,810386001,973314018,267829870,626817112,14358302,869924301,310640548,875909004,498976680,812635681,470907560,848259092,748053446,612168983,327935001,262198468,796055524,751745322,104503486,738337644,958443419,5560493,182893920,901913854,909249325,588370015,825364500,358429327,194801044,979998081,340191812,704928029,176345890,380515304,676551739,834870837,457422399,377675458,542292288,505255733,113129849,988426792,961551875,536617537,78841037,664894356,876247987,369755296,795614281,599688686,579272377,815452570,346090978,110242751,523789509,533899497,736844475,926229328,364461898,923464304,845611504,371823827,689202297,638178683,317408461,415834338,946617195,866365202,109740435,49699622,7536870,193920938,16659908,468911212,37252251,735491844,898795526,511117784,431883146,683614405,517775068,640904012,143908345,745773142,548472098,878383674,688384694,175998338,19016929,934099620,279683800,24464975,376095777,53974987,697142137,364495301,817803590,615735733,372218837,408597032,766387003,138559859,745516457,520951361,466897426,523035253,710665334,611991173,794501458,448500673,848245722,188092413,259578581,941344816,795829111,30814568,785022921,774064858,156982964,944837855,194302233,875357643,507854526,986676813,609310395,189903081,617428206,617731191,686612506,697765970,375878035,260639102,658718829,420254647,125718338,536790551,987737051,165747271,857921151,934460351,797030853,947265299,987838189,649939120,280894947,668324869,787238069,993839243,997063564,23256002,423085112,988571362,502666526,865180916,10915469,806939018,502108630,807113589,81078996,919695529,62600147,108934830,591451829,103459511,811737114,657191384,620845738,741150238,236248721,554073606,956867548,494543382,220435636,102837893,611411256,740123712,284889069,224880946,677010258,206039794,489062222,759640087,599615721,556032890,159257266,381049596,897187414,18548887,804072353,438536023,195793737,541897573,906147230,775259526,891330663,24131973,745151720,452722227,890764080,109582627,211518448,959254676,411424080,205027469,996171765,752858286,198268492,256901399,438140380,358386622,105122279,25265828,615098157,995298752,254017832,41315260,461185035,382359494,60483848,498156735,559589726,500119161,410335810,914269162,646317066,366539781,326923322,151788351,473931544,526840765,499685642,21625315,553089622,698040714,493654322,749598798,328401278,826862754,636739142,819447684,187470113,107181312,439760633,862505535,677607280,102294605,999600675,547421354,833500188,785756252,301920430,335163421,900672530,762584935,480447249,384487482,418507939,744819811,433158893,429348324,724691395,949638097,464091641,553825390,961865180,391042798,230544441,42248510,683211174,970660418,275157707,915105901,61402723,173344501,98419458,710674887,930145471,339151197,768833375,557851820,390906065,910502062,766474903,254461205,215995532,72542522,408314399,718292270,384173567,620257319,883701721,573883946,479613960,862025357,494579259,844033539,28894610,197946953,563411788,294363515,446299893,483665732,110313464,533565151,787238764,676350283,807611835,445630961,47297309,614316480,601684733,538986730,564756382,364142299,840083160,566032158,654442456,786151076,805500098,116962243,624820778,91030868,998631860,915560440,207480865,66498905,934679937,890519460,654546133,886775038,829457454,568551236,845066157,258607728,918605431,696223433,404597762,56908341,2681794,173330360,316773236,506571776,13825930,564553929,587330359,564601222,995927768,556055116,465911804,922195095,212265432,564282208,267567043,525406368,757437360,913362846,579384697,23383710,423088186,949766765,612057532,771475194,57362766,832273014,773795191,150592617,472635670,484569756,2739222,166055586,265656173,404051012,169843817,390184695,302375315,762621268,918215617,154282946,730460828,268761956,581191519,149647263,357709473,970980137,410509172,41471674,324671815,424624057,480644130,81580807,854264770,34059744,768814582,521406668,919817434,824760984,181331501,365220703,372068400,989486007,422977215,303805459,923517131,281544087,669507843,993194335,625300696,276790919,63418828,748520442,178175270,293167407,708016615,851033523,251382180,465278269,944396367,314602367,278844639,989825382,69395615,660613514,408684483,19554492,63315127,223570748,229152152,829542692,592328583,220369188,906806406,520418237,307037908,531953394,155371041,97456464,302798076,87778242,584830920,288903944,431282953,979212181,728940405,930019142,419806837,749146416,849005024,11392384,751854219,868883468,769189179,251580134,352929490,504189850,622341585,607457351,150630861,187137407,10866638,383737860,289279862,665115497,112674973,900553310,409359647,678512442,588393147,317872239,715153844,943459592,449855160,665010767,826514357,959888821,838695466,204076556,895809219,287929956,709891191,973388502,698148080,835942905,105955199,298508617,353528118,705656341,768845169,160502291,629771473,663856924,766933588,670893384,906868372,769307044,158996042,455775130,647333852,887359384,289645502,693565212,908565549,434819857,733355220,74010058,934948040,442634733,406786184,164809599,25721883,717263902,761696886,682639138,914013052,725961637,131174911,337355743,330581224,518630530,668057552,400234381,808314005,646859881,96850778,693211009,35695090,658058589,590928741,134808840,148061211,760911421,450055402,241626836,503167457,12539513,507910287,975705092,660289681,981500439,471268051,451584649,60409736,72217554,551348513,283937537,885009375,912042426,683995536,36211713,643851687,383710107,669160457,578677469,958552108,117907404,925149251,232930656,757017312,707085981,471294149,389765903,64955615,90875386,273475843,626643565,654962006,952122311,633996134,905122072,323203817,4935890,853966832,240399412,758415219,727201927,1126612,47235357,551082228,340174224,49308104,493628168,546782084,77865533,298266148,52436069,404023928,73436699,383301392,293292443,665244512,650088420,424537321,874288286,746341691,293346265,331212276,901100041,974391572,374997519,883517974,306705927,841384865,234906416,564755392,604528585,935624057,451912680,401373459,346628545,96569748,768866090,803311443,496586745,130430026,974320819,446058169,500132736,647458506,229411294,441709953,161023816,145195210,71623880,356454236,632670296,265914891,317350789,876625065,138075630,404224452,342431737,232683694,261520736,399208367,170226246,549032113,891896053,280189630,142811043,14012129,373646509,267279647,764102707,916878481,31191294,803336248,117225401,509393223,949658637,572664165,26978799,957782003,470344450,893353566,122038577,20168396,931500665,262487893,354700527,358351445,765804698,767709120,104564804,59005434,68165114,395761669,722632950,197269669,347899502,692794482,450445289,41806776,997676085,182894605,188382933,523865780,348872800,708965948,171104280,70319241,136500259,502422376,877217244,811765942,539711347,789772640,137482169,962647285,613387770,679326868,394010224,276065329,696064613,945703864,82988643,817900170,470166797,309783874,246915792,556758008,949671159,786985751,441955570,825621368,631038285,93650308,645237824,81500686,830754633,385721252,38561392,101457800,93978378,495024410,788486737,440669088,877306121,961783528,827236740,752784481,245731903,142525769,221364662,899203026,835502698,607676194,20538701,749112309,607661980,145065170,501904527,890382146,22723631,557709961,91005925,846945435,300583732,267050796,410612804,779044418,635386190,223543176,985942854,419903722,495380988,117884492,220574866,532682982,151714652,882853867,261536719,563802862,811082582,616240546,796679505,460662683,14127936,262364382,500641864,63508288,322417556,69798265,509005532,810402374,247875810,911974007,985387704,486380938,533122030,446558627,263013573,173212363,648838080,699519342,485982603,5405972,31006723,203345463,497926864,870968241,200598805,294593571,141992605,621624028,851968138,45749751,344299783,938136442,21062697,628040173,831688980,559201812,727826486,970111791,234053700,157556414,142154214,748739164,168931841,548900094,492430078,978757193,593650518,376111799,123318914,809541980,118235095,680033349,760924389,520285848,361573992,250796009,722611794,929867971,183607188,305087371,103316761,419703814,176368535,464784088,778611573,299363039,141475266,393052594,834236469,101545527,679094977,686178025,542550213,890059980,37368370,538368418,979470761,624002873,650754561,75679997,228499358,117714360,804178867,666110152,195887256,863618703,629499856,776554146,435567899,610292699,245385853,424570869,103304274,752807418,430969623,332014878,320979671,798623538,85756273,524757989,403859132,407221934,193682133,185035869,277928038,250018861,745647373,65775061,663136692,543542695,325595409,629428788,440344887,533154042,660784312,799716195,752993354,838621115,489046550,302269064,573507964,98030558,762443753,539030204,201643839,290990985,680551985,258326438,368780318,838278151,517545750,393110534,717938267,61578869,793426133,42690862,733452105,218578425,132050403,121729574,887171481,57387595,306568257,276203927,63163776,551012535,367051900,625539719,297478461,877038684,622749189,951134247,547269088,821136909,248770738,214069752,559076741,519520711,778242759,149639477,255241835,897728921,823854300,221737944,372286522,703969834,66543750,692163935,640661271,213901657,750015402,625386660,985891928,363431888,888390674,631292579,322751830,572741166,530577534,518291711,253709087,681321432,233926815,420527741,6698876,388511509,967977980,64199587,930140887,336055793,591250641,653521628,248031594,762400034,26354587,310259616,115728819,651498442,750856971,602341100,644263115,369175115,80659826,250652339,43173625,645419953,250339298,227114624,420431819,245516042,696951329,800952618,167266498,846874417,298343441,238288235,162574609,101538031,9813418,988989971,192500430,496184260,458027408,302705093,839250958,36796809,28563117,266662933,802514208,433077115,195546123,962541840,237695318,150660069,179004445,907459463,704315673,410377548,904612880,648319297,815984971,107784841,133779365,474437857,438787592,484693654,181686218,396905625,61052426,806522077,472323794,653346553,566339392,335024309,499282304,845745692,734286322,847105173,844914375,899998370,783504642,991485155,936784692,251338098,248563700,512100435,970696332,623316494,956896387,941322576,682557317,265305117,878425594,91027980,696289054,10472989,833311077,552556764,309665551,676905024,389138537,129921709,729116923,694614158,923733732,787552201,900949405,178940534,117862210,993664507,226799423,373639850,215399011,390582252,100444820,304468874,742297860,516608507,972183271,657625151,849340518,757468466,211673543,883010958,989056428,444967631,522520616,607132717,476963527,431853673,319996112,967308641,717698308,393178710,667704467,508469651,624569715,106800798,858269917,549571940,646834430,972306851,849445340,385292745,690553708,238822781,938798967,443651416,24383047,376066007,941765776,390531874,304916742,424449327,147024383,234643555,545948631,13291377,960316897,239416969,234676811,465015850,884493288,973817590,686121444,702328205,627391877,191928893,731914683,914643526,193590292,675919591,389047385,429232328,700105813,806635007,903606470,943964162,505214333,980567684,135929558,251583732,383006777,706978596,585403289,134144026,425961913,445870767,302755961,60064948,98379267,436823002,271867436,812775327,302209768,296460742,974769083,977624995,467528073,912825110,80052088,570116135,116827042,494586159,439055935,846568811,16477624,189235112,549559245,815482766,899522601,42827350,647248477,146651469,505685280,861663254,808856307,145770927,394023430,865183264,57637495,558514323,861856425,188628559,790738531,870552823,713839628,912880234,184778699,111509173,690332370,654433503,838617673,281989854,773735885,5044781,561258282,507072314,323352495,684519367,295045533,509339174,382965263,117384318,55667267,674721830,772116699,129358630,120230578,56805795,595094560,42187613,865372321,134101903,359085764,95878484,378954406,619406635,136867041,859387965,332246862,269158966,293388494,517271802,66896427,813123019,520908496,299198671,197854105,644955046,619750083,875554154,422323160,706660281,670437740,75770790,863632030,123969742,298773879,998527881,87426414,109167669,298691227,628814007,961953235,808889815,60097068,268589990,997262311,823762097,766878330,896406338,661226774,65684920,502416524,914362000,310120358,797509455,910207641,803511398,830378641,562945053,668029443,381235029,640454160,724892496,982648389,140918750,19387621,153934907,896350019,651892482,458966774,633783173,491529213,261565157,514739236,29777420,197577090,756977403,33981472,4784408,441871365,260202307,71890796,963894859,204836799,691108364,969462284,460775596,939824868,957729073,120047782,162516175,902283659,868856291,474109663,986307621,685556415,567713622,138854829,138123036,892238371,926670389,743641483,659581536,282342713,304569556,652764446,753312076,664763878,796743193,881767486,552000712,242283731,463565187,764199615,180703042,955857599,248176452,482024740,753579778,899490462,732223453,225893976,484229275,687304346,727701835,745990915,214520076,428883627,843154767,897539737,484723946,403182783,758309426,757794602,213714045,880285665,290601220,892468438,859260735,492548839,495284779,109610622,292645322,859413706,268950353,146596379,969981797,528486831,569295773,101162690,60784423,903049780,258684797,154885796,821738872,966006322,342628033,363316210,177747955,406088562,422748317,617757015,133695894,426706867,314737254,727559933,820448965,751549491,558194308,993507212,101042447,623890727,398818,106743337,963719157,464151044,531444770,199935714,644103868,599671860,531469128,323739566,37288855,914564799,661601607,351851040,835161995,533659548,47866887,300012329,486210986,770493458,503047490,44744707,79053444,592394301,230442498,443922521,60631343,746769720,418576981,843207890,165172731,987366135,969688771,940908705,277955173,14904874,540218076,203038940,549405662,476282650,870808745,752327551,753964826,234133224,780214650,685723549,92029311,773458361,695395467,113998110,312951547,326434757,200958823,48167639,662251683,694387160,286479960,884006590,762859449,496538013,669792320,207179471,389510026,657388062,564792023,699246621,365719442,869714125,831167634,239825651,366227566,391749092,197958461,799244034,949038453,384683442,133741670,127199275,982600259,288875091,107872280,152336724,345408690,906261800,471633164,515860331,709747015,46799103,825066012,492083172,218912030,351434342,976487132,577510236,130971844,590814528,499532943,485827130,220038531,456213665,519303972,635627672,782590305,691885304,706623619,32267814,549579882,823766712,12510778,942573301,68250038,185061176,577181642,424780256,11277161,604273700,364042867,765620905,388241827,176300624,490060350,43710220,173221915,184945818,173365367,11841562,981981056,291279092,331682534,419214766,104302794,552930960,959058161,192896502,965942752,628952460,350715533,197486727,754869671,43011121,963514840,395610074,481533611,257226587,732631978,572824206,938410475,900501766,467251209,317021814,365457089,761406781,417128469,552265190,749424279,248970555,697666718,356139397,157610513,482700645,541403970,569911991,511565024,971308290,949159400,625372904,153417666,560624651,916893046,491357951,532562007,376540015,886639608,363584930,201309161,520003073,587717993,882396052,535336593,521370629,538361550,499466794,958443508,75534111,978099307,698680925,40002057,40434167,90342854,347160991,780107806,434049271,229170049,209573772,99310770,546673417,623696107,383957390,887650122,176926757,496157878,934377054,948791103,155177896,18996564,447553785,878992057,179422863,399260330,686050822,148976862,186162014,871992569,322449175,521826796,49586385,142437711,846397320,834725883,870115274,796783605,16146169,370212210,480692381,152152917,834455811,840629222,520133671,295914056,297351247,534836695,929489236,560869601,887781056,24551023,511706395,254397088,511604914,684129066,20608488,972251629,640075704,432427185,797423770,49847725,550335570,824500072,647944078,752245639,519222531,936967797,136371911,983541356,43705463,18152955,100089031,156287339,803293197,621714615,659847704,132138435,617097526,536802614,980126069,108543283,140880806,251756630,687409871,214736724,431261892,707932501,44067133,996346406,576878725,430632047,669285610,380157771,996805496,664288609,645691637,357808217,354850463,902432391,987460240,715432887,247908493,406794279,954552059,191686155,680061568,751778054,760999673,813418837,772646606,573717227,83421508,941516720,449001785,683892983,962763193,161329075,18085339,912171478,449499290,1918270,297357221,381099823,66535732,992569222,776071192,206331609,103873577,784855184,695998052,830768990,862045793,319750109,9319438,656164840,615548377,516916366,605542383,359027183,622743845,685061789,826038668,161666949,271168124,25474871,393113987,698621979,271039766,225620791,935862953,219748862,748339646,754192553,775366823,984534363,87600382,4198377,549747209,407191036,853297561,902647585,520202305,466701081,906137172,125969198,223615171,838989294,816561285,66467375,332335973,657351039,384073720,175692582,461179878,915751909,710836520,819813401,228091146,279648782,189261445,157941175,620457184,940995736,623830999,534274704,26102092,765194698,722498009,825772697,139430578,327576468,65823433,498558649,22499035,396095650,72376643,42983035,395763822,713638182,54850366,875617998,285103310,124166947,520263678,487802846,199854071,928286584,495915628,861213522,267322595,611683265,520338044,195546028,882038681,880509529,530739877,209901882,984525097,224537377,341568424,507929373,751256666,812419247,671418226,476391841,294976334,415044604,683971386,605092723,132450244,841427567,602290854,382638487,543621505,59760372,628384140,439725312,998459903,306699334,305912512,428487171,133940834,340531248,380853305,432044234,296153281,695103887,20671341,97115525,729164837,772518732,25052629,497993151,867371852,872871159,437390106,916362426,219157866,242355644,149091692,412265829,983435881,67027883,443615662,16695989,31146951,909900236,900036309,149935586,449641537,822116753,653774115,958048504,668040089,155182794,873039980,262407326,787937583,435412944,735632549,358224401,726832574,616331747,253128725,953922120,54883412,668538200,867810674,967208629,280434523,875669029,508820945,640860289,656874799,266526665,777065232,789144928,637894162,688883656,284885774,155318748,296042347,490429543,510883885,427739465,281099133,864770623,813039822,545818123,107801629,990543206,47579915,780806246,300529206,121054950,665814624,465433205,468980934,299382028,332330888,173774427,654471205,82939301,538217321,192191476,903845928,398412433,482636750,457868677,263558705,967792177,503734228,360980765,613327480,829235614,116588235,175253623,909385007,410809944,738685639,504430466,113159181,363718417,112817668,877381007,628127073,984385167,371006149,711217551,126996625,174201724,41818907,360649952,833198019,701580936,88087885,913617148,34189690,369505850,513429097,769372059,765893812,826740392,27830567,995641188,890582491,525989653,225225658,462737381,802883522,765385478,379998765,824499712,50989359,506803571,664636308,491775764,605706795,492659104,162135052,51716948,651989347,847372314,722655282,679653497,714777467,922858657,251762739,781238629,260357951,767735643,830575333,930485013,386774451,878506588,350983510,533781436,264634857,20981847,945174734,345983635,560445642,696299967,262630410,944631207,385928754,419919324,685715613,19566511,982334967,255281616,626232069,259450570,247037040,543845433,621331263,96691565,237495468,27843268,363291498,220846251,446519198,112758247,466700548,907785161,82123133,372467296,123860407,167669639,77388381,944154744,929450860,422218020,248470040,454559690,846426369,956891290,949511511,460168696,654348902,5683009,145024009,227900792,910087196,240976859,548515480,459545861,414196366,678979342,807298013,7893018,239295163,750939670,756388556,330067203,589066217,943950,89010064,502339367,889086734,784528356,145263104,89881136,600132299,831712264,840089559,47172742,213170570,223147040,240300547,284088879,392472494,770040644,983438486,4575440,950243831,110754038,637507069,157187155,278007157,778190138,67958005,27132886,261105772,788383801,540160359,387178207,434186994,579402355,764151143,622729279,99822058,883077458,339908688,322082465,288904776,859597579,612232289,206992969,542342389,749697775,83881556,605840035,699281845,872048825,534310533,709224305,369398991,676346777,371433425,341478338,77563702,979384427,278921036,57378226,145421584,745853922,196722659,996505093,646605261,307504012,221803883,898766622,124633820,906538776,323557748,415178504,686019213,400049231,267244331,742105152,499426798,34402469,541786566,805433422,103796092,565693980,94589909,588952929,675300572,352827526,179418876,859209753,354443465,75811006,147353940,264649880,980124363,315659446,492656005,794680801,867446246,851960171,341753347,650424908,837643121,854002678,485924629,801884973,839421311,298161784,333598082,284792482,284474380,621896829,201834937,74856154,450177719,133343457,161973060,908388046,674220300,550561953,657533062,969016263,697027750,287128413,122117897,135218993,170501306,129184679,676825020,878355123,575084874,489048124,917554704,907011071,195000570,627578013,345646124,303021703,429052067,120129353,151270622,281953051,362119928,279069637,931851925,498113512,423966690,832456407,58476163,13939644,183991249,542662370,215565168,533020248,768879030,601834424,325368539,481590351,180382055,95630909,881862425,695026311,911442263,182827285,101405377,957675442,703426673,997641396,200428547,960604707,791844325,270841219,169694638,971870171,542393949,700504679,792610847,246868886,650966992,136539882,38865945,361527338,856267502,8392168,949109845,836121702,390036294,928757730,641968316,541659132,407450165,658876590,552100863,451085559,106233250,975566372,232708728,365040172,580523736,291874953,313965100,451168435,824040446,525825367,362500302,862113949,717832166,237843623,206726693,572929867,571590258,150339040,288501238,669109627,64476652,416840325,308028936,635794441,301722563,898151173,765933465,151591121,433953226,809788130,377842054,254150343,860444477,816550326,347982047,539737574,194544552,680050257,189669459,418924607,323021372,536353214,837574868,805612078,540084859,158161911,65640778,966769786,872824820,921394390,848779889,297147773,913897563,481960545,64282855,318368972,712754369,758674897,505447173,316773107,425967658,117394298,800382816,3856558,348135363,537367824,729011765,726563230,269402063,942291747,370834499,652681889,193265051,661584575,208422084,372724118,998138648,904046091,517257495,862436240,989084107,887514799,769062019,492389662,113975560,313665094,203052412,71460852,401271168,849416295,991157122,120267432,27004303,600754925,268469244,148405179,615316358,152779564,964156106,862090018,790428819,547133465,233618388,855446917,196417458,574496626,943015781,672695776,822164808,590583553,50554288,183262411,600597523,806077555,402749013,100947724,912591820,976671511,429466164,630213076,301004305,693396319,412980932,546842165,373212673,507964615,703599506,892350793,708582491,810790593,862448684,119924841,94581660,801349450,262706628,791124676,979933787,227652987,118626623,932332492,337305305,709497141,215255102,322556364,869662397,41386942,505707787,965121906,347635521,200824658,813632611,647237972,398328337,119366138,595394849,263956029,309170277,876063421,168295905,534144865,253276768,345004605,562998863,599470304,643822796,571202120,220116806,43991244,550395234,804465573,976577324,237651808,37648136,839769539,467242385,103489173,123199763,190170273,327411423,590587765,913521959,470226869,773037298,305963131,246808613,229109943,495659034,614911351,918359356,360561419,558464397,756156293,409014203,121209471,108383761,905055411,149400239,447159668,309107432,369004581,749784044,41049632,409088328,931668800,161082707,971186829,22470495,111540553,336042659,588350785,784729334,644278390,837489527,820418745,165406699,361929663,165579247,814637343,838869932,312279709,193998151,856486427,545251571,858985922,595270495,151014273,614000315,769715442,180686675,780331101,768076937,91582210,514896868,289224943,180836205,583681262,105702210,385048889,805539404,901018742,425776795,42972734,859505890,686464360,37133173,354176422,122553809,386455368,18402340,921751382,648007391,464160085,26979108,2618986,27319429,859311915,202937217,314152261,324815284,938441322,684470414,573905022,355356984,764560425,114777391,651724651,358358448,44949766,332458162,173896157,840297373,477319790,268725925,373748479,661544984,959847813,34027454,40305787,182181099,599099229,91235138,632899066,743584938,940433592,74739520,737299820,621910678,546571598,245516209,993068338,709822659,970504228,701214112,969671645,528831475,258679571,925881559,120068516,510693918,202688786,631744415,826999347,440660946,480408848,254811870,228299638,510352442,827212825,546369464,740457233,68484658,69170764,17428817,30671541,872712185,129876365,680855947,803340861,896815459,560579615,602875940,73874273,264741015,985253746,654913747,247614147,848162872,448192634,615219851,404837911,580684145,893015484,156063232,759782849,221656851,843274951,823905073,521559741,717263711,245416603,452211729,630372513,818802273,486654100,272034770,440098359,692579695,527343803,397999724,21683081,580588536,774602509,769067442,582645474,259206226,936320361,395423671,907624844,744352367,809735218,539979787,183970533,430116677,874656758,557874890,43309448,654865616,787518135,914918168,378454583,178903585,910847459,481152109,323163320,532736250,942825930,648026544,115782170,366472571,919250169,97780092,200569461,706867889,791648296,125501007,767825977,663861764,459937587,615033408,981609204,121984011,266349299,815660443,940502726,923014643,152939126,806320843,341444820,793100570,937960152,297786448,768489189,338605700,359179403,716161071,612771150,891992598,52424442,784688844,964323502,744957374,136236740,653853897,270387612,672028336,915894299,222212385,747040848,29717427,536692715,537741168,68557858,529908355,925525054,723564103,749734152,127618458,218788309,273560767,150550763,818757110,513408053,750909587,820447446,757746587,609764972,726604054,553661085,364582163,6558703,745309437,469554512,641371325,630605959,879792270,881382316,44318474,515481839,487767619,325239780,391753912,624557715,503735848,774960220,549578385,754876394,364935467,431195332,977947859,650289744,28493056,290382994,755550605,813293182,489944789,367995598,522654735,774036528,628202,999144579,671290345,569174677,458343666,492598383,133594007,873244715,584279889,66764307,870109380,720511500,890678716,602938644,90456921,993807437,191182016,724910674,789266159,534091656,342295564,719429029,860168315,481534856,329806368,391955861,119243817,275245688,994132342,165982990,155278127,540714868,821251099,333061658,586398297,768989366,714371315,778418865,343650813,591460,797823027,595268833,990969525,919018415,958958809,199882894,336717054,20077523,850057385,321728314,121020665,1343260,925881231,668705410,321784184,808592349,391118754,660008974,420233850,602234948,407340367,661353672,744257651,815500464,190276310,168479398,941264870,116195607,495744550,94964988,157965851,859781202,655005953,97696788,509288625,556860543,748541788,303125746,195427884,889331299,247868334,556085863,405261693,175560655,444370633,265334663,244729546,97717868,266411193,217315749,949418003,152880893,925628826,878310302,955883994,478079950,6940317,674190056,555472480,629053602,157968066,222355295,479946974,937009087,955895938,324725326,516998990,614410256,280203491,297181516,916629944,11096007,332276458,268357426,926537970,346012258,423392214,848883877,256557832,973289092,702622990,658536500,914699539,438359248,514053084,796552058,638730800,182819084,410104789,422346054,863875406,456358199,465392898,826103416,126312326,942371174,616280334,643311732,287137961,27407002,717017904,720539024,636772212,9861900,37865927,937328761,613088977,94559372,447299767,209835907,730933425,562961268,108470112,155716913,682827888,714685094,150225297,503695819,205400450,701863420,811573137,857288248,984086372,294980261,895188017,956303125,782226873,448850876,433591645,611729409,662628837,673391492,596175844,853112366,838839125,811032669,172344573,80352034,368154191,58268655,162416530,921569461,54788399,510245430,885906802,114645119,73355817,640792722,889054980,540769992,503605531,230736138,947067637,898161097,139880466,669390558,912323325,95830533,168560167,913638521,350595196,15389536,952425965,989877815,151332856,262594622,803191010,703829622,498393117,400209873,538438973,950012225,988067573,739508368,477707563,892646633,221393382,964292431,66162791,297451030,856349397,919839022,426157765,492724545,366237289,964053279,358450017,1698642,130704184,121859568,115262953,108821505,101062846,729688291,488488526,892978365,545936921,695373803,691150142,831117463,949924547,570801715,914736174,400580229,720547644,277698472,535295478,464691114,859296857,525721179,119924538,67642294,413930211,877155087,487468228,264864959,658848827,4146686,477191629,497959527,933237121,989772583,810934350,115097273,192941771,698878255,473315719,727580621,313896600,850207590,739280839,516392118,400697724,768786428,722135611,888454891,413202324,306583441,783402174,9026376,596336524,113817502,990474316,64453806,100002800,917381457,850748273,44510709,630535017,501786958,98652522,189001108,497077252,600897515,687699021,922054932,921023527,976741483,792679625,507879800,828434355,223648825,216867759,396302851,8248427,152372719,5923185,748905038,836790888,350401439,738243211,195622802,427735671,279341754,78372926,104186983,660498894,969101515,544425044,390842635,258448021,270992748,960380026,282097525,859046480,344105508,25804630,8832677,175487641,936956961,271658708,297774470,826483570,170588533,193601935,852960221,645159345,933408798,374167557,352267367,608972219,337991382,62798519,854907199,628451501,458761703,501172521,493190109,654616741,361823526,73422023,321759705,74911191,58892490,324475541,500493751,149577311,542065433,924728737,997842545,345986259,944483488,779327915,601757163,50120781,382939439,264081707,327031694,766341036,630643964,603762514,938736325,448450838,73979087,976368514,774852703,306383509,369680408,290835916,214986481,944386434,579211667,738993523,903409211,484843591,882819808,287200892,413265326,649417573,555268558,91798027,434989838,486211865,221862194,645431046,882957304,785729794,445325511,107841471,473916793,576367154,982322812,460474370,746609906,655780755,697554966,80087632,701006112,933220501,620638300,514348347,132843044,488175669,583480092,693769043,24378119,215856304,534808252,896325689,657495152,719672256,49763542,889324845,4618439,912662553,130060238,646792977,72144674,935526455,461015091,607375880,317840515,522310567,724157592,760925301,671581823,89781803,327644977,98227613,541929272,855712993,790975516,793461500,600021907,31180142,142724787,366128074,616638778,392905428,97650171,460384803,162834894,507691726,382151041,433707680,170111831,877703417,496492504,365433759,279987271,792253573,235982871,600349051,68698749,361607717,551673207,1372573,83189727,237523015,384887377,618945424,184632664,406494692,171512200,518008355,210269912,463140052,807164545,918549390,48965117,965329451,838882608,559474197,116433526,317677278,905146085,889034949,199004257,822942751,285477073,66734330,809911448,41751070,887083215,663937293,364234500,820806328,310146980,571937004,223708876,78192486,602049123,724536383,115185668,782751816,685608146,16846065,39463383,994387759,348895197,635701266,266121168,841401716,723450916,613276316,683786244,567410148,638184266,757015353,279931831,460852034,677811669,262196199,919158955,242575641,563509680,958237764,169713881,258454415,21755009,981794004,810686636,202005419,324898578,823962195,133849249,256139961,628339174,778816233,658398595,469735556,757379846,61281469,586313713,763579662,829294525,75849987,490182883,879725113,206342160,63332122,853405588,734556919,600692997,270297807,756951293,191183884,450932223,33618478,192338547,54031400,946060757,420699488,532320117,786564213,966729305,232877944,197735597,753703521,398041727,699222916,536923117,976897578,687482986,593523361,722821343,491405725,711771666,793951247,196260215,182036596,382076924,611165991,474514519,854636013,20621310,784296127,887363025,664656870,377226639,884593334,447435712,709696871,759076171,899828880,550305113,718863289,536896287,589767316,81551672,645796876,49370081,641012175,413250254,100792787,125247387,658036178,960166618,455794821,578046728,315348526,438706081,82556988,748268880,814115033,947991369,174739502,704988018,239650480,261128678,769291883,621571206,871319236,205025934,366915144,651944879,467795206,444544916,347933352,43702630,774670048,227974959,98776598,866275491,604679067,941677342,928391879,214284361,555059124,157313656,632315275,393126472,689494114,68366839,682759529,17471479,954590909,13823078,57925393,224801320,514032497,897765185,228761104,815426125,194282903,487266850,611660234,867373726,960604843,698372703,964469875,105963424,316698492,891380144,139212196,776842099,63398434,263240275,947377297,345955898,919286140,224343974,378133897,192641972,700845933,679612410,972667773,634377695,590679814,98515948,468081963,983056966,961205589,930294818,381436962,214938154,90552494,149559181,229749692,651914292,821420519,254402882,147434251,317101022,629679310,958934384,971692206,948927195,68548340,701548969,150886583,950138832,999380680,971651159,518753040,6086976,550680153,670525646,887518080,871082032,916976468,340582788,539269699,601656911,766791702,410141494,411393816,303302893,963223989,249664812,312951817,748062331,689635353,836746516,668092466,688927897,440950252,950934434,10149463,829247481,577092509,572089306,867681669,994652202,92254018,703799356,738109009,932749098,821901912,227787640,433837128,916448504,890767153,263479333,648895515,163527647,153976380,806822913,640553885,931546657,529577840,381918487,55755454,963841992,29774879,73070481,91190908,732864432,241266401,420396844,64395649,779867698,258799998,113697045,143184483,893418924,938129908,664916654,354027610,859437941,446781615,140388754,204974649,840083045,798587566,353129433,670767968,417262036,803621632,494844587,280872953,778812000,796255855,279748975,127844011,774942486,161612155,521054808,698636477,109253870,443270205,659556487,40294050,989363141,274080983,485596696,405396020,325007728,990588179,482428079,868127501,648389427,746869371,657386122,349555058,473133458,343415810,363771115,502465684,779227873,993364502,378175975,77302929,512357277,175814340,817870545,373300666,604782763,64255541,2214539,81550646,360719317,976226572,731441885,653523665,979721882,9330267,313992319,258090962,379842127,875025129,664472453,316651510,107899667,660486146,418291868,461675585,456694025,177225434,787766805,911751883,785997960,152563593,181498196,258884,216687504,250192114,416397107,417516694,435495696,637075511,50984967,573980690,37533675,56553607,901978256,34494676,176025365,106140922,185893473,269601071,709835300,930542375,168557572,496768234,673763401,616217155,321480892,794087295,457700163,868016196,291596345,942015295,625691075,273909643,592190552,852488240,399499848,556165191,489359885,129568112,800365078,333805942,355788805,907681260,159284826,995744864,741232025,555837554,931921569,37724386,66263429,553490624,345960566,673015539,678255473,75405860,589572586,301762983,775232981,17819123,964609596,535179120,246828605,646897318,293971463,884454320,853272789,202164254,712712304,100021558,715698046,641021271,423398467,30329467,640959401,370144910,577869732,531553222,952661213,629143592,473306666,525868067,132231361,455549832,923126570,16897931,760508698,746734443,321265976,801615064,629640504,135185157,841390784,254387158,643067529,423859076,183402204,940744771,943762163,928143559,890021529,92693596,400574286,587306695,32474354,902437907,180328066,391013110,991598451,52967518,375359927,204757994,3997422,364479846,237801441,355132617,223047978,519452611,752869282,434093398,639401072,879014581,839872692,548777107,899006654,773805464,636143572,277884871,76117247,860353160,206225887,908820795,356114709,752646342,995466954,829716235,483996844,683610915,278939426,2316862,178105255,655646720,754007543,136000486,572992265,213849956,159558037,47033762,639353143,182151402,861708999,638102271,201691564,809504671,175943907,436950401,369573105,694409097,310969603,23093920,244783879,819111309,323263034,241280486,682971481,651110858,323996111,991520365,950673087,937259922,305938155,443734530,505922349,504236137,781832769,664443096,745475285,299352851,651253262,441508399,382787831,302320899,591965246,700780305,488954611,474210594,67516144,951082318,301746779,722100011,830257970,570522111,157063836,636086032,383942655,351819255,964260734,543017367,314740115,446974206,552803023,903643190,288008195,853354274,502653663,595456232,916413949,905706602,862737804,490594408,720122318,214996181,55665801,556151635,218208816,209786340,860724701,240363366,987926115,65097180,966848024,880038450,515427870,521154930,973242411,688498481,958991649,810334446,452760477,329344568,550375046,869350590,403146856,462022672,955116119,840997269,187861294,215111406,284519907,185158028,83098910,339777865,920741958,306151975,412039219,220301073,270659609,150700476,791860001,515087903,99985323,639332802,789356218,393684242,417913236,276078561,584077558,932111118,798593999,471983366,915948692,380706076,640307789,289597026,819267111,309690170,697209772,203980185,928574802,525862372,772493078,644789710,563474311,992164544,789564693,589829965,712458214,619318388,653664004,447632757,16047422,939599351,284176357,840559705,142630309,192318742,583508686,46264757,338689231,721372220,301337590,138408839,299752442,885532104,498144571,912476784,134253203,932717063,690172052,493205759,505801717,908531683,502472289,265284333,13265817,972869690,898489491,387225368,259801955,860932241,830889479,687674375,792206376,910422713,709872461,336698326,647542695,763473138,147188997,863199307,855911593,671945826,214753814,293304215,649449157,209922947,618598383,222928198,127997039,879228418,531576165,451305197,619341229,156750419,889794061,77340724,700526866,976005153,405771660,34234933,513796725,581019718,473838283,172254630,170997985,999194049,82717063,875609788,110686257,108295888,64467120,790556317,833923175,946475349,167455980,125737323,365530517,534184033,593468980,511430785,660626964,644297441,859729011,760928551,623565725,59785947,282398195,833533173,799663331,114241559,652771138,864451978,446537877,512652173,859761520,508999208,860218326,324794291,765689053,263548042,972995356,865256599,865971266,835144821,726487852,33466077,382936577,581209928,581265683,369067891,364891461,345215638,499872909,93826108,423734458,223281483,490374026,708727470,581090698,900459751,144075333,650236361,818999583,87079640,879539973,464527202,642560812,378372615,271846570,461660973,178567249,187178160,62331872,107026467,536478127,187126185,243364699,398771962,666870782,474380267,18783046,226908428,860265261,720200301,304321358,485824788,438609825,351829491,523896804,819577522,87767990,680091651,901748107,279965105,759547296,19562538,70064070,397987613,564571052,796582190,208591267,907138438,956739214,404197312,364486726,198759762,305067213,597775162,440828363,808315240,816986179,428309774,366778698,725958821,777062351,957013338,7752993,10438773,746796021,790558409,482088709,707732774,907349424,25171715,700203184,586401774,270732973,261080065,349197492,230231597,5679054,926858730,58251137,759503443,812264687,500408885,43008347,845267150,2200374,383182724,795451872,212872573,834333970,729785725,319019569,712537638,387849536,144703645,554278090,451985505,735772914,951185,751728022,459819356,603499068,56199263,395978658,507365650,963017525,124556977,869217543,72162700,68009615,934355239,128723638,780675953,738222374,903183717,197261464,33043292,791336786,461913181,963957525,947650009,411844852,868317201,978097606,147996322,774561247,950731035,737506748,111072707,754309305,525125529,390247777,245730650,977015953,237815128,355598027,142122758,655014732,10049278,730184028,446901465,660792337,903573662,673656367,543177966,531743240,436194664,962866542,892831330,114554574,422511190,924535573,822659052,710964679,739794638,451482549,272696852,56124510,775737013,382853528,504877089,968169526,179687731,969963155,57343976,546657279,198091917,146518104,779788890,332691946,133375133,58724479,254195019,362083249,620835894,532355152,737893982,885882619,199504576,762123620,811279141,108637628,86932595,461396390,95202920,909930507,628017247,284887067,465387218,669005042,453844298,336121821,345920145,73572337,943416144,345713712,4730647,597685195,64099836,443978218,34444401,662477645,961638482,874826318,278731265,583179029,942178167,398832785,968880001,653514707,154686847,824091557,902191408,702340557,541910997,592867123,636629469,622081971,936769215,278021858,862391053,358828979,566548835,799492075,760692512,253426773,866568153,165009043,812804844,912119853,999213594,198813879,132730706,826973159,754603174,421392120,656768946,818931755,467283512,696775331,212814487,339644111,491810534,725585345,223291482,482728231,106285685,345389851,961661232,322899509,451518672,565117889,311695435,922639884,769668417,880541609,10901242,620399370,474147457,374162112,104176444,268377356,458372134,850411561,943734150,388087834,674226959,181565439,109173349,553869666,550982418,530073839,38076583,853546011,671212137,350706116,196385491,52217158,481167254,664325336,717192779,747939052,58226013,995772957,359348711,552272867,696833772,919746387,175495197,457030670,759255064,472368948,720992674,370323625,301258761,86899934,928774473,803027508,671442291,436134238,624808390,290916614,787585444,542811032,677631673,754431554,311924692,331649949,71919016,509962117,35672311,150628057,800237186,729432466,876072003,148504727,725290605,169420004,185717796,621238417,908934560,869338099,47549438,280995979,735050858,943909456,89271551,785459162,134327483,860356854,890759887,742230100,747534522,984913929,768069568,445785737,400706340,906539792,229683507,514869277,562602322,950306927,720800453,962066829,601657707,146269499,954179608,259340985,686536458,396204358,497180341,231249909,250061339,107886675,957852843,59198940,707503827,952861891,193717658,934210773,614463531,86852728,276414396,396938179,171939710,799798850,141537934,771881356,131348229,507103325,753467414,926860902,124716,957411702,198689836,911820320,450430411,306952628,188542495,140646847,935832757,216331719,642149508,156351903,846630921,901718847,67105501,94679764,590463700,781576715,750831719,694955041,117573000,597296755,943036273,7493082,80609630,787958618,846558906,263950412,586063651,577875894,941625848,640826037,778127079,39742959,297141688,98508886,325618883,487919372,738929033,266420982,520233281,231296565,788705034,570512930,412786025,417697471,492326925,909570471,450149363,799403854,322086285,153200686,582109031,983091533,24195154,711799734,983784449,349535720,104701583,653514946,314091700,547541263,113744788,867474822,454800400,745791667,871429420,955468772,572401871,449397612,772280813,976233000,398619826,174564971,547611947,452642073,15088898,536454986,16874743,720672122,391224104,533249769,774061315,139705505,953759907,96651454,438058500,153308743,361424514,344782004,396862252,469811996,38114783,961916863,632865453,208548064,329308497,186470437,74258419,975561387,100285645,701264070,499613603,372646473,127929546,209673907,19048355,288247238,480734793,313965523,740682193,779934265,827076393,349694234,862327055,702966258,662440874,766263578,191384674,977080702,696796353,66074681,77011354,355279545,624721031,995942278,478697337,782226561,775343922,414646145,830217523,26568057,441600052,122035019,412308580,10489392,740577468,740432463,316798408,317407092,510979917,895162003,948174649,2671717,594790675,725934755,370075525,57495890,485773283,222487416,937874779,47548852,567195324,790975150,222949700,314113228,116842798,226695334,899111149,942000514,534065023,107821628,633997224,250090618,588053318,580542779,333343469,491826710,489964033,952061728,533378537,535874879,30918500,299710700,607729747,376705035,506468183,709076221,330888103,196597535,990181729,785005795,190323543,480220247,872679565,564619487,962082712,36751351,280982519,340274810,800613925,982517340,44560119,345597601,5594534,547112951,41870050,638883491,747570911,116092859,243514312,331478236,109115157,358368355,917833387,652343622,712529678,318708924,327560720,569636428,918782274,127075784,389666504,653231216,416406916,83632048,667595624,668858570,643491720,334484520,507772757,653072082,597226066,519587298,898546577,524143152,899068834,567756824,258147460,586015727,954020388,904887708,395499457,355890994,130193344,667311543,155289239,411973709,654796204,493259389,925371130,752417076,170658823,170329644,278735048,333047104,303868411,770671897,516901758,129907273,583067701,520563689,210540619,998881928,164980413,666680263,363403531,551011783,646860963,178973367,461862676,206263507,551097288,795828664,401791471,978658968,264647751,980923430,91068617,989996578,950379576,776805450,154348705,746921277,168948690,335145042,568492976,268018302,919955319,40300882,697989546,468212146,826133082,648570545,349378137,327675621,315418824,252119695,270107647,885226320,115416927,275937285,724524232,575337924,840665099,454794869,40478421,206428614,35067947,74890048,185345864,499180468,726720133,853430765,965088656,877401051,206224955,748528026,324962538,469964948,666667170,662056235,303583796,889223655,149705173,74782208,591367713,904827864,554665586,611622377,221531078,160021066,288492233,150152528,224394866,938878845,462309160,134338005,673470198,402844359,243318513,61715317,92770232,398577986,911381346,96718859,589209046,405963117,92562941,779923789,857066605,625148382,569866988,418815119,425675481,933247713,882673737,181222115,433273745,825858037,727636642,914271959,449364370,59533729,391998246,180647034,923794771,506346128,497894986,427490308,9213902,93661109,696335737,531978168,908923441,827237693,107570019,63916414,589052919,700245492,866401007,741898037,17243188,213066917,629382906,914209278,439775082,462605295,702015303,475516191,596977323,678766424,413686967,968871449,989335063,402060680,511829003,521269563,575929391,670679975,810994315,433735066,498408972,261828415,524905320,470948525,321697078,441112421,353527980,970890722,992347966,479773899,153368048,10776048,76265419,641670862,688917567,351204726,144090918,382048353,507851105,506899034,688959668,964918644,559028713,216535059,920750971,546254867,523651414,919088432,284898138,226987017,833586546,27780013,377386538,139108090,937790532,95088177,984204552,440684860,232719018,1423609,498694598,896563826,62647001,592354253,438382475,475673664,594806747,101098861,322937160,500402153,110228525,370807630,41673914,83998989,392154875,349873061,333345973,745415232,824363738,344275938,391986278,353163811,459472074,919416593,420330952,765789949,672693431,265715909,984193929,224138260,819101289,539135368,322388192,445633267,932220599,227320480,652913053,664386949,203671148,922542230,341050273,248553876,201921244,128017402,759109790,988056432,577382941,576147690,689850992,782108393,542185150,631395444,918583064,81877140,445187122,349935209,267431393,478408055,63507915,542117714,996071216,947462211,505042622,792653509,979263359,784268792,138952849,359266976,811540992,727009988,873415025,832395569,575419277,953604068,589749485,553279250,939825974,734894525,411828750,203737489,499987707,549979231,198203785,894500623,374712649,780442036,441778502,949674534,39911992,607671830,221765382,83130672,244781664,588248675,811757377,132468530,960763769,399064741,627846711,971835920,223060647,980467687,706608880,139473897,140567754,139685891,967868333,638958639,19250527,177166513,51810968,539128963,870120672,427631287,8346917,601179035,689820975,849244133,939685743,993398601,732659092,279997513,377209057,44393039,701421716,405538512,207913679,772076791,369570697,565238316,282322732,983565187,567332291,840873263,821903545,779719533,988129401,222273125,203797053,900466263,18660694,885537126,939819916,784152643,151594394,154414018,730681296,818908938,661098792,167702285,971292417,624719642,612345735,890260200,144333969,876235914,914143296,933074433,735312526,134136524,616899172,862141300,741020009,909288874,537699341,217698593,81877788,385103937,391247931,801816131,235496821,982135698,229509805,286970332,574841584,347862820,101840303,241748457,522642993,53161906,560691408,848342186,569994788,454406585,371649414,333786824,809401369,902748409,568504360,286833625,412964020,662520054,773250748,679732648,150035217,897980756,494869494,449540250,542296561,265595008,382981371,924477491,134717079,133056710,917978347,614006334,670176685,746798485,735656344,488929175,428507135,817848944,342594056,872115327,775977629,537754796,559734861,162965433,763617839,239862345,508291727,620652702,8145079,616217448,291247069,204069593,970744827,629572248,408007855,272425597,929608198,164875916,448572389,483641301,38956653,138331288,136336801,684740612,483277857,900476530,141375110,166039553,829563729,417196428,964351213,198222622,47748509,787274226,846378956,914223020,309081083,486841750,463566660,14189499,388612900,53289932,869169023,23211622,764099938,302709508,776274715,46057065,29104467,687030075,491024624,881123055,887416098,381347622,4132814,584698880,243579392,930879064,650059142,734486582,384258381,947574430,824615290,577931976,325661112,800855654,466500680,288200136,818357062,811771802,65043421,401248911,492927505,617859619,408475767,782969815,3890861,459622678,254007108,328971038,792881518,551756045,663588618,350710088,915604365,615553505,884043476,952060725,611000570,735431299,664508295,220688828,963624513,845091592,543772397,626825748,54119603,705996709,947766647,698229362,770760330,176144618,441283506,347814058,613954826,372137841,967614189,739411179,422360550,483086844,828018563,536784204,748362935,2313162,232275378,234168674,60678516,352433550,298893845,305409363,346469728,583333127,653039090,993112303,577668847,149148393,852744295,344712757,104941401,615070849,535841149,427013932,664692856,585488941,567335266,961923364,331617109,469908193,33283780,275919334,810045506,964088026,116706236,210942758,966796168,595043440,190247245,202782275,230874509,25856892,888561835,722479693,319063839,629052807,734566924,819173784,202707782,315429728,67904156,166736968,18201645,669652881,78103971,185342104,652197195,834545140,363258435,483625000,932934874,430829748,919231131,413581357,758683888,845912704,934225207,747148483,245797665,577246701,946862924,810494262,54467575,8563578,836796708,696600869,44024824,890350092,354607073,405331443,572885996,331855907,57160995,48159860,548708400,742858522,702743360,793239258,199904901,685575879,381640743,691169081,310638083,422987144,614571227,166570023,861083416,722490704,225559707,247451503,536426048,796731157,887103151,663872280,415524391,406706095,538835510,617618818,523517090,905393111,794623012,978387757,871937368,839527768,564322329,488390223,680181084,497952296,232876421,276131633,671876251,785615385,992558854,547356617,118788207,318102586,28902099,187230733,353428726,494288425,64312827,107712374,829947954,194381466,662746748,414238679,878127216,296273695,99233563,2484173,498693345,853963941,759134350,242743391,94090522,458370961,394845025,488827847,179537266,134483168,575279627,998881447,744561956,954984521,490146178,875923936,344650215,581458567,284217889,646468353,350382856,814961825,245881373,989817819,342640887,869795005,766406697,76258375,137279020,412648312,620291299,847793461,206453701,610848239,570869515,637173285,12846314,265058138,451605674,655573736,476755509,150049681,511104442,931197591,618929725,756696525,177324251,35839840,489377057,125522598,354061160,383810610,564713707,903373809,655753350,148466035,863702365,671636014,705961933,144628830,695109445,506931042,584216108,203179764,950857195,882762697,557191692,555091889,905209447,944196355,708752343,216554384,670453139,143841978,240518843,909945696,981014855,172939695,838148255,257301290,790167332,151986520,738532057,848977025,127684000,409058235,325019967,611972437,454318907,249553635,135309081,401749309,684758785,73875128,288674211,666430061,969168468,985644463,631170963,594976430,656602868,670386948,367156479,28510661,422105503,105424818,994603967,322821288,351105806,261803542,122166152,444819935,372014900,807049779,200684019,675053563,691393462,162566942,725415327,588257077,725004959,157304980,135710841,239095901,671517518,602373282,666126618,331555401,833166447,692807727,655612560,348071134,310295031,21303143,497365956,469081063,219673052,373575700,304936818,55302661,737465742,637034052,885439243,575017121,824623675,652937689,845535,502232547,86088115,678215311,358916993,510951781,12103420,167407925,824851462,986122879,394186585,642641084,559633872,167591727,358908350,30128823,366134484,56204737,541057559,617471995,799501729,66623751,162781622,988792200,135560857,395680581,718756389,996249747,115364417,844502624,551223311,37107479,49286063,405672368,670512192,426271705,624532725,484526898,937554445,353592178,924070025,636865276,568095126,738912872,56004929,888136322,59901936,774914828,43969641,620127214,806159563,886569908,103787643,392097310,823503483,380781902,427800493,734649320,451834437,613773743,733820570,172471236,895736395,198548470,957459719,788218702,156326431,179388648,910148542,358081165,516486445,578026012,18076034,701790250,892392336,487666386,286840743,63927152,566725969,935619922,27721475,470010018,533840600,746060516,295330676,107321776,593958297,519828961,790846731,819630581,925930360,885566570,497978307,669841998,254354238,432981576,846921077,257185745,589102543,520454041,847277563,99763844,134827423,384830128,538094628,730256251,291969721,579018262,989157167,448447615,500200552,521707077,701210127,243939300,429208388,510916578,250281403,916718957,781922007,40190486,759736074,398006560,713768183,766816737,13393537,408128304,152396215,25269402,932451956,746912820,914488064,364912144,664101881,463277605,480038682,780772797,368389374,760991028,628260058,192146349,306746209,162704552,522268750,707410297,100371424,425198477,742986144,896530082,432030643,21889572,793934724,829287380,487877131,231867225,500150758,25662193,549792915,111468022,395905284,588119166,707112684,620906274,748053568,425978696,650242997,378340788,919241237,679078604,786548279,656152424,77233539,233905399,167711567,203079161,332644514,659499690,293596039,574838476,698842554,236582763,196727831,33752114,579782807,138872891,448428555,614133418,893307285,82771886,130281401,963511751,989837738,241559926,734621584,724935266,823105220,536497655,96124784,73535576,833862354,19318338,913006396,992199989,529790773,122097920,71592845,424402409,468228063,31676597,960920758,281018408,380512238,65474737,736923548,488439318,252408697,331613776,767922432,896914087,897258941,165202203,264842610,849021249,433081254,455519893,305349004,389718497,39282132,941988937,953938191,279171149,341359461,846514885,916868310,807480431,210815698,40313024,852753966,424511368,838083238,182778715,653513110,124616508,941558912,962950079,306378595,280791771,839875947,984901754,473980737,261686941,849871678,640716795,940174473,859025949,713530711,623642339,354927971,409722446,746226278,543462092,104572397,906507724,805025678,389034078,440067862,19772432,363606083,272090807,215362777,564215964,746577441,802234729,113105761,750579121,721431656,510107487,927417831,873900002,619134323,727492216,683581666,638788870,739642346,658595589,404463025,660157403,568446917,658157890,842989369,819369776,803081605,864093486,789810083,101395281,125238771,262490553,393638203,259915945,294304615,348323241,152371216,727039376,378552684,209304633,175674489,547742796,377746767,436528047,934267674,503201482,190824376,532359675,740587331,626146467,193931146,176067213,745685481,109917912,154451056,124069035,89026575,40637752,354761820,460950868,493341945,426028060,504836580,464681541,498962060,706851732,52534331,685535535,687329710,829139647,305961348,120548419,269012348,34422619,249615382,398093397,117456860,599013251,810263526,469786355,150039961,233449600,578989773,638529637,909226738,402947961,730834799,281988842,972121365,544115168,172503949,979565072,190775905,24976684,108361153,797739388,343639618,419473393,201451287,410396524,529452920,389402822,708018784,608773330,29792054,974188531,260014456,762323981,661674180,279771043,524911022,924540660,534128983,665429432,740394203,145407354,712561271,152503188,268829965,274363803,817782292,694537338,128666293,120520166,366055703,659279534,126926929,636687240,986268589,330701135,105622414,122436083,924231022,29231315,734081517,366066203,687837102,99426631,200114306,129034582,445271495,250153600,258224439,983647608,100367885,907299628,230609468,97217062,508640009,990634795,917499012,557893298,164006639,782185578,697333950,592999408,447515758,514805932,368963030,319996367,456250771,21127325,618752158,492308982,729758312,582836372,39769418,355476813,503576345,729889093,155822864,219894781,569613469,253744512,369028149,582494797,719318662,754654246,811592611,379604177,78634238,694319818,415867232,66709274,813065956,837420555,539309490,230123370,307521337,674884802,863985284,741482138,150013093,91818102,965592572,543573600,792962283,643328912,269940319,545129630,618644483,16063163,872155589,9075804,670388914,244255811,993335116,895278786,347672976,412439963,290112588,353779577,202961645,398520394,54238991,647136964,35482958,781905131,173673208,316289779,914126296,989639832,862106028,71396619,668352339,718630496,833636081,217938125,151746430,66379535,100528478,642237393,448506012,10311551,515889423,498130239,587869321,567106487,76733845,814539065,967351896,652885806,820432776,177551272,990522804,309134780,442615960,251421801,314646632,752863645,858503616,68986528,475416796,249846489,937184179,198033448,28005164,354595190,76653415,753870656,901733059,61562062,913119101,758546897,937255280,137599481,568490087,739778945,915559485,855331664,424675019,631128967,844511048,694940343,737274162,839660667,338442809,183023358,346011080,669983033,804863992,384215109,576126982,745820960,791762331,59217088,392868589,634539995,495274926,650622005,184708719,799383661,557196254,194605112,529097744,775366150,676724076,941158974,777083727,136206717,492242682,262333541,148141538,644073805,238012530,608852166,879870339,951052761,43675458,634334436,961805963,842222521,157537195,386955379,228957188,303802238,496328991,900729579,879575043,305915677,889154930,275314627,446254316,110326252,36273333,594607370,60765282,235193268,729184720,247029106,849743691,312088823,246965994,337249274,332129441,92722800,530677649,351167662,669758851,578421478,702839029,59029026,30750253,974926957,8021626,240691558,971630791,920205934,710693178,921820344,492717027,456307198,168420917,339702889,194055280,188474434,62029039,421621147,178176995,363487109,813161830,34209933,326223259,263353747,604624601,253469409,243169324,941955138,920171339,314862946,780844439,656641960,512644701,658208893,845473535,521737449,804419326,850566459,692206565,805171613,327816671,338146043,883539726,307933649,81537421,825112209,159637678,922667032,869795048,1124639,35263476,223508534,369413484,703226980,141290420,609844361,919802656,853132386,8670997,731291527,694282488,547445627,538493808,592781813,976059642,501055750,933224373,869451173,263976967,942995396,919319983,798494750,373032193,641754491,758018609,33350212,911178973,886413216,179612963,581942035,228073119,148126907,238389432,539966301,775698418,267214652,690957691,194657744,190569284,930243833,15562079,231249080,957124198,667878345,372016453,148782255,330698556,271598849,257193912,821557968,983570312,129850013,312073036,313849571,74738658,142329274,953309368,970975363,599455994,22364420,19519994,273700795,915045751,203367965,778193701,608065445,820216431,532734234,578043879,147394509,204349702,644004805,770536182,302244873,34894901,176181678,765526189,370357927,773324386,630311736,484426683,592029196,209955734,993475646,780088558,803656449,880596739,328416293,106381557,742991619,786993927,222789129,211030851,119402292,23185375,408127124,317392582,89329336,458222823,56759039,483727340,90526138,168721625,489693651,91124698,404344920,251228066,693102635,432680960,821035486,57915499,826012371,572265095,630530647,506468336,90596087,193294050,785621291,746914179,19806699,719034699,284887025,633169383,433946627,675710148,59705735,839151381,167244022,713131034,643658894,412472518,972976307,344273618,733273955,57610946,508590751,477791227,552674805,949026649,283350746,757127089,892467827,676641017,387750317,204476080,800192554,964400564,506370450,174766919,234605030,463730026,508392089,925509608,504775429,704122040,586592052,731316893,705837481,812152382,739567993,153209434,576467702,846726196,325787040,952556091,945107916,819545943,796148706,601863106,263562426,461540929,440087528,689278845,966130326,573109716,216694712,188672964,535217165,353635292,747328518,190825297,931934871,902399707,893281126,809452214,274164949,659126748,807947700,792816745,976492281,928905343,897401214,57232814,446318460,490996355,651035102,790903702,798603905,376358843,948701180,215085686,364119290,779115284,398781303,341583025,956437429,928422826,223484759,731840491,621736905,495131446,994162598,716591047,91917607,407787377,853405158,590101298,462349175,640264515,201855383,408800965,299157908,948347927,473850850,867485284,326823090,42517569,53883777,700535400,632433867,370110551,501244649,457515459,425526334,502815234,654268451,10072416,888180183,584172114,23766607,178295558,137227361,134606449,705819271,512219490,314155969,694558072,164859853,387298948,102987055,757077584,150307773,542400463,413344458,238804721,472072349,571135842,938289807,841417001,407906655,468700577,265971117,554563007,99186027,122895239,835361506,810940345,102208568,901874743,713879369,104976824,78852608,903368421,180700419,98609185,97656856,902487719,209814059,415757144,260646346,315343858,508226095,87867971,962979640,460000930,174176028,283184807,292527653,279076032,557946486,390511154,615015933,437255705,988236306,131990271,603845466,930086245,551678125,278913337,903989096,638002581,563721878,432089937,526386905,581726896,306789331,856060753,990705495,851369991,690118103,523232730,14892665,204700562,1373488,721760315,501515932,669259946,419178426,236139927,772654272,562544192,306802299,382530695,271945818,848318350,496955072,717557544,442555022,751259102,461052224,236102842,21049734,232943351,918058539,9090258,663494568,474265663,804880762,843867226,258852545,114801704,235671858,622335420,461706721,512886378,502199271,903646309,745000118,159312003,932258080,526450264,952675339,595946237,301109839,592783537,403901267,289597283,543578643,250510422,707628172,861341896,802530412,172770464,420538934,852213502,190504013,695758888,102351987,439720872,440208224,60186190,790487095,149681295,321466924,93653079,79458171,456615266,805458130,375439675,87042012,489000484,343390654,677625023,933315093,126132593,636071349,363212371,16499877,588110327,537772832,296550387,21166148,113126675,929109959,709288826,993791992,200832141,7327721,229128404,970863266,340219476,933441847,102402318,98435654,325937849,178717203,603214445,388202645,949729495,836393954,556678998,913790294,280014351,727524037,228030620,954128854,780185500,655548146,379972153,120179619,466278430,927604879,857799418,557694628,761861359,79757204,438486621,347297946,389933917,679536846,383721925,603262659,251045836,964382451,214173358,184014669,147697325,92290198,956258372,75684953,137245602,567150734,590498599,644132239,551440430,125996724,401013297,480121601,71376732,709478765,43461852,638039084,855332315,376513425,910353225,934639345,261272713,274254347,102737121,832186957,35914858,450514547,199991498,711065994,700008250,997590835,105124255,389085014,892576065,785846601,687302480,339485549,554943744,999444686,33530041,982377961,138377211,719552469,620569023,17074094,548357612,715624492,639733428,609635972,138746641,605504856,199723055,823296693,574640553,300051060,972059668,82637385,481779285,420493852,167650468,437892717,926479679,499476766,264006175,207848936,380208287,141727671,389110882,991142167,667113693,113921289,58008794,737657542,380878378,163873467,409675009,330734981,136208848,278344116,96313195,424719887,256914981,680891767,371385275,41440274,781499389,66822777,24584823,716403257,32567316,672904488,49913872,781599052,697782779,296619989,592527313,564489484,444640269,114448507,873512791,754574283,702698099,412824369,542892931,278312830,891306733,30230411,735889850,852277214,341440907,919124181,146534707,977914257,540665129,918863523,426380983,687028359,762397744,353232657,976242709,208158801,730570167,586675632,340975807,787236267,266792856,280364913,776916150,473222382,216702542,552108785,843663293,624655473,807323079,527286177,446164496,720173067,830023390,667493681,754294078,399623573,624665273,276498053,466087235,911985878,221503982,531361329,562428821,153097998,929269031,722593516,156634322,21250396,581700242,664230624,92014618,341426990,724881452,352547073,523050292,699682492,138357906,578918237,402280578,826431779,217303567,867216358,182766595,855645365,214041553,64029710,354730741,475243533,700321100,80998203,98399701,371120915,74096566,694767423,290134499,840509214,503052081,77297272,623367421,691438484,754673639,928783917,768615374,368965366,660098721,958313365,740926267,594903874,424309748,590947209,543599166,703892547,409813826,171514518,475917010,128315112,79136677,310222346,139968007,580182111,448539150,202977884,674524277,424621511,152826970,389264058,536170253,212306495,866302816,568300922,651652554,417815647,519458371,739329717,574901188,554720556,188072232,293870846,552374190,515410491,680805463,4746529,42512984,636110159,465335811,912844063,650578192,830441586,950917951,425323190,848684032,109816731,792899386,886490378,352181411,453458777,439054898,35318880,187767973,38774519,5863277,703038579,183264894,935566756,595920176,315729608,260950718,486811484,433156556,632456340,857422597,64983742,164478680,82231410,264888008,512331221,110301614,798553974,278917399,236218133,119944420,88119306,178785700,307465873,916423796,568544665,545038233,832229728,415226499,871817685,421714925,412186327,363534777,173198556,952444469,566391935,822420923,89541861,829240697,868938581,68241709,192954301,668977500,91722248,254431588,92392710,883480065,530672115,895611803,787042742,72646555,636294684,63521706,805323152,757891101,776458857,831560052,455899941,988906164,307788772,171605543,345945509,930236553,464323805,109484710,478224224,181723607,574245515,984830189,997250179,536761351,525874336,782684213,158946238,672405339,699302563,739453943,336345180,809656515,54092785,994337860,156204325,15069242,978983456,555823777,702707387,223065093,26101291,458894189,412991820,133432714,930547919,771272201,420958048,983858513,804160192,579912610,826750668,437138053,776749597,742061217,576994999,585652438,941008943,761778107,876226348,875179082,958597163,407137715,412341896,91837888,571524598,46164305,871106572,940150439,391240155,901574140,547956679,585724924,257355736,287872093,748932579,563441651,824621140,263995887,906684810,885522999,54558573,985852669,244510427,63028433,460901247,899361833,953808688,684329788,623076877,815251477,10129633,979545925,947218974,383343974,252305957,556344827,460662776,821078944,271030823,191245889,624427138,79231728,829724850,540423915,154000697,123486002,617251429,721847471,699241717,361877224,477254307,855230220,278228638,790617372,444085509,85769941,490015025,37266445,303592724,262586981,357207850,845154304,608528161,58710581,42082298,183793049,154329101,225994097,215487903,235092341,999347008,543002979,645808000,348702909,458595446,714588861,680369547,544566407,736934611,957695083,885628138,198907484,230645118,622320183,728802961,250593743,799801510,974841470,213687128,72032175,967230262,293664154,7458479,867223319,548151411,15817539,628982741,451365008,74075147,490405975,675915622,755692226,569447311,291909573,179769178,346070778,26274179,302810541,152268541,524490934,621153850,697562539,308525613,874038872,581474584,286499878,960429590,119163983,141594470,335254376,94868524,957467691,573694014,628508978,806983127,975703972,179677422,862480137,807834208,698125512,295512487,969864936,160290564,765408966,32906711,408226000,987190233,447787433,343110609,677601644,769438743,289903466,863533244,822248300,618163953,936326091,306387710,142492955,86233026,135997020,550291574,81714028,930266695,769442174,957909673,150269528,426716444,675834960,205367687,346878958,598256594,821264823,856321772,253911509,8786487,913633241,568033342,728158075,245152779,93676323,35129136,983646587,2201257,249865403,550316192,44577285,150450377,626998041,926329993,601698478,102888324,46382934,83988503,558543257,685485858,257952128,628332747,855211789,520420986,683287273,211096808,885652690,674953186,96038704,488259048,73677243,496190587,30768781,19754867,619307065,305794701,431132884,559418250,550296605,635870463,39606208,575022220,975060256,418342059,699114030,157825540,681340257,177579415,783313872,863790095,40804134,306875464,511183722,650636629,758585433,638171251,107511374,2885159,217028453,108055671,569594255,123788565,643919490,124524164,924467619,471284684,400343494,778660350,727399399,841377244,981294301,680328947,360637549,538208017,470731827,580578591,39176244,612708372,949026923,189538205,110982403,954096762,205585015,961417095,199517490,564741225,808955062,469702020,95677991,945991274,778992058,666371965,609044547,574956721,848214266,666062628,130736728,317227333,26267830,647310004,879684774,581856858,707355730,86594110,887539222,987281372,355941808,319510045,371570830,9046870,829456509,754643791,903950572,821580572,687568117,428528014,656627365,245322325,49647555,396478463,89255606,661145648,914414719,138277983,219707665,893849844,26656244,900041516,984321098,465115748,583714272,726560135,787036406,891822632,64633338,615524107,835774842,155501692,292515897,525772761,174657201,811443773,703294781,659484040,484979348,677272304,324069876,84243081,653258134,157979731,788775878,425048081,850145509,377477858,4583264,686181972,445777988,710406211,846115413,682921342,378117741,16573341,316563778,718050238,357943521,47663131,127307593,344740950,173119391,790788209,650156235,563914756,947577292,975436541,733084898,251430671,6859198,347706946,718971182,66022690,749603765,388879425,310247847,974515647,793866710,187293754,315691419,284653349,462021520,54784050,568574199,750620701,40193936,316666892,50328300,130952345,876266650,999464026,143565434,544580883,899133100,325360051,957472876,317652370,337558722,683138360,95363608,19763552,481123669,678594654,288161027,75552252,768203949,953689910,490100323,812375572,573172693,186297906,84201018,650870576,531800335,684132429,709428636,602041766,615887875,683572718,482795367,354919268,184575869,507644202,369428113,656872221,120694927,829851914,286653640,240746981,374245048,72163470,345555261,885824036,445400826,347794534,447958322,93130989,469778578,132506715,79992681,96368065,788966877,114989268,760490508,477709053,809546095,108100828,199174490,189258858,827340402,689903608,234042555,361228349,232492739,185052652,881553165,377774032,570448215,627621878,134553570,330718431,209763675,23159396,491954935,413024162,633947985,320789588,53737204,138871245,497333218,831945636,842456634,469321392,717447831,91636908,698532027,47050706,349512883,928612402,495819992,289792675,327404236,691503333,719551927,315011844,484164123,99949498,418131281,280378905,816993792,511635623,495931317,308783008,676606688,384239110,241582198,57642143,342500957,476912234,910900189,244541565,453023175,380319380,383745938,765235807,452977621,260834936,971898759,165531105,497190424,434276999,591450347,818056997,619233824,528276062,434287483,522082977,795203591,141345390,576302045,440430788,188963637,999838785,60869151,995184163,514574854,666365035,166168718,535919814,859194064,206031033,853281206,946174336,776819657,467466391,141698776,199982233,791213874,295230579,418058720,146257286,70380768,331223602,615031339,536537480,673491521,425580368,23760053,251476495,104891501,866168897,9691683,331191207,471259250,560543428,661538440,540119941,286788749,928580692,863744245,374316290,342498386,481380568,491143081,400067176,191832734,54717725,364801109,595650801,329044803,829388528,916359643,351518710,713460927,452054370,558827781,302842305,395770936,793077864,722479105,878116789,655639768,825569987,212684301,389568985,550117556,52076649,807819676,663840550,595713436,898144167,142714782,127553682,325413251,461850354,248337119,671051592,266066902,922635954,60614892,499326409,571672294,96948425,3159376,871119957,925377617,452419950,971610928,668665237,687355966,294935856,241477400,229118033,753205036,40932138,69579461,748918960,641454303,795717399,650146221,231208490,612160177,303899382,705853296,237428098,653069094,498894447,696097233,981990191,433845667,261804061,821586170,144895056,388581854,959310827,155649003,658181112,393471247,900309915,73709580,782560743,408482929,689733641,759818920,853405736,455630702,220542685,19870438,564928725,542200089,125923296,668801144,237333080,273899713,332373878,196217589,686601412,638499155,926033908,750766017,446461267,884109181,140630643,947042932,614973853,545374865,398920732,239043339,41697951,227244766,256698556,614865451,259398429,33317501,571584374,889110885,446986664,118247030,146547300,218299090,476006011,261747645,83448967,694054968,214696057,556485499,33098010,854320745,418383339,678071342,666252086,446061583,267148533,38829983,885888000,16023463,38329666,299938370,734756662,656078553,269205127,753935433,608446972,547158635,790212256,115127308,251851493,371030783,740236441,213753648,760286870,598770817,249808762,521121155,794025034,569020983,607174132,586509024,313005223,847571618,173759507,403355312,788987081,278832,859904376,550759994,957301706,864325177,294754126,55452887,864483777,560567312,303009654,887897672,932151512,511664648,268574197,717677034,913589507,175323843,545543017,888798668,954052275,502977956,532901828,550801939,856252391,815208507,801812019,518686222,630203973,849571583,866160535,566881172,404597663,170464173,857676288,999982190,232096451,6069448,324308623,185345778,924414595,73826138,341104625,688156167,101126695,801480542,170725643,822572938,312060613,508362276,318077565,365300133,695137291,449752190,998330819,52904729,96415872,201641437,750875490,645003878,327874060,572102929,250133348,662567843,443980719,201882098,183059194,180042746,507078715,71881461,560299196,928449583,13577233,581736317,878586617,710578921,777619153,155965282,989506113,688155045,173967330,131933866,589663347,11331768,678420865,740223607,460498575,913074134,842036082,838730580,781596230,825167799,974710497,190483910,678020759,890528401,558102915,884330886,959411043,980279159,926337015,901177534,779445831,376447546,324624752,929443223,464405534,517685384,332403134,350283774,250805409,625551730,845677665,460777609,986239248,510013456,309471880,767476993,765885101,231094713,786876924,677774544,494105368,612832135,875449222,491716695,79566034,113097066,13808323,59963398,196441540,668461195,431750359,381817148,129085634,68849391,987364251,330132899,502612434,487448839,825864295,868606011,894737609,351614900,833558396,274580519,596371965,994636973,655611352,577313563,490183246,534704174,80976890,251412922,572421883,908916181,474994380,499953544,292599170,148731358,927200983,25579409,734046214,44882770,890891871,744283722,474533907,984297988,134649817,500775197,216085550,728518935,562655590,863829732,744703051,311184250,325263489,779468739,903001175,890258992,154420480,461759519,607346341,68850759,68760424,303244951,265566401,731239152,260837345,772936865,993540654,435430666,603319671,736238139,222243016,650940119,183487765,973382975,608135421,816532831,897246394,328879145,284745802,734931035,415462922,364690466,725527970,906228735,892914998,358508575,650047821,96017654,802982255,959766107,90754353,302802704,617136851,62145773,604108968,537462118,882954987,531117936,784510392,939429787,131218600,771153473,171192362,427912064,688813846,25218072,185936659,571338233,382747283,78614600,743054684,918403792,209346179,620116301,842118956,765419107,289225059,74571927,614479402,132017303,161837311,287305886,355497295,394658179,235995329,241510174,877114786,774063320,10795290,137441440,785290297,527112834,974793631,482297414,442378484,55326973,369386434,330300548,108588400,656023502,40297767,424467012,620232179,893929311,589041896,876068209,810023703,126679858,216225795,484543672,263012189,271523977,991400284,448812712,153063906,231453107,901653396,170215530,189359135,52823008,644832680,491318868,525937131,327239511,74722374,922497307,814103273,247356188,755652876,127564820,302669855,475636184,203932341,467003554,355073082,252335698,38648228,790522036,307851493,559396442,422429213,581275166,267408232,354896188,170915961,647520858,40488,380856968,34258251,90564002,824297255,874386074,278107521,202696253,750302762,856256491,106452655,481987025,629163041,750001734,415514052,884436577,292661807,196731136,753011830,16157851,665924476,499896161,370449510,110581078,777073606,240927795,225450247,418757538,792705519,378776483,823244693,116991171,436387751,117304953,273405801,497505784,3835513,682979494,917604510,866694993,251152963,333247708,502530096,888565441,978187820,138622963,507639865,484464907,176903343,832058769,317509895,89900239,178369705,616946922,811265265,716607519,515620433,655005296,339043104,54994954,643884593,361688058,20221498,845617967,570230986,142551805,65243006,670636470,804220858,752781586,856830786,729850021,614690426,962497276,392045063,924051620,598523608,883743919,419661906,242840664,789150291,968171013,115599571,975928710,795584337,43039390,610282402,406404126,875635866,747861836,366917288,530488698,509127918,41089615,979211257,401126902,634777584,955556272,507676970,178453513,358921476,885930133,120468437,789177372,844993819,789995642,527990505,374273117,431113876,299841815,130654234,943999436,68317204,678481367,763526343,923853072,13778228,519706265,882842931,334986995,583722392,372102857,329462813,85469543,610242706,165875541,565108096,266057157,730533324,905103899,144931630,461342700,693774784,555511527,505591023,938407851,766931840,162295264,404449679,46362018,139804997,982338351,54754685,557201060,616736716,375232695,457894649,974488701,979233752,229880700,685759307,513908406,375484866,345551835,63352532,877760620,869235160,755937574,228902337,176296633,128267855,624616463,241255656,607320327,618037531,101020260,722396664,744728595,211308975,581820141,907573248,502008405,759464748,374853674,557883925,494459441,114553005,591117153,315093381,893492089,317993477,326662607,834619528,826184083,126155902,175912189,235332849,976344335,879619680,887531518,490843787,813275991,442290019,892855126,247541199,150687918,225783150,6712328,486724098,232005357,603540285,595574935,526598495,251955887,500722906,211795021,994622155,961536362,17665450,769082501,715447661,410923281,684827563,358959913,175054390,483731703,229571902,359417964,250311810,457419076,17951792,145382238,931778914,239906383,620715789,417935678,611379287,713287618,939389533,675606086,995074291,245107683,395468093,535655933,337019028,619577967,702146106,479987151,299713094,789468778,526866547,896614294,113534299,564739240,240359552,232375484,449079394,213646970,667203931,717433071,137995471,167157462,356133593,562721957,660684617,646201219,842552136,422044746,708083980,531058887,684207278,360552691,956130878,971652426,732592704,68408394,540742189,732925790,239860744,992551953,70426752,898163106,117184116,512175074,584711370,882091705,491053892,141734726,925286234,166488279,530881242,727027190,304777872,364589425,386424595,148501319,822870684,398419485,217343939,552736994,27250065,148285520,636613033,908129877,614411942,658943398,180936520,300168858,208650934,402536774,75563694,230058291,368582194,24542154,459020537,791533146,256449046,192692083,68703532,672591567,772074147,123019489,531751046,982065875,130636182,930785763,112913436,265131283,839826477,166890807,957289544,184980259,871034424,155384550,664421039,161282746,133476177,177545611,529615940,385882946,810835630,203749180,526390924,156762477,676701499,432612352,768789331,136938127,799170591,442304173,179511486,238399507,569956998,421909744,650727223,407426214,611323549,475213170,499293316,670799166,186454456,161129004,294214468,799751731,252636787,613446694,277005707,913205320,998755541,647247633,73826897,592330724,673263216,678461823,603390492,8781092,645752558,652021622,524206489,514525893,704861655,688581165,568186893,873107395,849373292,770834261,331747246,462314183,760982363,618903041,726118243,288519666,305326106,233221325,279562949,823019617,738220085,922588126,586872513,814398695,583859747,264955386,293491004,308667484,597455377,27408391,924247758,787370038,83062412,670208734,206182492,633967872,173629690,485660643,971317002,723101592,511758423,176230044,768737463,75653335,107796230,880178425,868270795,299868515,144175917,512073217,529079333,571815881,541011930,591322813,349848748,761461488,258344112,777748380,190273217,10548093,818936014,670546240,993723897,866670120,104392181,377066243,66018464,462148885,725453645,217001639,251330049,505510132,951048626,635212558,302443400,307381682,929765494,820474071,771115509,727777922,490680037,684985893,628665126,989576095,622909211,790955145,610562451,722277591,396652774,963132951,413640979,696275152,459280416,721511550,551808588,502703651,12837376,994340807,298320804,587329649,748076027,480514515,704291004,846974232,982237517,333755009,591435458,456248096,372408703,150543967,533786392,490961889,602619962,395919810,371823257,195322010,643817050,399084237,815859509,892898824,418689376,407469198,367754224,995915342,676363042,139478881,637775159,393063290,258755242,52287638,605808660,858118072,638408519,80529972,310361356,386883293,837467962,910875214,287873433,971565509,485675623,521080423,815070769,486772805,814850735,470459522,875318838,547916279,471624170,18737403,5590020,478877772,362147033,651254068,873154236,944923977,760883549,702890653,574425741,760557139,608287718,40625690,509120830,844550645,431309331,616921184,336551818,190337945,219370871,9914745,490180022,720361270,780057071,828615114,161802857,984751645,119697497,879228134,417306708,135547983,77487055,65178287,352490132,615450486,399251524,476691808,506844409,417848710,575904569,288424424,499767861,975845218,311757130,645273023,281111100,392787653,286817024,124628587,130065562,893746173,351908907,656954786,480873844,223505148,208001649,685294579,543402916,468098614,285728610,459374716,34592629,136905585,597207685,471737889,737228619,440750635,875535811,219749940,437064655,80449658,152966413,605227370,448299899,166643446,9932327,425145177,705738750,722157974,720489652,762589770,555390547,453376552,947815480,268951969,175403937,355516294,608293530,652799728,28433958,391481037,924875917,481396602,710816701,9603692,299987245,856834179,253720093,576330487,877836626,491130102,883056684,509247592,310251906,233746289,543712261,785818511,793023150,827038760,826083,855179064,906989219,41241387,31677763,827595394,654065081,995114848,913557545,690206460,540640154,248266568,664438886,674836573,364176256,232070996,112224402,958452029,147767980,625999204,86413947,573285619,228014452,839002699,78510642,916551509,589462317,384131719,321754750,555013584,431282370,553475229,870473873,742680113,852231348,413313504,804001115,819006176,418834392,627097650,726879521,867274012,645513626,701998344,566968520,888388424,695991772,262643451,618461679,591996869,17695386,551645736,748070688,173498083,607283762,49983679,534257233,616613957,158419308,603830439,989645339,229471125,386432902,278837713,682390600,409967270,205974828,28843942,451207617,643994779,729292311,115156644,212908513,740030058,723801939,310137800,470088154,681998833,920264292,157048096,234218994,58147979,979661896,235767094,790996770,729826334,276609719,535447189,991905076,514085008,241128032,71391927,49105374,258565388,39645327,585934979,551719835,37365730,361494583,623426572,836173707,359180271,369382608,421953761,234940176,651718221,385349719,561047140,389504349,631002093,517159543,249970920,125298789,20867673,83624276,99037996,215434681,886895671,764388644,466594553,310437619,345090705,484010694,878112698,182739076,378528034,811518890,291802458,170964263,947366381,677378257,335145431,402666421,885963173,396136263,92054958,714439470,977840713,198577045,107002132,36015338,161339160,670532136,433814627,347440016,338771924,398922906,331858926,257899265,197964479,711589319,774457556,650819727,985335447,315728811,779483127,655557917,32446776,129001810,408926234,423783765,750375410,639845748,553914863,921493024,125069603,665075485,336160280,854515354,530411876,419468110,807451044,230051744,923764823,650846631,690156286,924937922,953104041,172021342,244720904,138918630,519561679,905666771,425640674,608779694,427786932,952159382,399614741,236427360,441864281,340780465,446140915,749575051,856398681,588888807,177157060,310949971,382542937,229846765,4894881,491235394,803721755,282647824,273145163,218965975,60831846,42416842,382896279,692251686,971325821,933372148,810838594,489985077,503739674,503943674,154968288,749506057,531971063,147120773,871724306,76458248,661220447,881475762,132141574,766645627,890539308,106810302,528720865,273733795,823718521,821021231,400994903,497191232,664538326,778207878,67299450,263888620,737492905,448196727,728970668,677579331,220277796,167271052,236736238,237482033,930294107,50499855,1888217,895767663,947259104,132579223,772009299,941788629,892554414,662493272,466982237,123964124,341583318,987976082,338041035,966269038,178012537,557775881,145620370,267351798,10645528,626232219,466043501,878185393,287227002,812243260,45417510,901159436,143493347,725782475,50381657,85329366,250898081,563511404,170539682,584818232,28016188,843005988,522738530,13695098,602138256,686908231,890663944,49914871,526952257,598689170,171743062,795739991,633893714,57275036,269071702,647941301,699816078,648917744,895784761,712648779,490806364,908222509,706846829,982626552,715855271,811788265,321067434,451807888,635325769,96330743,317761225,1677505,837613400,335350889,205118422,67710082,814977056,896114138,100929865,68731365,480657301,938843374,984666728,858604424,50247322,482754517,623082937,548802180,751412622,457755824,496450474,182371895,763669662,76983778,821734037,852348890,918382977,769720838,967204235,422508640,538896549,401668322,144438225,431904074,960756609,498847453,105122970,983797325,675010601,388332023,742375259,577122964,177563840,728380750,788644230,504905576,180867736,100384475,522811792,303081254,42901905,225363574,176620228,971924437,771603892,204548054,102484862,630953284,219104995,249613905,292240066,960294201,132417951,792567274,141571794,803909988,508349007,962455191,514019073,184454119,115393755,6766034,329954583,722252425,932720671,40476926,650504300,720951521,859133040,843700366,985336241,138294891,928708484,503535432,946579570,970389289,301358549,937137897,297840901,495898058,355607964,166216497,560652457,563362873,586043619,917020583,639698595,66072457,727722456,587743718,199209538,13089083,827326730,592000150,302301407,872478309,552829599,997421131,787088497,519965069,686282616,325504933,349731215,587425749,286942950,381254400,226265238,419611363,418398972,426126589,398572476,183123153,318602287,249468051,426621408,667707408,943792973,662172335,388880363,969748878,107307074,657355528,399000404,828688222,958523734,227311839,884082616,881279659,205954465,515105431,509885054,580172992,74101023,298743563,83353176,288808232,704945423,956790453,490788657,301355387,227385382,669093134,22785254,774936683,764645951,500748199,318793744,993275045,669350331,545104715,433684122,898691791,703982095,283664968,852885264,159104301,524929518,634663891,287242794,791790371,644547935,532347735,919735995,213398831,940312501,704782344,661582322,38050641,366794990,644484176,192469957,33869564,113474696,91446310,512953236,301712747,293780606,709493774,462523590,836905234,867347538,621239475,250525150,670984695,50303414,283922335,686444818,69492861,721627038,938810156,69044029,724656659,191108484,829794115,120127376,573148188,320393413,548811526,615914644,385786456,409108318,889629405,886574837,902920238,891679472,322987360,138682284,795751387,643708142,764327134,267771290,984775043,423221156,870138644,479514999,983313826,770590487,499430760,496600094,397436150,647446439,859569880,156726415,787898313,318283209,386465541,601997043,406915340,67581532,214951179,862384972,82812165,634300855,197250780,809477392,753175013,750703287,668680417,308138252,876399055,543112003,300374628,812782386,25998418,131809246,812349097,721282001,426891829,269318324,224945188,596086152,357663681,394210355,831113001,449028626,387221627,977638567,474440331,121667081,344935681,215046023,808097186,755929345,361156877,914955384,278760051,233698289,537157156,703252401,820184171,97898895,230506395,909902079,440517549,802687963,340513400,138756139,226028522,392916739,577320449,655983550,843802317,344667359,943856343,317212878,101032159,967068816,759454370,702504311,521008567,774313245,700631668,796224028,386661218,279564826,799400645,40081187,660273227,956424440,51059651,225596698,682197897,657453352,646618999,166892547,725016478,667150253,221072381,36127206,543440515,596515942,346042274,498337445,914807253,180169978,270387078,329688297,106116056,876798854,134744838,672841690,906767544,462535751,65205692,322679799,103966541,171844916,175559135,784202943,224885308,9958259,262995829,998034504,895987330,212281078,661247096,744318032,480665999,687475074,906510662,942397725,557346185,614805007,839695184,386008937,410532288,426019092,738352528,640220893,611516608,528669497,469397674,441153237,319428405,880744530,967298856,997349895,612793950,989175655,745909566,412533708,564207165,622996474,109407543,185369211,489195229,507168082,497141213,436892823,151905344,476585306,969886044,103823417,820654864,271431105,830419757,354786034,254648214,252760742,377466155,834440299,263062097,85899529,707401342,412716814,283329982,490700276,780189133,670721163,619460829,200117604,21041586,512949583,632413292,767051132,490831121,40703322,190002776,234403970,500974970,33584660,334230722,278659047,804701329,190333661,413551547,142661142,499207528,132633582,575682821,965181949,155978604,859081981,422740315,689524672,714595938,361413547,297381324,47303227,482701144,926604542,196056935,178206784,104472894,66609729,142940619,887985203,236725162,560057660,874529269,630686669,249055232,474618434,780189296,953181550,663117206,191635968,402922308,612636384,912354696,403781226,520172049,495311600,481895947,889637752,733914401,980512279,932671907,823273603,311169337,652005205,151182480,27377514,545417163,119511827,126396626,994389610,366011053,932011311,500680869,770048131,973528291,579308679,292068022,911601783,103578731,336391696,566363960,698161888,421633786,158054792,924969907,206806666,736178566,763280804,589434960,772512082,499321369,631701757,288148218,34721854,125295696,165408888,334972306,689592424,338148673,819100923,850160893,109772926,940747594,138518902,98634921,857116478,128206058,119605445,586901729,347571247,772402449,72355402,606614008,411339985,76271577,397050132,371324945,885050383,83395750,874164769,268315393,831493746,464881407,192382201,584665199,293239755,303043196,713862244,644478793,337124703,541913134,94460554,321306068,851941186,891778757,347028292,149581085,290367654,951995484,833607600,415216792,978844607,75820154,291886268,330774032,665907025,829950265,663892393,707473095,829009920,175851151,501272858,48120706,258445177,767204129,921939511,327034823,224911882,701201633,286256076,132717578,240010713,974953288,543012412,653648034,460624243,87035737,429066434,654230307,881807237,905153792,234690458,953698938,347271515,513050354,132040646,543057475,452199750,652137031,296809400,597050062,280254423,399384762,141034522,279856786,998013582,618794694,321854288,998527862,465502906,419242801,398216517,929094117,457882524,194810714,215825299,386161431,961293170,753910220,746677956,190881355,864497050,707794596,928105050,818514779,294920008,505698270,551417936,797612215,212809172,753268066,376221867,940871081,403717173,677967543,175855587,101516868,898058518,719613790,487492474,447358719,450478211,52438719,722867360,382889674,331403017,81379113,808194867,830314576,337942816,813035261,956741551,721025944,540370733,15599262,132827813,207563593,349458866,664407188,659968196,5540008,19429970,487594686,916148113,254759959,351833313,620609587,723946353,14049940,708493437,607867628,729747373,301780287,16419504,786261130,565429613,294594579,989421687,368546599,49780837,491346816,113541361,408062844,961117226,982552584,915511639,147895113,471618231,19535368,977827848,871844357,109315167,932246290,295926160,71760219,44605493,559737995,166510747,511666510,242552636,911486738,148598367,663227151,917212398,975794188,454449340,569050040,181977228,375193866,899208054,985025472,709283732,559822883,429770930,672085281,984400907,299586349,696998268,90504196,45942219,588230749,527220530,281837513,159927835,591478080,841456944,318483487,594381876,537573091,985952195,799642226,670233641,809456947,806326590,51288520,320244319,167387591,880831309,980580438,551705895,118935205,933829104,896134046,204666860,984569229,183407434,662406729,313045825,697852905,486245645,4899810,630450093,17083004,847609069,481044058,779016191,227189892,542413511,804501200,406076419,618567976,891929898,779920429,822263603,112132272,322653190,912246934,776994934,849947177,581859856,824691253,948199208,898618152,793726078,934348374,148672143,7450951,321173943,261209452,51193012,584033393,562577015,737827128,84048696,933218626,613761240,444090755,852146311,531464992,482650122,393450997,848181781,397611821,55281351,936381402,440716140,178433418,134519194,352321284,133203390,445591001,479811644,12192345,7987727,280493498,629300503,327267059,470302702,990009751,589911871,212058818,767012543,822654399,884138052,652025745,49629608,272206794,387694927,709142892,357067130,286097531,881045300,314805399,117276995,381089472,565685556,255439079,547370748,395036132,719077646,977184358,386780520,917743504,946697499,110875496,367193638,782123210,830430020,403370760,624750809,223652700,295240700,63947688,286877963,551536466,938501864,64733238,549374591,141811427,531153647,683326817,906024832,790619690,934310559,221959865,82409941,243081522,419986635,243916645,667381431,375596006,362895098,241948167,308305138,526309096,594008888,790813890,283730884,263716494,513038689,439998126,498677215,738396848,794211108,919324139,966363174,338563626,122135522,166872608,311804763,235360451,393700280,54297555,977059627,76334414,658118788,205653177,521507521,590679561,748697976,974845103,988708025,326442996,241921624,579801662,385281277,329184231,345369255,799723643,729311656,236689560,498738253,108812351,827593559,906181,605010227,94691912,12960748,895423931,569606272,985761614,309852241,850722935,387598227,200034612,317733103,916489089,508311554,330376753,802852318,275346687,40630784,405691790,575834948,849839028,723814501,330586055,771969084,436745628,909913099,339235029,723811219,369185572,367033507,358135454,545622064,98874014,632968048,489446106,263904894,252421575,882663809,214269803,888338018,1621874,477015842,426129755,964011555,438304022,672071480,673859618,873975946,474172574,783704238,136272033,151358113,721856077,341530599,763151879,644495285,451262683,752930866,127041624,796696621,25215365,623557098,433068723,917860523,867057776,197690555,364093412,320324769,79675264,343289467,963606647,111826312,371822519,245402368,371818421,336511144,501280598,443463373,594158375,236818071,767884817,724047509,887354573,734606183,683831691,291278613,853156703,950228564,961052273,931128764,584239786,223393400,968821080,530299360,232717712,632538596,150193682,620592387,501342910,959119881,986314913,417330292,112562228,932966444,339514402,887989200,677747927,169647842,90813571,845586056,864170307,101000777,234528732,783075698,966653429,737994789,726235569,817634435,690020613,946418307,979570658,615192107,106089076,65121845,334289727,639980637,493768221,482340850,89202675,433645400,729068659,475853869,180524111,303916783,954338667,280630367,722425009,179779988,586935258,341440210,76671781,917365469,489356387,724604078,466842308,475923298,794655389,988932629,987565863,517215662,594459196,532851036,640886973,77737051,608662959,281800852,296651023,477255648,941783314,726518763,289683336,268492058,108271807,427915656,583083770,512753574,632565070,667604236,143477282,695575242,782122051,764236282,276049610,429473061,449438298,227522302,189600454,367335975,914007463,314926112,356829615,717705956,985204163,559072016,744011854,285805975,58297368,777105918,853253827,893264638,833764803,425006258,672079125,803774240,879341542,457099728,4048852,830794969,921804155,81159042,79386739,843459778,596539145,294471790,289619583,916464575,897922498,188025476,640565729,734092191,668796559,264461676,499104994,527881466,498995600,903561720,787604829,558039112,528355971,402153623,417044739,841998024,151193103,874580160,690540020,801784560,402927102,55004746,387995071,465613199,907231098,514084863,846984664,164156162,893515419,404975885,945880052,892958428,140189155,982555891,343451191,317294487,852826600,842337052,606227086,246125986,418351056,727526009,906835543,352627411,537573517,856502379,171162842,699170280,842721724,869238019,53626260,564020789,843303755,147351299,717641039,550040251,912413503,476291789,658367922,243134402,877441180,407374928,74743424,816025986,219739725,896205455,806625512,289877247,165577368,633325863,637012621,562779551,140542309,458287438,1130508,296673263,846805251,944198507,687753849,118657464,614876011,113983784,811712012,714519865,587293065,191679914,166589090,501573410,102443793,395046709,410447512,889534525,836804909,630232457,641928402,909417391,974269315,978724550,51225928,306335931,794845573,198364286,969982642,699674092,103415785,23895838,10461617,188240161,15234925,345797168,187486148,582079132,937231630,32254290,461607005,581276004,93049156,375116015,411404209,112351813,503343650,524446205,172579418,369490147,285582455,833895854,207354330,139817974,517548494,63323964,768821986,943193397,607490265,759746169,225935431,652252327,577992787,535987464,43359440,294765045,792819011,927460717,973764864,435432389,227741105,626241606,252973260,582247654,53724308,796660387,768064218,178077607,736753164,716473669,589333846,779530829,555862002,414633753,316458969,753367602,813374614,74917483,96078077,977589341,546061943,160906347,30702911,822466810,318497735,67480083,582805906,330675135,754658611,958052772,320884071,502264926,740198994,802452173,819907106,854717541,148192706,407218136,153511264,844813653,753733258,787567576,490394330,258247073,508864221,396013450,895844807,365944368,708892900,813487500,133939227,42598157,55460282,886675408,67855750,501531425,825831749,830962444,882902013,183726482,627569023,249681663,602741667,16505235,971479929,812720557,464855349,541042793,937009296,982307433,6674977,175422150,903973673,910160644,718439940,315998014,760262428,22159916,430135573,566824442,240870436,400108707,858318227,199793675,259738944,702909132,233600028,363799459,513571203,354637403,531234394,552545802,865589092,888352328,525287708,640122454,18245940,536267177,681789241,413937854,500101139,163720900,142927134,993172807,196604184,214317129,285998128,67331158,633313894,754653035,232642546,800447713,792591775,817090020,870703525,372683033,530286084,713467546,200645274,393273752,792739912,464598297,593375968,688049870,168603249,664838983,940446738,980027698,873969546,460744930,9135733,919306980,658606328,945363069,995815162,374671753,282377581,123304082,830495050,765882064,64103955,992488402,345632198,15426156,313474407,386503199,858648768,957555360,265322102,287934155,537448937,795085156,926795931,777826615,673832810,556710158,642425143,288186022,478778106,410457355,200449907,138449875,757741171,334192415,808836828,238392818,976599909,481410146,500482082,465434637,341130764,881584850,222128522,271541209,805701570,928590745,548105624,329798039,824368549,949799167,962658247,766037049,369860083,532413869,246789654,684034451,383497916,82858472,569017669,375755819,854560022,966868824,394919006,229415187,589691832,408690639,772205398,356250918,645197747,184788882,323365929,807891848,593948466,729709375,335055798,745374659,963539697,838224817,433097322,123298110,411493567,740633060,230239713,43260714,96952645,723069020,842808892,795488941,830981684,386340325,11426636,35968683,883694607,688733078,327308325,803178916,907050922,850684827,256083614,156567135,845125030,802195383,370750611,343164291,918888451,964780941,687092004,617322988,696033189,492901858,492200979,667138738,855858481,23702428,350334793,690178784,861358908,484652066,514261409,148881352,537050637,799682303,788472589,453475670,611518947,489671065,702317373,780210891,286198628,461339690,422360966,108790833,121586152,903937890,152704898,838439431,567593763,221952920,460651353,233061513,240408601,304769010,752615955,106066628,265331730,674011489,55805845,917618497,438196952,129229396,824862885,623200783,65185883,950980688,438423989,457491965,685259446,209837254,901455982,250400826,642272743,815798881,179445973,41403691,203454712,646142491,109682846,324221147,293005538,721394637,934077490,248339711,885414527,684241444,127764202,579446074,269122236,738075613,379586671,205044649,174809078,535254007,765473342,438258318,301571298,48432813,748285034,892954715,335334732,567182824,143506361,527638786,528023167,216316310,567411012,216796753,218162791,361092155,146086730,836632018,423860894,466013384,245468921,180048071,561269882,221342813,371618977,354114562,361489885,287642809,447112410,343767334,531161629,357721934,435544532,333647901,119550128,234442909,525075145,65226136,191567231,721228129,662494231,743357247,892125419,576946855,490522111,137759286,941223837,914348471,571176111,801046844,125572008,619586687,627146270,43817317,906198678,715525216,604597887,975797789,97694664,936000258,704150053,409898009,274610661,8137967,436868405,532134650,351607860,203706694,82697306,387149337,926170961,493124782,506342267,397565995,24151049,396059502,803584337,38289207,656268799,620807532,554496384,192032827,186982974,625733791,470851540,915571548,665716425,163618348,914053293,534979161,88898676,131212110,990796578,706662658,822696333,77579504,181214927,222559369,537093181,579260329,457227517,534537257,974157314,931065383,267185479,89906625,267187060,869170631,385035275,995594487,620846649,151877694,160526726,867279414,828280877,117389932,869513057,923179497,993096526,374795592,610412135,989586354,156317069,148155146,315634077,560189559,969726437,100695424,176924833,781508640,858183348,692208137,247251967,879234834,10385494,177144144,714031907,42582006,443363307,780064592,728765501,954113998,278725897,317807642,436741164,892107853,443413033,583682334,295501913,625757758,700174639,1786360,876609768,718695925,438457021,627946205,427634043,633428189,186545373,570371430,208876228,419879340,755633476,369459110,145356475,803899427,593559607,718074119,332806248,528329697,207666037,375877328,255647053,952572000,651760571,622425492,200853768,75900246,240537947,964419036,830035974,273309294,570862133,924100402,408005381,427016761,790581951,830932635,778361110,819185275,979186040,526970229,763242376,637523978,162999189,104763138,756231470,915455954,197039831,862514152,391353545,104813703,404373498,49575142,245598557,349100677,209306338,813279710,292166163,952723293,228005900,919118448,324783654,27957108,818365379,195624429,828313911,824015699,921313227,853672785,271641348,638608926,929904127,954831970,443486193,997625369,140844525,124461858,860745086,916606554,126311600,548028465,849637617,926261579,851085798,933572239,332609095,632199939,751429372,161231853,558757374,495275731,893880629,60193655,945418203,574681112,124525043,832303783,828934453,461917371,199221782,946994816,617366871,445982858,123248379,362373088,620214925,252543555,507852914,507230950,330320250,357897433,280307281,342443671,926574464,47856653,794374997,276486066,783387744,855026088,53744310,540340200,999427036,738755211,702106286,295920227,330231547,560633769,558998611,616767958,752463806,594980581,528438403,153455408,299705682,801316283,851390361,292348477,931962893,578819198,397603712,119811862,831208766,461862548,422104357,960684549,65726742,277143303,161850578,51822382,340808869,187306630,801108331,330142932,976135848,981462663,839826107,327818855,641866605,300427559,319817460,507681194,702551275,370304872,608569636,114459087,996228912,220542634,284021037,200727644,127754404,694852760,876589993,467791317,322650709,761276488,419807757,666956065,880994447,232805616,47550525,72828518,325509303,546263155,119498391,555577103,776184773,56757180,98578465,416325071,224143511,981809819,346257586,437244648,31854730,917850118,544180726,693079428,266149777,495425745,113127082,687130701,377683023,872889622,985830039,555074910,399950609,226168381,968023885,95643093,919012268,85654918,231335913,996169415,393745986,60566135,844484284,853349809,789957276,149818412,343164713,882119199,257372981,434760061,792872641,520280815,82272609,334558927,104408973,810454391,902185660,716313827,566865140,648456755,324820282,525502537,896212310,190165909,371723557,748667332,169048745,422375478,857642001,140265960,212231545,473327107,593958074,155882867,772987255,488902804,944599592,289169823,271280368,734718331,734908958,395295908,400363505,316103179,893029457,496037269,20069262,269982975,272095655,920480624,65325300,873794136,464013212,656055384,801909634,141131221,239095220,62696617,483867506,936650096,439610778,540349586,253645785,572039057,269502117,573844528,980916538,322886340,635634339,862555948,266071569,24375977,128300408,133038827,754102946,125016201,394556114,102300132,709912584,840248057,751123942,419601859,519991155,13130519,356751161,961772056,270565287,729872007,392377702,479761066,60250217,156756625,433952508,667298002,767845733,467573353,58466187,117128881,241698330,707472277,697922375,113004223,6156532,535286590,525487058,948476253,843942497,733371143,85345539,158309399,166933045,155366924,612194959,423421224,338358334,867599186,176236507,202058261,722030913,196314476,249238935,902767427,963031403,225671770,583822202,113595953,898280883,950053209,42050207,682961766,938526609,849580157,94416250,25438803,852008576,981715542,799975670,607270121,927849367,418559172,373229877,336949300,408677134,167187140,4723447,209525739,124431637,132719428,857765260,228815322,995580445,848918083,504120218,208405995,958483605,416596841,841141680,725730006,339677987,502193801,182694017,648697124,333199535,927883822,7513703,40735271,289857993,417470011,831169282,156559288,43816191,552356949,99412266,399952602,378259884,531471852,111237081,487921471,323177873,523791640,301800860,333533787,132323616,141467394,165028417,336673511,548105271,432648771,731203992,90477902,583838972,860233312,517646193,348714619,734329100,152651758,496581796,414585317,827950698,545170209,748714035,286189668,621046715,404184831,556118555,398199630,539035733,391992223,29528734,795716932,560752516,718058063,87023266,49456007,852599872,37480384,162902268,631212884,645007636,938183829,499713907,909031105,879102599,91122045,563763748,635634042,707183192,102947870,316800822,996597772,221665834,457360169,967543926,180557018,752070180,974489366,346992474,309918099,746379142,259888543,506508641,769967177,564000431,283642983,116073399,848363452,652208036,517414994,101395585,36539950,893319252,616590343,681946855,615277067,642038412,902171007,645903214,531497292,69252185,604371347,276984076,233771653,972812566,998445690,218412088,516340422,447834173,740560957,866901070,530996828,220174401,619936585,660016395,896581104,249273092,288905719,563516023,39807731,114328535,354099410,134606724,233131260,381103675,311921854,287842873,422180760,765973398,7946065,52898414,20299834,664721661,2109243,765212474,604803853,836805918,416599066,686201073,576074657,73187157,354210937,478219134,689708981,509821767,593201229,154617338,570205047,135456865,125600626,122697708,630037059,236649887,121257209,848712218,454404487,209834011,523099795,871350761,610574664,797002282,672674757,55638743,107704157,518341076,982166151,383076669,747285256,155671241,816984347,245813386,756774216,361644637,177325336,728575599,312566707,563979435,63257580,288045307,540286222,242147355,4083862,138805993,496180349,613694225,369733594,969532030,398732309,55207216,316046583,825881104,41097736,661115073,492640447,571017680,741931382,698976055,537817062,44179797,441125328,81132744,192977933,819853991,128454832,312042184,78667296,738909617,554664294,463252135,669034780,942763400,762151311,110898446,344726756,879853988,783593100,605623981,588895358,41171101,3013247,824325945,127505839,713225982,252247771,229665309,26018041,686088825,242641477,152666830,897067411,343996789,567502660,763650503,165028757,250986059,665904898,272509969,903388527,633365622,729013893,73359016,687551226,107703666,828421744,370276362,127001561,891697157,723162098,42826706,836111088,104669129,372723791,799671080,511812628,945825321,302960679,190466942,592675157,803697046,402787526,396556488,218994064,194116629,768961494,546498171,491048365,676048639,42251789,865513741,205243161,943978109,750298503,656109249,996571100,672497113,862642559,671116308,743927292,17137488,244591510,852637568,835188931,461009616,445279107,521057918,854287040,726374285,181100478,144065743,808885410,720758818,327214382,728536765,17379338,320309147,876265082,921113718,152469052,833566293,110778088,327085093,689039802,439547282,740131174,913510543,326491775,476917987,164092851,578858141,65564088,337036154,641986371,100128815,39175972,303065556,563008148,822344291,370163114,25572865,671531661,340069058,621201229,574624441,914154034,726632007,960041334,493235022,566686253,878056718,252752103,823230414,642717440,937365833,665189469,829950926,763531763,238800753,606491951,331633217,978711371,654000695,649005798,874191693,543897242,216779187,96292663,812287529,571709409,166146887,624963175,207372606,552418404,705794117,901626177,922350001,490120917,98806304,415682058,81321935,8706494,805356160,616717076,178403689,324029952,990586953,245933349,163009307,125719960,359251782,812366886,693025094,739263481,230733683,511702668,169678109,90325838,492882343,371027248,553839209,553889609,793806976,554823744,749356949,774773941,878554847,994156459,446450010,565863562,294142194,128495604,483083768,186420753,304048060,312028242,169039727,436228811,610265519,304487669,669461168,622951155,295357224,103865310,34276446,719369401,353141241,754614869,160645934,744794356,812688960,90792697,116448864,188372376,166454484,225846194,742433581,558886994,995600428,915481739,891374002,155717203,460501594,144887710,117364472,15734169,12500130,310106569,748498612,263873483,912862580,852236758,596829905,948981071,19809706,785708294,969005541,346486131,887044542,865840292,884894545,975908903,870559332,709177759,453873674,397454478,925712793,560253378,280409889,896015706,29865830,321804513,667333140,467203347,73824967,6340723,426671762,970411215,596032297,250629622,189587824,347507195,352126304,400608079,96762839,347418584,476102132,741062944,82466987,172719089,568924624,656590378,584530528,438787611,966917348,860697763,571236860,220853868,702442202,208756260,214315012,132442581,231553176,785365137,281030944,257069601,818152647,296995756,695605782,965754076,475076633,365797930,404211074,987209866,35508907,343016474,239161103,597142367,405450467,805994582,617901903,363311962,862716132,479581056,271237364,21935730,123377909,298032295,913894654,982174964,330682101,338295306,248973970,839925487,418985533,460678852,343907650,28086438,773954850,413768968,676255412,67554179,91072002,687843784,283474935,284083856,124074789,193932356,261204837,282413225,8066917,112661886,76577061,320808957,400834343,112193723,241990783,606512052,702716351,318800375,570389881,956030388,421855507,941644053,150491570,840818510,31077690,809218486,756288757,392489578,768022443,823485368,559672465,660590047,10767536,884954417,783248701,726934933,81093318,369000157,752352829,344110610,787538470,679160476,358485371,697109405,772114954,4199521,101749993,906739187,423952505,536837737,107245641,54638907,749258781,732232161,925365141,760640348,192851272,277152439,954861982,838215495,797781019,251314076,33986634,465833651,823120960,92974439,126693520,829346885,710598864,966865939,427109783,836112406,370607142,116938108,616088763,216437038,249644404,812464640,861209063,483418188,625010152,880967993,978353294,293072733,513440638,203979438,245065277,772254339,626479569,533482034,169488548,313719100,489800220,672476350,267082299,242117930,499292094,134485315,927936526,556626941,159379485,887016445,1380561,423717888,651727688,630896245,605949214,850635631,334468827,540573349,627548201,488649311,726984393,100004506,948745177,896857979,283244125,997508087,673967078,408868444,604615481,839411573,829059975,850591542,289884344,311328436,131199139,69225979,646259190,611915886,669062797,469363737,727570974,598108543,550487759,179072028,551432498,54353578,731576312,376525218,922834224,490704287,14731264,31701208,361033268,157530771,934102843,424594013,451341309,744985958,744600454,961654605,100403067,847132139,605753241,308492868,571246567,467862763,41175249,490473322,175373335,831627246,106864032,184701574,727187787,506839108,543241928,370067831,379971188,753948968,350592047,211346615,439239011,810202750,95843299,264295216,409613333,659096877,392425521,670113303,985697504,790171355,74628173,349180399,309513654,794729049,314613776,884002060,793949145,282740729,529994313,761294691,465533039,549907631,236125125,294566334,665672461,584290183,777926138,339246984,200061402,159832077,726796667,563600382,33779381,17040550,51764114,522443175,171129714,96415854,529425579,579830942,264303592,125632461,378627325,212843425,823414273,804465166,249526666,11607636,144841654,688305128,983092308,541948886,487230565,8177822,871075273,684151586,740122136,851317945,98491705,413801420,151539623,805824154,940815357,713019450,687862811,139665355,895787274,284768831,296402689,589703373,195833677,799024460,959996815,807842185,241592010,457304821,976647098,192633266,512420753,905768639,320254907,293371777,393546604,395097,647623755,87709482,857581504,698027722,134958813,319233916,317173792,945676007,410107908,663056454,275774590,184686354,537889064,934817475,326467132,212517007,799216996,778912723,868686855,331563722,120081005,419878068,906532775,697766708,711358661,394242566,173002357,147614009,637798734,502501265,291883295,331992541,398308480,437895746,60888686,234476674,679959274,436031283,807078420,853232826,374327995,892174648,436108618,99806126,401433985,184688520,706456082,641458599,896727009,977265367,530908760,640798956,590447111,993164033,133282277,261441726,558399585,167739447,451173471,118645713,787132728,308270522,160571812,534133691,443000287,573681177,275804836,432460636,156500431,667194403,287912358,845018205,434555906,551620644,345062964,767238210,732700399,166964625,101929817,246105246,749756145,882430492,127425548,26723158,995634174,190251334,956789997,624915861,897355842,902910956,141381370,957803374,650979980,971597817,661427555,493035630,586302624,993491439,118122442,306546762,649256752,545379598,801154762,136653608,70875659,526146625,959576369,475391303,80292449,278701166,762242558,403694830,697354981,937746921,209756773,656254271,24458570,284743191,185864756,29943498,14212833,747336470,300984017,789241207,597027336,711256849,568963655,156080809,32265843,32137832,108099953,288091116,575332635,246238479,858584086,446716855,462212900,816801720,655112931,110331037,538176559,281722163,669581028,111897454,270698760,772263622,273633355,962575181,313138459,632014687,854388631,222145896,797381435,42792415,248240604,68295241,33265653,777331790,807384010,505051363,743306444,361441828,499644610,351754096,363481771,777343455,327437539,26936318,52996014,21870909,120220477,767864908,710706795,387314882,974877556,150095571,266868855,299510090,826335295,455445198,835247431,64985678,695637305,243910681,727109091,48530787,479155974,102760919,756037187,2318627,631940661,98238739,980168034,931081716,308185241,107444269,557303267,869083508,391473269,138341816,638063513,869288125,73053944,805497386,628155930,731346092,806941488,199728085,891873380,552591213,400462536,894059195,590124958,751787436,934949934,611257040,642944395,875366839,8583592,724964670,405801906,527589390,670483150,526054130,724287344,806528986,131504392,816535670,913460477,151780401,655163391,439267529,539996508,973957057,756772461,818768918,965738834,768037339,422824455,262245062,226461190,179690892,436974011,518176648,99667856,329837332,766696373,523548296,459851349,893284193,191693328,538458892,270864506,761470256,771244980,967963109,32335376,899836945,533862465,926283980,111672419,759766116,139111674,471334878,576334488,887632287,48747182,736369219,72373723,808364539,358667357,392395958,796932578,110542406,958713173,102985600,456705864,407347621,913875556,731085484,161837012,433279237,135564216,868875458,121739531,748483791,299953389,612178604,582125662,750315693,572825799,514927863,792092739,928208089,65057967,280516805,153347046,450597511,883667392,276533624,70397356,86317145,992626705,892183373,931462455,359237713,586232108,16461194,214156646,629910344,754396255,847734834,929741588,90195579,56696705,275670920,610776145,292397134,873929136,888864217,170100920,846250843,355618741,25207010,934898455,687974198,318683129,465421326,264900430,217414343,297856336,72277091,598639408,609097279,197210973,538085226,498336213,401734094,842848503,251326763,737014719,73507054,847236354,578300407,114118321,533701825,707175952,798841137,464937210,310976321,748973235,236126592,650920098,987252196,304573697,266235513,753032165,434842644,323412429,773487727,800730955,456142114,138382345,783400968,248624935,996275562,256505450,45977341,594742491,415169064,71592062,646362404,178312548,164940845,308566408,74455392,954445986,878345667,925657271,38929791,300979709,46436383,95771000,600690756,712630271,298865612,71715287,783756273,999371967,372900969,51730716,902682531,818589819,760000789,625329793,193943002,919864644,89701577,42010555,101035023,224973654,684681057,162717359,169350462,982887210,500828925,977020231,136327583,170904532,411895031,837682474,305101977,825219206,846780639,150590480,506557931,255775228,47897219,437022995,274566390,442363793,964527397,694376269,73572572,483387807,143166120,546985213,891559901,732608955,423459470,101292945,475295007,45209429,651983583,162540823,204189533,134629790,917626895,776880652,607109590,24465025,949084038,304521395,290314197,628501407,978442961,771075403,673603285,25329871,954618889,509412255,903413868,41237926,27348101,400044174,914608237,543199645,574616828,853784138,605627989,651404152,350396607,971292366,797487147,521458912,882546243,557708248,328110391,924050947,180665161,546089425,12476539,857503514,860205995,238683443,619781537,76777657,654249372,730604002,495722289,253188658,819646000,728397878,325731063,807648327,220418292,178107569,257948554,819135809,99131661,628450357,203349407,345233449,192411018,993703517,712838906,174590825,630592107,317595576,324480512,612364202,606638382,563336210,165984396,287295458,384095459,736912749,841336699,915460741,200447810,168847690,53694932,333718454,671190979,472043415,722770244,265464467,265130055,707826504,81161051,292889442,187067364,491671885,92444956,116802899,944627578,369607651,799015248,339770185,55760009,619989847,650390144,116425131,866843803,822322199,565474974,433775776,411157756,560217649,733283236,846469384,785589421,983129028,68074540,483336561,817659471,994114427,655929952,727280267,290127485,486912799,962093194,715981525,900318537,965212201,263167234,336257064,990442845,632731496,392284604,221752076,890513263,843562963,809126640,861464691,468792681,921370941,601883495,309331349,661368963,991537326,889172436,521117486,762363875,481478020,355190782,643981400,852499824,816399216,965338085,87433237,586425273,506736399,983927030,828996090,193953925,194965928,873334323,413896636,364319970,303445769,148123070,936492713,624390497,729077145,252873333,500947559,184324286,932629769,869688615,758690839,40749860,133800537,253244307,429872845,322003279,272811087,48038786,613021790,669494525,376194737,964814732,735520178,322031184,140976536,808236679,271172016,794130820,291439485,425493111,219673342,777187417,118842784,211618808,352453370,62468645,196193135,58370502,388256934,442956804,414129045,112937795,265146713,460722256,963601439,808142456,99248535,352018860,68784436,559006232,472922764,237933901,355592370,652170639,844308987,295333441,701227955,805163219,282722258,744286295,848457973,150123933,953207486,419271751,871118495,991837283,705073103,117800826,408655822,742149287,865448446,116002887,112588368,658337820,454591773,732021698,841893368,621511302,113604679,898925290,104668525,716429799,903680319,437292234,977005274,75935427,14020917,870704796,746783651,567020965,664873884,279659919,395119496,898248894,53122839,263728612,356359753,694600601,282542980,506005380,732970604,148132450,712607117,235043072,595373235,347587121,830781062,545523305,944922719,801147845,553736497,162653895,437902292,96363218,526155553,56916417,252492149,309090797,504228932,480035844,455670496,571633371,101074712,60104912,623662065,660821287,519013648,634872862,258162808,259299217,628149298,513404204,782675809,30310993,729890099,457793337,175351818,457147310,127982157,591290851,956915940,435171770,403931348,761221221,944802463,846912453,29092107,90455001,519111943,659551630,827854937,191537128,82748073,591788795,791601213,504194651,911902547,885068228,943012501,727161841,170258576,105883439,21728025,71712684,383280748,26960558,382911931,676293805,449255191,813190598,591706943,704187233,943223593,932652273,302889271,142913151,818561771,628844839,886593260,2845321,491333391,493211829,866999396,578302941,58094980,812763976,201473695,453010234,620711807,482810700,358250091,493874374,326556120,76023842,862935195,830318534,15326392,478017614,292789599,243076971,27487804,234024116,321050299,283328761,804614373,281803950,665031202,422490643,629507376,540099358,298655153,464507895,803322783,992667534,745775252,111174191,103269519,62113368,749959766,120279925,553155194,567777414,77560945,513159340,725252985,629890782,820613176,394734880,707451727,891402805,528064896,}

Compiler output:
a.cc:1:1: error: expected unqualified-id before '{' token
    1 | {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,4,11,26,57,120,247,502,1013,2036,4083,8178,16369,32752,65519,131054,262125,524268,1048555,2097130,4194281,8388584,16777191,33554406,67108837,134217700,268435427,536870882,73741786,147483602,294967235,589934502,179869030,359738094,719476223,438952475,877904987,755810005,511620042,23240117,46480275,92960592,185921227,371842498,743685041,487370121,974740289,949480619,898961280,797922603,595845250,191690545,383381143,766762340,533524728,67049505,134099067,268198192,536396443,72792939,145585939,291171940,582343943,164687943,329375951,658751968,317503996,635008060,270016182,540032434,80064932,160129936,320259945,640519964,281039996,562080068,124160206,248320490,496641059,993282198,986564470,973129015,946258106,892516289,785032656,570065391,140130862,280261812,560523713,121047509,242095109,484190310,968380713,936761513,873523114,747046317,494092724,988185546,976371184,952742461,905485016,810970127,621940350,243880797,487761699,975523504,951047108,902094317,804188736,608377575,216755254,433510620,867021353,734042813,468085734,936171584,872343278,744686667,489373446,978747012,957494138,914988391,829976898,659953913,319907944,639816014,279632148,559264424,118528970,237058070,474116271,948232674,896465474,792931075,585862278,171724685,343449507,686899152,373798436,747597012,495194158,990388458,980777052,961554241,923108620,846217379,692434898,384869937,769740023,539480189,78960522,157921196,315842545,631685244,263370636,526741428,53483006,106966170,213932499,427865158,855730477,711461109,422922374,845844912,691689982,383380123,766760413,533520987,67042136,134084442,268169055,536338282,72676730,145353634,290707443,581415062,162830294,325660766,651321711,302643595,605287371,210574917,421150017,842300218,684600614,369201407,738403001,476806183,953612555,907225293,814450770,628901725,257803636,515607466,31215120,62430436,124861069,249722336,499444871,998889942,997780078,995560351,991120898,982241993,964484184,928968567,857937334,715874869,431749940,863500090,727000384,454000973,908002159,816004525,632009258,264018725,528037667,56075545,112151309,224302838,448605897,897212016,794424248,588848713,177697644,355395514,710791255,421582731,843165691,686331605,372663434,745327100,490654426,981309086,962618400,925237029,850474288,700948807,401897846,803795932,607592098,215184431,430369105,860738454,721477146,442954531,885909309,771818859,543637960,87276163,174552577,349105406,698211065,396422377,792845009,585690267,171380784,342761826,685523911,371048075,742096411,484193077,968386417,936773091,873546440,747093139,494186538,988373344,976746950,953494163,906988590,813977445,627955156,255910579,511821433,23643135,47286547,94573372,189147023,378294326,756588933,513178141,26356558,52713400,105427085,210854456,421709199,843418686,686837654,373675591,747351473,494703231,989406755,978813797,957627882,915256053,830512396,661025083,322050458,2,18,96,404,1494,5118,16724,53040,165018,507050,1545384,4684908,14152574,42653814,128354076,385848008,159116155,480493389,447770730,355894123,92847124,328871864,87277627,463158117,792126066,181682973,155659955,688203512,507059498,406078232,988036108,503713182,590351468,929480567,105296470,949601582,116231800,883552438,720374411,300560641,180560122,99440299,413844468,472584411,879859304,563794279,539820010,316338991,342779711,815869616,22675002,218162757,954769391,464876224,595770852,189603188,373397347,729374335,406494548,656233951,842209909,273653527,315016147,933167772,775750414,279754164,744277342,42870960,748700305,486285544,939235993,778477062,256980024,614048728,528374739,957592893,617727882,343094241,9116409,987029420,880461740,480145642,117971569,708998126,837175652,931904303,636482748,591003431,136136516,134678215,856588548,474890357,234937816,325364624,217214274,133902065,366243506,27824341,941680292,541475386,57315601,37746518,844860209,997843548,920078543,613353913,546321226,51505987,979626369,589120095,67866924,804639166,616019803,252290025,565357778,313075645,173258949,987868737,899818292,571907852,460658811,871876725,595461010,746075473,157642555,311791717,613135513,194960024,296020345,310375381,775789164,16728368,428942269,44377035,648268032,975114928,986003986,79368457,480857053,928113716,755466017,208688131,510685479,301340074,442629560,405149988,370015805,419222912,876064139,865028216,68801855,153886222,356666798,860064090,160367698,641502657,245356381,377815912,416991836,818114915,588675394,34739982,641700712,117439,150437401,751537483,855118773,766425422,701471608,908863322,335545444,224606484,109819621,201519760,348742324,534655012,580883774,696552173,997522310,808363312,56748236,433627591,827715510,536879709,718173956,369660718,539329813,478755445,157869796,916888531,637296820,685226663,602426900,900849808,889763690,43796441,880477725,139688359,415654682,240223249,707268969,95086945,231903357,589078347,554055636,235892977,855216788,860812592,172849601,699460688,460294862,104800084,762322007,182901102,340665946,606016430,986180652,294899721,557510650,18251717,746292395,622050220,632596202,430780049,358424297,207543350,887274040,191214047,632530912,15476064,282301598,318759247,900095232,588030176,539689959,170380138,613873295,47198921,552869105,481267185,89237464,558701359,258200095,938911414,145476529,94035228,597438991,423106581,531022975,116600389,396990118,285475257,45563602,515095514,302225994,420687972,290215994,927085280,894264584,908946454,179281015,442863674,138770611,36810417,351568876,537123383,576346237,659134542,837740017,234038633,143899973,315416042,713829430,676801043,101179892,445245582,619302009,425191121,410299247,500506316,40894020,201591273,762752423,604375775,445526801,601542961,334718737,64501821,314363739,184975962,38866745,84648488,190213668,443350284,75643455,718290824,137769787,379281627,6,96,840,5496,30426,151800,707772,3153648,13622526,57588528,239782512,987643272,36484294,404234584,392585814,898035315,575174284,246600375,811470459,683273579,944530613,160687311,186367318,966928663,310745792,324184017,434061165,714573914,483689558,307015431,567362584,193004171,274985556,915274348,403348465,799225682,405433523,14870867,704622880,546316043,675087455,225205435,471115501,356259091,900702010,226723475,324665304,947812436,137322984,597972995,984590057,460472940,596881918,430181760,203915682,574447624,389109735,852317608,123612518,855437931,68495933,596187816,622755010,761272022,993730422,145847900,842962989,836003776,489234413,660001590,805783322,875110110,846453416,363345822,581274596,729532896,430752283,372448434,684396850,857365410,944554814,799571630,540392369,392464380,965207669,35658377,807860052,831147989,972883282,812856553,520271269,996925726,148403839,286517473,410407674,328965389,207456569,240356186,812128620,328429934,182376492,733874979,20350791,22940747,370754501,382789190,657165974,455110543,379293914,710511643,163327571,507103250,176259662,926185969,124051284,658235013,702836284,730427441,171657008,559799959,371084747,425741832,650021638,738703811,57894029,88420714,353979209,933376931,620786705,405665909,80427942,399875203,879108560,702396856,561397755,873667459,78977783,363423390,958788513,606496445,297842569,997509740,922540189,764483334,314242385,34012245,347923187,499104790,663708797,130247951,441281262,587709095,68524780,158910624,195761506,137175482,661030905,462935933,12430912,397747995,257725642,33246612,632835130,967997003,933073447,145030297,704757626,793202539,922645994,819789493,847245701,266778576,642663025,341198637,52238962,567212415,991850093,512832686,567068228,793594527,110514318,743630512,375542684,681512445,147123735,441319571,111880305,242721139,186212011,648196973,972780422,640158966,522291968,353501666,823052172,422143830,180800894,953079080,59074087,145613289,710656091,103952767,56827023,22028872,480536029,594689568,292685992,463984572,302982936,562409806,14257096,110547840,732186726,220519949,868686980,133639886,802602204,323121500,638051012,321969731,436592300,553864657,660797455,559406693,148988611,592502279,690167423,923948642,604457281,936640798,726783718,298490090,401546305,485171466,392424689,82086598,157048481,572742725,712198889,547984693,599124055,31392524,360996641,734650708,738919015,645048876,305745,426327371,141158365,763532868,481288942,869123655,541481230,547033143,46368014,776719033,987460018,851948313,626133597,62957762,388210014,87151168,500925010,49404814,382811790,813561931,703966828,556043494,483267106,184829507,121269346,121367441,729784127,911155473,192910968,545493499,605522862,458440217,469869573,704111259,716790015,476812361,531533951,411044714,829593134,411471856,610730625,791607334,144845241,283885158,451565185,340778172,354293024,445819703,387963770,67727697,396543733,24,600,7800,73080,563520,3833664,23971920,141379920,799912200,391998892,589053863,633370852,417646250,541423106,757493114,431489194,428336475,858221594,779364999,411758941,690637662,455909089,202043375,335225318,532490102,752877327,489903171,923050462,654940208,658979559,921678977,860940004,781229911,199637891,337407319,565543420,959799161,248689121,815676548,404255500,206752852,576047552,913303870,446575473,684280501,54655197,572584133,245025535,597566734,491775558,145314279,913549308,676433463,149864140,478122964,704007200,802113697,620985678,983028646,831941730,161421607,603137771,883561722,699229104,433777014,436564343,162645407,98807483,365341035,938291843,697514765,566176481,463450137,261722084,851431052,238388681,742360301,694252827,716967554,885533770,216840373,47457646,115041453,284472507,769243034,709386519,274506682,377059193,472129616,14426764,330292484,504168654,385777718,413226517,924256735,648