Problem:


Score : 600 points

Problem Statement

Let us define the oddness of a permutation p = {p_1,\ p_2,\ ...,\ p_n} of {1,\ 2,\ ...,\ n} as \sum_{i = 1}^n |i - p_i|.

Find the number of permutations of {1,\ 2,\ ...,\ n} of oddness k, modulo 10^9+7.

Constraints

All values in input are integers.

1 \leq n \leq 50

0 \leq k \leq n^2

Input

Input is given from Standard Input in the following format:

n k

Output

Print the number of permutations of {1,\ 2,\ ...,\ n} of oddness k, modulo 10^9+7.

Sample Input 1

3 2

Sample Output 1

2

There are six permutations of {1,\ 2,\ 3}. Among them, two have oddness of 2:  {2,\ 1,\ 3} and {1,\ 3,\ 2}.

Sample Input 2

39 14

Sample Output 2

74764168



Sample input:
3 2


Sample output:
2

Submission status: Runtime Error

Solution code:
ans=[1,1,1,1,2,3,1,3,7,9,4,1,4,12,24,35,24,20,1,5,18,46,93,137,148,136,100,36,1,6,25,76,187,366,591,744,884,832,716,360,252,1,7,33,115,327,765,1523,2553,3696,4852,5708,5892,5452,4212,2844,1764,576,1,8,42,164,524,1400,3226,6436,11323,17640,25472,33280,40520,44240,45512,40608,35496,25632,18108,8064,5184,1,9,52,224,790,2350,6072,13768,27821,50461,83420,127840,182256,242272,301648,350864,382576,389232,373536,332640,273060,208548,136512,81792,46656,14400,1,10,63,296,1138,3708,10538,26480,59673,121626,226787,390144,628744,949472,1355952,1826464,2341600,2833632,3282464,3584160,3765600,3719664,3531924,3093336,2642364,2010240,1508544,963072,621504,259200,158400,1,11,75,381,1582,5582,17222,47194,116457,261163,537459,1022981,1817652,3040352,4810720,7230928,10360160,14178912,18577792,23327872,28132048,32571504,36310464,38903904,40028724,39552156,37457388,33941412,29314944,24179904,18835776,13777344,9452736,5716800,3211200,1742400,518400,1,12,88,480,2137,8096,26860,79376,211811,515308,1153268,2391936,4633331,8438664,14557048,23874176,37407760,56117824,80906752,112162240,150052400,193572736,241706624,291576384,341323776,386160048,424359540,450394992,464545584,461528208,446428476,413557632,373573440,321120000,268449408,210332160,162330624,112550400,77788800,46540800,28497600,11404800,6739200,1,13,102,594,2819,11391,40344,127508,364587,952559,2293742,5126898,10710633,21042989,39117852,69175664,116857024,189256368,294745440,442503456,641759376,900689616,225195321,617201401,74227554,586823330,140227131,711888699,274217080,795069832,242715461,585116357,796764497,861974465,769155485,525176285,146566301,650715556,73773796,455145195,828946802,226153586,685663993,216281593,828705600,536385600,309484800,166924800,87609600,25401600,1,14,117,724,3645,15626,58741,197280,600215,1671266,4295107,10259436,22922995,48184950,95816051,181136304,327071752,566117888,942525072,513281017,349163810,532145419,154557773,309226767,88509354,563257605,789064441,766807654,474675580,795689314,599134613,627066840,658988947,307608398,337632800,295701193,44870369,150212311,705302359,336038622,452522163,797367958,62674553,57993322,777736994,845298906,452367755,90655804,810196653,976943895,564798323,582118351,994783972,869862386,697759993,660441600,381024000,1,15,133,871,4633,20979,83313,295803,952299,2809009,7656027,19414457,46086247,102967901,217634463,437195525,838372452,540635289,722168530,638311860,640827391,196046908,898688562,478199884,793020369,808862771,562236075,94791602,385333320,237794527,197694759,398043392,504456766,579736664,78137089,793367253,961295251,280517488,179779783,947563092,901772777,859566930,199212409,920781370,362900807,735004334,297264154,482748036,653703312,140400674,623159781,320434095,373194802,13313867,205909676,360223815,570584277,68075848,372652149,961247580,23084534,261139053,151302323,715359965,625702393,1,16,150,1036,5802,27648,115538,431844,1464468,4554040,13096378,35069940,87969166,207781760,464351910,986188668,998611836,879505923,237509223,15110629,621334822,88677622,257578542,963016850,235638961,442107823,429101453,483004748,329733855,718448185,266304376,413950543,256286771,626720357,318467482,59069608,81901162,352730851,104241055,503595237,956355036,534522134,457799859,108929893,887297322,424614770,265024591,876853471,515703045,692038809,210906163,20070317,468291405,145357835,797577421,232358134,747771239,343859985,833879609,78548665,289896769,449285934,313197004,379603290,397630660,609910102,442642726,627950853,722186028,705163253,998661511,771071664,636940611,1,17,168,1220,7172,35852,157132,616084,2192506,7159090,21631676,60902460,160707468,399489140,939796228,101060910,481320121,151453550,952463061,931694473,957528293,554162053,990142499,644946993,651797781,791594351,556120466,271969917,107619398,710253075,280526462,615698879,99748930,775178221,257586036,645364809,806795120,340635512,801741075,790520661,68328385,331513794,351728404,931812262,91105169,176869824,445724501,370449983,359815736,918724628,869062973,659791249,657727222,395793733,32692523,78858425,151369211,628504487,842750087,152091477,889718876,908002421,944598446,656459208,712920845,47550280,92244967,110652620,951703750,217822851,901098263,655149074,861896271,859184013,992613245,768042116,807916959,335381553,909568095,153171069,827990317,681893483,1,18,187,1424,8764,45832,210072,861400,3206786,10957868,34666130,102239488,282743580,736889224,817936097,262532028,534038590,412279142,965109380,86702267,846482566,945052509,644517943,548776024,679330947,152291502,882910517,188127435,636778925,902059202,132531208,193904122,893705022,246193070,652079051,958060250,148697872,504141990,371410212,807466717,514477363,565424570,560794838,11419155,215137208,665710713,791504234,359367396,224050172,509091270,125989128,782600310,957126038,667219607,386301613,605448653,296557741,618019404,194294675,222923480,765962783,743934970,24324611,512643153,214242880,286900578,228877964,91240846,430467141,533029377,904804693,373207899,916503101,83598539,560288494,363356684,6828244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264775,785155020,673315179,883230707,320461657,209574161,896187167,641537195,580708044,615201169,907420567,226969633,44823693,653925850,618905940,556249274,683808190,595045606,406684866,817926872,498013040,741888764,255307898,750076370,226664326,45791371,138249186,182084615,925519009,32002450,507648904,36302093,164244320,134446595,176304234,443232913,204696272,377207389,330407781,317016375,255990328,346121343,776903928,865285835,180645765,94169320,523805568,66571932,958229276,706032441,157122799,174128102,265560802,960871567,814597354,840895548,702037,848074074,17426708,276377856,55696613,206160180,32721003,453495162,587538197,204676036,610254246,936113705,842825687,202272844,145230437,624393323,739106533,700708897,523328161,691038973,656087189,213848962,927815456,921255504,609475698,113463094,529085932,807792149,579407091,163833313,694176222,471399591,346973697,718259544,297359882,892552532,451373341,120883534,8029910,624607649,606649877,815313728,231664869,673443919,615486405,94571095,110823650,950289120,646876432,928906934,684469503,297251947,919054473,285157267,967739040,274416446,465229888,656873003,825576691,53305194,539107135,609069516,669008004,585520763,526072937,91836656,101778461,538228891,424599066,719851020,234795290,701214554,914481398,497763115,504286064,212679726,409710596,134500525,154608785,554889670,267547678,851784437,749366191,681515762,587313005,604179607,297539881,51380469,30897443,988568867,430543091,168358864,325894509,131217074,122226126,289735266,2541560,697428098,339809826,339814711,568813016,256466301,865405619,710940331,7424767,660900037,729644940,444,450105203,690939247,459755659,92556107,42398758,782901298,483436309,73995240,784415989,602791285,655683750,744368335,684929720,939318197,1937536,94209990,544006669,195169186,297173575,151918090,559870646,425964491,818978660,571568643,60393204,415731654,547756555,991386612,383053326,997830526,963081859,107336308,898219937,906988404,550036125,981857264,691293427,481189647,501756531,316529056,476096058,168221459,165690115,553028411,960794528,453386272,963889156,71983103,494867184,462967097,635240847,989817132,23786457,968645733,163475174,884798755,971346358,8231228,947835970,751371876,21594745,702982989,997528759,30899466,874470660,839706683,64336797,183002010,415355406,851375333,802315034,662347966,459017349,83113197,807783874,686211775,665742332,548408223,38712773,947065654,224142524,544199777,554457822,161813447,59932464,324817969,826816639,159675767,610260222,802832692,962264291,230527850,654881259,493134625,56109407,491401533,163680598,892934948,889185132,78662275,741528574,616484511,204394884,120980232,4959172,884202370,468625389,987185268,797914336,292935354,542176515,965256954,25044127,701524209,669825969,264620823,983915826,463815578,325409981,142164710,946513145,626025918,890502327,456729879,921471703,889764153,10834930,550258959,888111963,456661896,560525119,254574198,379302005,359197537,748972811,432885247,174603143,495215302,304225805,499574,89067439,956588800,479903186,900293862,918419160,874312513,779518268,750190343,34999197,204187488,29703716,310295240,212734818,705461990,880565621,542764103,578132976,871657196,920555643,635330221,603836039,905337022,446003049,531829391,914627500,109964459,793773872,883594493,588890899,761763418,850946563,47045637,406265955,398330580,175033998,98562597,74022406,109783010,888406279,62923507,851720727,920064661,659715101,731241623,740764931,68490942,26861674,832409630,156628069,65837301,277330611,504531610,621094682,513712789,824543274,863846088,522929299,50674845,205053841,391074024,703020653,598865065,977680558,126857946,571772915,596794646,195429545,328266420,36051456,451216030,522276964,948367998,561406981,389510759,585943971,108053297,459413669,288907310,136029766,802792879,520247265,414339912,337619243,597859489,40005835,350918,321070418,199829979,141119131,515535428,350920730,314377413,808898947,900198037,799762368,570476717,244997759,402733111,626061442,103647198,938528989,898060580,652361018,641847472,149112119,134262079,887185896,606038263,859408453,950373236,692335861,405660442,565431386,959094106,393940636,423632434,612413824,143336067,663257107,9730523,471491852,112828340,936303905,998673093,55233966,416039620,144081002,565258672,539355694,202448366,14002378,539019751,307827209,288622328,788194350,570120788,965430343,472467292]
X=[]
N=10775
for i in range(N):
    num=ans[i]
    index=i+1
    if index!=3 and num==1:
        X.append([num])
    else:
        X[-1].append(num)
n,k=map(int,input().split())
if k%2==1:
    print(0)
else:
    print(X[n-1][k//2])