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: Accepted

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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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)
elif len(X[n-1])>k//2:
    print(X[n-1][k//2])
else:
    print(0)