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

Solution in C# (Mono 4.6.2.0) (judge verdict: Accepted)

using System;
using System.Collections.Generic;
using System.Linq;
using System.IO;
using SB = System.Text.StringBuilder;
//using System.Threading.Tasks;
//using System.Text.RegularExpressions;
//using System.Globalization;
//using System.Diagnostics;
using static System.Console;
using System.Numerics;
using static System.Math;
using pair = Pair<int, int>;

class Program
{
    static void Main()
    {
        //SetOut(new StreamWriter(OpenStandardOutput()) { AutoFlush = false });
        new Program().solve();
        Out.Flush();
    }
    readonly Scanner cin = new Scanner();
    readonly int[] dd = { 0, 1, 0, -1, 0 }; //→↓←↑
    readonly int mod = 1000000007;
    readonly int dom = 998244353;
    bool chmax<T>(ref T a, T b) where T : IComparable<T> { if (a.CompareTo(b) < 0) { a = b; return true; } return false; }
    bool chmin<T>(ref T a, T b) where T : IComparable<T> { if (b.CompareTo(a) < 0) { a = b; return true; } return false; }



    void solve()
    {
        int N = cin.nextint;
        int K = cin.nextint;
        if (K % 2 != 0)
        {
            WriteLine(0);
            return;
        }
        int max = 0;
        for (int i = 0; i < N; i++)
        {
            max += Abs(N - 1 - i - i);
        }
        if (max < K)
        {
            WriteLine(0);
            return;
        }


        K /= 2;
        int idx = 0;
        for (int i = 1; i < N; i++)
        {
            int cnt = 0;
            for (int j = 0; j < i; j++)
            {
                cnt += Abs((i - 1 - j) - j);
            }
            idx += cnt / 2 + 1;
            //WriteLine(cnt + " " + idx);
        }
        //WriteLine(idx + K);
        idx += K;
        WriteLine(BigInteger.Parse(A[idx]) % mod);

    }

    string[] A = new[] { "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", "1225195328", "1617201408", "2074227568", "2586823344", "3140227152", "3711888720", "4274217108", "4795069860", "5242715496", "5585116392", "5796764532", "5861974500", "5769155520", "5525176320", "5146566336", "4650715584", "4073773824", "3455145216", "2828946816", "2226153600", "1685664000", "1216281600", "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", "1513281024", "2349163824", "3532145440", "5154557808", "7309226816", "10088509424", "13563257696", "17789064560", "22766807808", "28474675776", "34795689552", "41599134900", "48627067176", "55658989332", "62307608832", "68337633276", "73295701704", "77044870908", "79150212864", "79705302912", "78336039168", "75452522688", "70797368448", "65062675008", "58057993728", "50777737344", "42845299200", "35452368000", "28090656000", "21810196800", "15976944000", "11564798400", "7582118400", "4994784000", "2869862400", "1697760000", "660441600", "381024000", "1", "15", "133", "871", "4633", "20979", "83313", "295803", "952299", "2809009", "7656027", "19414457", "46086247", "102967901", "217634463", "437195525", "838372452", "1540635296", "2722168544", "4638311888", "7640827440", "12196046992", "18898688688", "28478200080", "41793020656", "59808863184", "83562236656", "114094792400", "152385334384", "199237795920", "255197696544", "320398045632", "394504459524", "476579739996", "565078141044", "657793371852", "751961300508", "844280523396", "931179786300", "1008947570148", "1073901780288", "1122859574784", "1153199220480", "1162920789504", "1151362908864", "1118735012160", "1066297271616", "996482755008", "912653709696", "818140406400", "717623164800", "615320438400", "514373198400", "419013316800", "332205912000", "255360225600", "189570585600", "136068076800", "93372652800", "60961248000", "38023084800", "21261139200", "11151302400", "5715360000", "1625702400", "1", "16", "150", "1036", "5802", "27648", "115538", "431844", "1464468", "4554040", "13096378", "35069940", "87969166", "207781760", "464351910", "986188668", "1998611843", "3879505944", "7237509272", "13015110720", "22621334976", "38088677888", "62257578976", "98963017536", "153235640032", "231442109440", "341429103840", "492483008192", "695329738720", "961718454912", "1304266313504", "1735413962688", "2267256302640", "2909626740720", "3670318493172", "4552059101472", "5554081940040", "6667352777520", "7879104296208", "9165503659392", "10500956428536", "11846534605056", "13167457892028", "14413109030784", "15546887406144", "16514424730368", "17287265145600", "17815876978176", "18093515829696", "18081692165376", "17803211030784", "17237020190976", "16437468406464", "15395145465600", "14197797676800", "12838232448000", "11423747851200", "9945343929600", "8513833939200", "7105078598400", "5833289937600", "4638449318400", "3628313222400", "2730379622400", "2020397644800", "1414609920000", "982442649600", "621627955200", "396722188800", "221705164800", "127998662400", "48771072000", "27636940800", "1", "17", "168", "1220", "7172", "35852", "157132", "616084", "2192506", "7159090", "21631676", "60902460", "160707468", "399489140", "939796228", "2101060924", "4481320149", "9151453613", "17952463180", "33931694704", "61957528720", "109554162816", "187990143808", "313644949184", "509651801344", "807791600000", "1250556129216", "1893271983168", "2806107639040", "4075710281600", "5806280567104", "8119615755712", "11154099827008", "15061775283648", "20004257726064", "26145645547824", "33644807030628", "42644340934020", "53259802113888", "65565790979616", "79585068885480", "95274332180712", "112516352516016", "131110932730032", "150773092160580", "171132178067748", "191741447066688", "212087371934592", "231608361436992", "249716920472640", "265829870923776", "279385661746944", "289894659756480", "296941397872320", "300227034794112", "299585080955520", "294995153434176", "286559630510400", "274559844672000", "259389153907200", "241532891409600", "221597909553600", "200222946000000", "178056657705600", "155765714011200", "133960048488000", "113119093036800", "93740111308800", "76150952236800", "60507218246400", "46991901427200", "35618655398400", "26247862080000", "18741859315200", "12965992704000", "8612768102400", "5463807955200", "3321335404800", "1815909580800", "933153177600", "469827993600", "131681894400", "1", "18", "187", "1424", "8764", "45832", "210072", "861400", "3206786", "10957868", "34666130", "102239488", "282743580", "736889224", "1817936104", "4262532056", "9534038653", "20412279282", "41965109667", "83086702848", "158846483672", "293945054560", "527644521632", "920548782464", "1563679341888", "2590152309632", "4189882939840", "6627188173824", "10261636850752", "15570902168192", "23176132693440", "33866194141184", "48622894045376", "68638246673536", "95331652746368", "130346958972672", "175552149926736", "232998505772976", "304896373544484", "393517810221336", "501151517985420", "629930569834080", "781790566267368", "958203018126576", "1160192223258552", "1387953675426384", "1641014802991332", "1917708372791352", "2215616239559484", "2530806526806912", "2858760146000448", "3193254804953088", "3527942981821632", "3854735694202752", "4166293415465664", "4453493636623104", "4709269329522624", "4924716652492416", "5094443229955776", "5211032259400704", "5272343802869184", "5273290780848000", "5216027060836800", "5098521548332800", "4927360248734400", "4703346319824000", "4437548259940800", "4132222120166400", "3801837457080000", "3449289557174400", "3090301926436800", "2726643392294400", "2374757933126400", "2033123097830400", "1716958572307200", "1422188373312000", "1161022076409600", "926313159168000", "728630289561600", "556427128320000", "419039170905600", "304359431040000", "217738374739200", "147809421043200", "99831514003200", "61623875174400", "38449487462400", "21056097484800", "11937532723200", "4477184409600", "2501955993600", "1", "19", "207", "1649", "10600", "57852", "276620", "1183172", "4595034", "16384606", "54107670", "166643130", "481442164", "1311240788", "3381378852", "8288429500", "19380463765", "43370477631", "93171663563", "192688515141", "384626048292", "742789886992", "1390845000560", "2530070564544", "4479230453440", "7730267787328", "13023970171584", "21450075214912", "34576104315968", "54608889372864", "84591394082624", "128635820301760", "192191363362752", "282341199917888", "408120100587200", "580836495115584", "814383795723136", "1125507150179712", "1534010392737072", "2062846096006896", "2738084274713844", "3588680525700924", "4646066536308348", "5943452916265524", "7514938005668568", "9394273423038600", "11613460498009848", "14201019755829000", "17180207431594308", "20566948993624044", "24367967746188876", "28578772050288228", "33182017765823232", "38146083522361920", "43424269915815360", "48954142843843392", "54658293518596032", "60444945095508288", "66210070142082240", "71839575055280448", "77213243010520512", "82207343908763712", "86700434810715072", "90576623563417152", "93730705789957056", "96072209169768000", "97530722522596800", "98056260716097600", "97625062817092800", "96239585923041600", "93927509616830400", "90743816268187200", "86766992680248000", "82094766931483200", "76844121200049600", "71143861680360000", "65126311716672000", "58931088741676800", "52694570792505600", "46538151814368000", "40578691448160000", "34917059252563200", "29630131391865600", "24782142857760000", "20415986836070400", "16546150497945600", "13183767580838400", "10318463849433600", "7914729619641600", "5944661640288000", "4365745634476800", 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}


static class Ex
{
    public static void join<T>(this IEnumerable<T> values, string sep = " ") => WriteLine(string.Join(sep, values));
    public static string concat<T>(this IEnumerable<T> values) => string.Concat(values);
    public static string reverse(this string s) { var t = s.ToCharArray(); Array.Reverse(t); return t.concat(); }

    public static int lower_bound<T>(this IList<T> arr, T val) where T : IComparable<T>
    {
        int low = 0, high = arr.Count;
        int mid;
        while (low < high)
        {
            mid = ((high - low) >> 1) + low;
            if (arr[mid].CompareTo(val) < 0) low = mid + 1;
            else high = mid;
        }
        return low;
    }
    public static int upper_bound<T>(this IList<T> arr, T val) where T : IComparable<T>
    {
        int low = 0, high = arr.Count;
        int mid;
        while (low < high)
        {
            mid = ((high - low) >> 1) + low;
            if (arr[mid].CompareTo(val) <= 0) low = mid + 1;
            else high = mid;
        }
        return low;
    }
}

class Pair<T, U> : IComparable<Pair<T, U>> where T : IComparable<T> where U : IComparable<U>
{
    public T f; public U s;
    public Pair(T f, U s) { this.f = f; this.s = s; }
    public int CompareTo(Pair<T, U> a) => f.CompareTo(a.f) != 0 ? f.CompareTo(a.f) : s.CompareTo(a.s);
    public override string ToString() => $"{f} {s}";
}

class Scanner
{
    string[] s; int i;
    readonly char[] cs = new char[] { ' ' };
    public Scanner() { s = new string[0]; i = 0; }
    public string[] scan => ReadLine().Split();
    public int[] scanint => Array.ConvertAll(scan, int.Parse);
    public long[] scanlong => Array.ConvertAll(scan, long.Parse);
    public double[] scandouble => Array.ConvertAll(scan, double.Parse);
    public string next
    {
        get
        {
            if (i < s.Length) return s[i++];
            string st = ReadLine();
            while (st == "") st = ReadLine();
            s = st.Split(cs, StringSplitOptions.RemoveEmptyEntries);
            i = 0;
            return next;
        }
    }
    public int nextint => int.Parse(next);
    public long nextlong => long.Parse(next);
    public double nextdouble => double.Parse(next);
}