#include using namespace std; #define rep(i,n) for(int i=0;i P; #define fi first #define sc second #define mp make_pair typedef long long ll; const ll mod = 1234567891; template struct ntt{ inline void add(T &a, T b) { a += b; if(a >= md) a -= md; } inline void sub(T &a, T b) { a -= b; if(a < 0) a += md; } inline T add2(T a, T b) { a += b; if(a >= md) a -= md; return a; } inline T sub2(T a, T b) { return add2(a, md-b); } inline T mul(T a, T b) { return (T)((ll)a*b%md); } inline T power(T a, long long b) { T res = 1; while (b > 0) { if (b & 1) res = mul(res, a); a = mul(a, a); b >>= 1; } return res; } inline T inv(T a) { a %= md; if (a < 0) a += md; T b = md, u = 0, v = 1; while (a) { T t = b / a; b -= t * a; swap(a, b); u -= t * v; swap(u, v); } assert(b == 1); if (u < 0) u += md; return u; } T max_base, root; vector dw, idw; ntt() { T tmp = md - 1; max_base = 0; while (tmp % 2 == 0) { tmp /= 2; max_base++; } root = 2; while (power(root, (md-1)>>1) == 1) root++; dw.resize(max_base); idw.resize(max_base); rep(i, max_base){ sub(dw[i], power(root, (md-1) >> (i+2))); idw[i] = inv(dw[i]); } } void fft(vector &a, bool inv) { const int n = a.size(); assert((n & (n - 1)) == 0); assert(__builtin_ctz(n) <= max_base); if(!inv){ for(int m=n;m>>=1;){ T w = 1; for(int s=0,k=0; s=y?x-y:x+md-y); a[i] = (x+y>=md?x+y-md:x+y); } w = mul(w, dw[__builtin_ctz(++k)]); } } } else{ for(int m=1;m=y?x-y:x+md-y); a[j] = mul(a[j], w); a[i] = (x+y>=md?x+y-md:x+y); } w = mul(w, idw[__builtin_ctz(++k)]); } } } } vector multiply(vector a, vector b, int eq = 0) { int need = a.size() + b.size() - 1; int nbase = 0; while ((1 << nbase) < need) nbase++; int sz = 1 << nbase; a.resize(sz); b.resize(sz); fft(a, 0); if (eq) b = a; else fft(b, 0); int inv_sz = inv(sz); for (int i = 0; i < sz; i++) { a[i] = mul(mul(a[i], b[i]), inv_sz); } fft(a, 1); a.resize(need); return a; } vector square(vector a) { return multiply(a, a, 1); } }; //fast_ntt.cpp /* 167772161; //= 2^25 * 5 + 1 469762049; //= 2^26 * 7 + 1 754974721; //= 2^24 * 45 + 1 1045430273; //= 2^20 * 997 + 1 1051721729; //= 2^20 * 1003 + 1 1053818881; //= 2^20 * 1005 + 1 */ template vector anyntt(vector&a, vector&b, int eq = 0) { //今回は2^20以下だからこっちの方が速い (らしい) (:maroon_kansha:) const T m1 = 167772161, m2 = 469762049, m3 = 754974721; nttn1; nttn2; nttn3; nttnn; auto a1 = n1.multiply(a, b, eq); auto a2 = n2.multiply(a, b, eq); auto a3 = n3.multiply(a, b, eq); const int n = a1.size(); vectorret(n); vectorm; m = {m1, m2, m3}; vectorr; r = {1, n2.inv(m1), n3.inv(n3.mul(m1, m2))}; T mm = nn.mul(m1, m2); rep(i, n){ n2.add(a2[i], n2.sub2(m2, a1[i])); T v1 = n2.mul(a2[i], r[1]); n3.add(a3[i], n3.sub2(m3, n3.add2(a1[i], n3.mul(m1, v1)))); T v2 = n3.mul(a3[i], r[2]); nn.add(a1[i], nn.add2(nn.mul(m1, v1), nn.mul(mm, v2))); ret[i] = a1[i]; } return ret; } ll dp[64][25005], m; int n, a[55]; ll way[25005]; int main(){ ios::sync_with_stdio(0); cin >> n >> m; way[0] = 1; rep(i, n){ cin >> a[i]; for(int x=25003-a[i];x>=0;x--){ way[x+a[i]] += way[x]; if(way[x+a[i]] >= mod) way[x+a[i]] -= mod; } } dp[0][0] = 1; rep(i, 60){ vectorA, B; rep(j, 25005) A.pb(dp[i][j]); rep(j, 25005) B.pb(way[j]); auto C = anyntt(A, B); int f = ((m>>i)&1); rep(j, C.size()){ if(f != (j&1)) continue; dp[i+1][j/2] += C[j]; if(dp[i+1][j/2] >= mod) dp[i+1][j/2] -= mod; } } cout << dp[60][0] << '\n'; }