#include #include "testlib.h" using namespace std; #define MOD 1000000007 const int MIN_N = 1; const int MAX_N = 40; const int MIN_MP = 1; const int MAX_MP = 20000; const int MIN_Mq = 0; const int MAX_Mq = 20000; const int MIN_L = 1; const int MAX_L = 10000; const int MIN_S = 0; const int MAX_S = MAX_L - 1; vector fac(50000, 1); long modpow(long x, long p, long mod){ long ret = 1; while (p > 0){ if (p & 1) ret = (ret * x) % mod; x = (x * x) % mod; p >>= 1; } return ret; } long nCr(long n, long r){ if (n < r) return 0; return (((fac[n] * modpow(fac[n - r], MOD - 2, MOD)) % MOD) * modpow(fac[r], MOD - 2, MOD)) % MOD; } int main(int argc, char *argv[]){ registerValidation(argc, argv); int N = inf.readInt(MIN_N, MAX_N, "N"); inf.readSpace(); int MP = inf.readInt(MIN_MP, MAX_MP, "MP"); inf.readSpace(); int Mq = inf.readInt(MIN_Mq, MAX_Mq, "Mq"); inf.readSpace(); int L = inf.readInt(MIN_L, MAX_L, "L"); inf.readEoln(); vector S(N); for (int i = 0; i < N; i++){ if (i != 0){ inf.readSpace(); } S[i] = inf.readInt(MIN_S, L - 1, "S[i]"); } inf.readEoln(); inf.readEof(); vector> dp(N + 1, vector(Mq + 1, 0)); dp[0][Mq] = 1; for (int i = 1; i <= min(S[0], Mq); i++){ dp[1][Mq - i] = 1; } for (int i = 1; i < N; i++){ for (int k = N; k >= 1; k--){ long sum = 0; for (int r = Mq; r >= 0; r--){ dp[k][r] = (dp[k][r] + sum) % MOD; sum = (sum + dp[k - 1][r]) % MOD; if (r + S[i] <= Mq) sum = (sum - dp[k - 1][r + S[i]] + MOD) % MOD; } } } for (int i = 1; i < 50000; i++){ fac[i] = (fac[i - 1] * i) % MOD; } long ans = 0; for (int m = 0; m <= Mq; m++){ for (int x = 0; x <= N; x++){ ans = (ans + dp[x][Mq - m] * nCr(MP + m - L * x + N - 1, N - 1)) % MOD; } } cout << ans << endl; }