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S2OJ/1461/1461.cpp
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82
S2OJ/1461/1461.cpp
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#include <iostream>
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#include <algorithm>
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using std::cin;
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using std::cout;
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const char endl = '\n';
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const int N = 45,
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D = 1e5 + 5;
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const int mod = 1e9 + 7;
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int n, d, r[N], f[N][N][N * N], ans;
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int fac[D], inv[D];
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int binpow(int a, int b) {
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int res = 1;
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a %= mod;
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while (b) {
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if (b & 1) res = 1ll * res * a % mod;
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a = 1ll * a * a % mod;
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b >>= 1;
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}
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return res;
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}
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inline int C(int n, int m) {
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return 1ll * fac[n] * inv[m] % mod * inv[n - m] % mod;
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}
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int main() {
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std::ios::sync_with_stdio(false);
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cin.tie(nullptr);
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// factorial
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fac[0] = 1;
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for (int i = 1; i <= 100000; i++) {
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fac[i] = 1ll * fac[i - 1] * i % mod;
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}
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// inverse
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inv[100000] = binpow(fac[100000], mod - 2);
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for (int i = 99999; i >= 0; i--)
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inv[i] = 1ll * inv[i + 1] * (i + 1) % mod;
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// main
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cin >> n >> d;
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for (int i = 1; i <= n; i++) {
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cin >> r[i];
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}
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std::sort(r + 1, r + 1 + n);
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f[0][0][0] = 1;
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for (int i = 0; i <= n; i++) {
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for (int j = 0; j <= i; j++) {
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for (int k = 0; k <= 40 * 40; k++) {
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int t = r[i + 1];
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if (j >= 1) {
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f[i + 1][j][k + t] = (f[i + 1][j][k + t] + 1ll * f[i][j][k] * 2 * j) % mod;
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}
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if (j >= 2) {
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f[i + 1][j - 1][k + t * 2 - 1] = (f[i + 1][j - 1][k + t * 2 - 1] + 1ll * f[i][j][k] * j * (j - 1)) % mod;
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}
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f[i + 1][j + 1][k + 1] = (f[i + 1][j + 1][k + 1] + f[i][j][k]) % mod;
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}
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}
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}
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for (int i = 0; i <= std::min(d, 40 * 40); i++) {
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ans = (ans + 1ll * C(d - i + n, n) * f[n][1][i] % mod) % mod;
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}
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cout << ans << endl;
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return 0;
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}
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