This submission is migrated from previous version of oj.uz, which used different machine for grading. This submission may have different result if resubmitted.
#include <iostream>
#include <algorithm>
#define int long long
using namespace std;
const long long mod = 1e9+7;
long long n, m, a[110], dp[110][1010][110][3], sum;
signed main() {
cin >> n >> m;
for (int i = 1; i <= n; i++) cin >> a[i];
if (n == 1) {
cout << 1 << endl;
return 0;
}
sort(a+1,a+n+1);
dp[1][0][1][0] = 1;
dp[1][0][1][1] = 2;
for (int i = 2; i <= n; i++) {
for (int j = 0; j <= m; j++) {
for (int k = 1; k <= n; k++) {
if (j >= 2*(k-1)*(a[i]-a[i-1])) (dp[i][j][k][0] += dp[i-1][j-2*(k-1)*(a[i]-a[i-1])][k-1][0]*k) %= mod;
if (j >= 2*(k)*(a[i]-a[i-1])) (dp[i][j][k][0] += dp[i-1][j-2*(k)*(a[i]-a[i-1])][k][0]*2*k) %= mod;
if (j >= 2*(k+1)*(a[i]-a[i-1])) (dp[i][j][k][0] += dp[i-1][j-2*(k+1)*(a[i]-a[i-1])][k+1][0]*k) %= mod;
if (j >= 2*(k-1)*(a[i]-a[i-1])) (dp[i][j][k][1] += dp[i-1][j-2*(k-1)*(a[i]-a[i-1])][k-1][0]*2) %= mod;
if (j >= 2*(k)*(a[i]-a[i-1])) (dp[i][j][k][1] += dp[i-1][j-2*(k)*(a[i]-a[i-1])][k][0]*2) %= mod;
if (j >= (2*(k-1)-1)*(a[i]-a[i-1])) (dp[i][j][k][1] += dp[i-1][j-(2*(k-1)-1)*(a[i]-a[i-1])][k-1][1]*(k-1)) %= mod;
if (j >= (2*(k)-1)*(a[i]-a[i-1])) (dp[i][j][k][1] += dp[i-1][j-(2*(k)-1)*(a[i]-a[i-1])][k][1]*(2*(k)-1)) %= mod;
if (j >= (2*(k+1)-1)*(a[i]-a[i-1])) (dp[i][j][k][1] += dp[i-1][j-(2*(k+1)-1)*(a[i]-a[i-1])][k+1][1]*(k)) %= mod;
if (j >= (2*(k-1)-1)*(a[i]-a[i-1])) (dp[i][j][k][2] += dp[i-1][j-(2*(k-1)-1)*(a[i]-a[i-1])][k-1][1]) %= mod;
if (j >= (2*(k)-1)*(a[i]-a[i-1])) (dp[i][j][k][2] += dp[i-1][j-(2*(k)-1)*(a[i]-a[i-1])][k][1]) %= mod;
if (j >= (2*(k-1)-2)*(a[i]-a[i-1])) (dp[i][j][k][2] += dp[i-1][j-(2*(k-1)-2)*(a[i]-a[i-1])][k-1][2]*(k-2)) %= mod;
if (j >= (2*(k)-2)*(a[i]-a[i-1])) (dp[i][j][k][2] += dp[i-1][j-(2*(k)-2)*(a[i]-a[i-1])][k][2]*(2*(k)-2)) %= mod;
if (j >= (2*(k+1)-2)*(a[i]-a[i-1])) (dp[i][j][k][2] += dp[i-1][j-(2*(k+1)-2)*(a[i]-a[i-1])][k+1][2]*(k)) %= mod;
}
}
}
for (int i = 0; i <= m; i++) (sum += dp[n][i][1][2]) %= mod;
cout << sum << endl;
}
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