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 <bits/stdc++.h>
using namespace std;
const int Mod = 1e9 + 7;
int n, L, a[101];
long long dp[101][101][1005][3];
signed main() {
cin >> n >> L;
for (int i = 1; i <= n; ++i) cin >> a[i];
sort(a + 1, a + n + 1);
if(n == 1) {
cout << 1;
return 0;
}
dp[1][1][0][0] = 1;
dp[1][1][0][1] = 2;
for (int i = 1; i < n; ++i) {
for (int j = 1; j <= i; ++j) {
for (int k = 0; k <= L; ++k) {
for (int e = 0; e < 3; ++e) {
if(dp[i][j][k][e] == 0) continue;
int new_cost = k + (a[i + 1] - a[i]) * (2 * j - e);
if(new_cost > L) continue;
(dp[i + 1][j + 1][new_cost][e] += dp[i][j][k][e] * (j + 1 - e)) %= Mod;
(dp[i + 1][j][new_cost][e] += dp[i][j][k][e] * (2 * j - e)) %= Mod;
(dp[i + 1][j - 1][new_cost][e] += dp[i][j][k][e] * (j - 1)) %= Mod;
if(e < 2) {
(dp[i + 1][j + 1][new_cost][e + 1] += dp[i][j][k][e] * (2 - e)) %= Mod;
(dp[i + 1][j][new_cost][e + 1] += dp[i][j][k][e] * (2 - e)) %= Mod;
}
}
}
}
}
long long ans = 0;
for (int i = 0; i <= L; ++i) {
ans += dp[n][1][i][2];
ans %= Mod;
}
cout << ans;
}
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