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;
typedef long long ll;
const int N = 100 + 7;
const int L = 1000 + 7;
const int M = 1e9 + 7;
int n, l, a[N];
int dp[N][N][L][2][2];
int add(int a, int b) {
a += b;
if (a >= M) a -= M;
if (a < 0) a += M;
return a;
}
void addup(int &a, int b) {
a = add(a, b);
}
int mul(int a, int b) {
return (ll) a * b % M;
}
int mul(int a, int b, int c) {
return mul(a, mul(b, c));
}
int main() {
ios::sync_with_stdio(false);
cin.tie(0);
cin >> n >> l;
for (int i = 1; i <= n; ++i) {
cin >> a[i];
}
sort(a + 1, a + n + 1);
dp[1][0][0][0][0] = 1;
dp[1][0][0][0][1] = 1;
dp[1][0][0][1][0] = 1;
dp[1][0][0][1][1] = 1;
for (int i = 1; i <= n; ++i) {
for (int j = 0; j <= n; ++j) {
for (int s = 0; s <= l; ++s) {
for (int S = 0; S <= 1; ++S) {
for (int F = 0; F <= 1; ++F) {
if (j > 0) {
addup(dp[i + 1][j - 1][s + (2 * j + S + F) * (a[i + 1] - a[i])][S][F], mul(dp[i][j][s][S][F], j));
}
addup(dp[i + 1][j][s + (2 * j + S + F) * (a[i + 1] - a[i])][S][F], mul(dp[i][j][s][S][F], j, 2));
addup(dp[i + 1][j + 1][s + (2 * j + S + F) * (a[i + 1] - a[i])][S][F], mul(dp[i][j][s][S][F], j));
if (S == 1) {
addup(dp[i + 1][j + 1][s + (2 * j + S + F) * (a[i + 1] - a[i])][0][F], dp[i][j][s][S][F]);
addup(dp[i + 1][j + 1][s + (2 * j + S + F) * (a[i + 1] - a[i])][1][F], dp[i][j][s][S][F]);
addup(dp[i + 1][j][s + (2 * j + S + F) * (a[i + 1] - a[i])][0][F], dp[i][j][s][S][F]);
addup(dp[i + 1][j][s + (2 * j + S + F) * (a[i + 1] - a[i])][1][F], dp[i][j][s][S][F]);
}
if (F == 1) {
addup(dp[i + 1][j + 1][s + (2 * j + S + F) * (a[i + 1] - a[i])][S][0], dp[i][j][s][S][F]);
addup(dp[i + 1][j + 1][s + (2 * j + S + F) * (a[i + 1] - a[i])][S][1], dp[i][j][s][S][F]);
addup(dp[i + 1][j][s + (2 * j + S + F) * (a[i + 1] - a[i])][S][0], dp[i][j][s][S][F]);
addup(dp[i + 1][j][s + (2 * j + S + F) * (a[i + 1] - a[i])][S][1], dp[i][j][s][S][F]);
}
}
}
}
}
}
int ans = 0;
for (int i = 0; i <= l; ++i) ans = add(ans, dp[n][0][i][0][0]);
cout << ans << "\n";
return 0;
}
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