This submission is migrated from previous version of oj.uz, which used different machine for grading. This submission may have different result if resubmitted.
#pragma GCC optimize("Ofast")
#pragma GCC target("avx,avx2,fma")
#include <iostream>
#include <algorithm>
#define ll long long
const int MD = 1e9 + 7;
using namespace std;
int n, l, ar[101], dp[2][101][1001][3];
int main()
{
ios :: sync_with_stdio(0); cin.tie(0); cout.tie(0);
cin >> n >> l;
if (n == 1) {cout << "1\n"; return 0;}
for (int i = 0; i < n; i++) {cin >> ar[i];}
sort(ar, ar + n);
dp[1][1][0][0] = 1;
dp[1][1][0][1] = 2;
for (int i = 2; i <= n; i++)
{
for (int k = 0; k <= l; k++)
{
for (int m = 0; m <= 2; m++) {dp[i & 1][0][k][m] = 0;}
}
for (int j = 1; j <= i; j++)
{
for (int k = 0; k <= l; k++)
{
for (int m = 0; m <= 2; m++)
{
int v = ar[i - 1] - ar[i - 2]; dp[i & 1][j][k][m] = 0;
if (k - (2 * j - 2 - m) * v >= 0)
{
dp[i & 1][j][k][m] = (dp[i & 1][j][k][m] + (ll)(j - m) * dp[~i & 1][j - 1][k - (2 * j - 2 - m) * v][m]) % MD;
}
if (k - (2 * j - m) * v >= 0)
{
dp[i & 1][j][k][m] = (dp[i & 1][j][k][m] + (ll)(2 * j - m) * dp[~i & 1][j][k - (2 * j - m) * v][m]) % MD;
}
if (k - (2 * j + 2 - m) * v >= 0 && j + 1 < i && (j >= m || i == n))
{
dp[i & 1][j][k][m] = (dp[i & 1][j][k][m] + (ll)j * dp[~i & 1][j + 1][k - (2 * j + 2 - m) * v][m]) % MD;
}
if (k - (2 * j - m - 1) * v>= 0 && m)
{
dp[i & 1][j][k][m] = (dp[i & 1][j][k][m] + (ll)(3 - m) * dp[~i & 1][j - 1][k - (2 * j - m - 1) * v][m - 1]) % MD;
}
if (k - (2 * j - m + 1) * v>= 0 && m && (j >= m || i == n) && j < i)
{
dp[i & 1][j][k][m] = (dp[i & 1][j][k][m] + (ll)(3 - m) * dp[~i & 1][j][k - (2 * j - m + 1) * v][m - 1]) % MD;
}
}
}
}
}
int res = 0;
for (int i = 0; i <= l; i++)
{
res = (res + dp[n & 1][1][i][2]) % MD;
}
cout << res << "\n";
return 0;
}
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