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>
#include <ext/pb_ds/assoc_container.hpp>
#include <ext/pb_ds/tree_policy.hpp>
#define pb push_back
#define ld long double
#define fi first
#define se second
#define ll long long
#define ss(x) (int) x.size()
#define mp make_pair
#define FOR(i, n) for(int i = 1; n >= i; ++i)
using namespace std;
using namespace __gnu_pbds;
const int nax = 105, mod = 1e9 + 7;
int n, s;
int a[nax];
int dp[nax][nax][1005][3];
void add(int &a, int b) {
a += b;
if(a >= mod)
a -= mod;
}
int jazda(int x, int y) {
int normal = x - y;
int odp = normal * (normal - 1);
odp += y * (x - 1);
if(y == 2)
odp -= 2;
odp %= mod;
return odp;
}
int main() {
cin.tie(0);
ios_base::sync_with_stdio(0);
cin >> n >> s;
for(int i = 1; i <= n; ++i) {
cin >> a[i];
}
sort(a + 1, a + n + 1);
dp[0][0][0][0] = 1;
for(int i = 0; i < n; ++i) {
for(int j = 0; j <= n; ++j) {
for(int sum = 0; sum <= s; ++sum) {
for(int ile = 0; ile <= 2; ++ile) {
if(dp[i][j][sum][ile] == 0)
continue;
int val = dp[i][j][sum][ile];
//5 cout << i << " " << j << " " << sum << " " << ile << " " << val << endl;
// 1. dodaj 1
// cout << dp[2][0][9][1] << " 1" << endl;
int dodatek = 2 * (j + 1) - ile;
int nsum = sum + dodatek * (a[i + 2] - a[i + 1]);
if(nsum <= s && i < n - 1)
add(dp[i + 1][j + 1][nsum][ile], val);
// 2. dodaj kraniec + 1
if(ile <= 1 && i < n - 1) {
dodatek = 2 * (j + 1) - ile - 1;
nsum = sum + dodatek * (a[i + 2] - a[i + 1]);
if(nsum <= s)
add(dp[i + 1][j + 1][nsum][ile + 1], (ll) val * (ile == 0 ? 2 : 1) % mod);
}
//cout << dp[2][0][9][1] << " 3" << endl;
// 3. dodaj kraniec + 0
if(ile <= 1 && j >= 1 && j > ile) {
dodatek = 2 * j - ile - 1;
nsum = sum + dodatek * (a[i + 2] - a[i + 1]);
// cout << i << " " << nsum << "AAA" << " " << dodatek << endl;
if(nsum <= s)
add(dp[i + 1][j][nsum][ile + 1], (ll) (j - ile) * val * (ile == 0 ? 2 : 1) % mod);
}
// cout << dp[2][0][9][1] << " 4" << endl;
// 4. end
if(i == n - 1 && ile == 2 && j == 2) {
dodatek = 2 * (j - 1) - ile;
nsum = sum;
//cout << i << " " << nsum << "BBB" << endl;
if(nsum <= s)
add(dp[i + 1][j - 1][nsum][ile], val);
}
if(i == n - 1 && ile == 1 && j == 1) {
nsum = sum;
// cout << nsum << "a" << endl;
add(dp[i + 1][j][nsum][2], val);
}
// cout << dp[2][0][9][1] << " 5" << endl;
// 5. + 0
if(j >= 1 && i < n - 1) {
dodatek = 2 * j - ile;
nsum = sum + dodatek * (a[i + 2] - a[i + 1]);
if(nsum <= s)
add(dp[i + 1][j][nsum][ile], (ll) val * ((j - ile) * 2 + ile) % mod);
}
// cout << dp[2][0][9][1] << endl;
// 6. polacz
if(j >= 2 && j - ile > 0 && i < n - 1) {
// cout << "CCC" << i << " " << j << " " << ile << endl;
dodatek = 2 * (j - 1) - ile;
nsum = sum + dodatek * (a[i + 2] - a[i + 1]);
if(nsum <= s)
add(dp[i + 1][j - 1][nsum][ile], (ll) val * (jazda(j, ile)) % mod);
}
// cout << dp[2][0][9][1] << endl;
}
}
}
}
int ans = 0;
for(int i = 0; i <= s; ++i) {
// cout << dp[n][1][i][2] << endl;
add(ans, dp[n][1][i][2]);
}
cout << ans;
return 0;
}
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