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;
#pragma GCC optimize("O3,unroll-loops")
// #pragma GCC target("avx2,bmi,bmi2,lzcnt,popcnt")
// Ofast, O0, O1, O2, O3, unroll-loops, fast-math, trapv
typedef long long ll;
typedef pair<ll, ll> pll;
typedef pair<int, int> pii;
#define Mp make_pair
#define sep ' '
#define endl '\n'
#define F first
#define S second
#define pb push_back
#define SZ(x) (int)x.size()
#define all(x) (x).begin(),(x).end()
#define kill(res) cout << res << '\n', exit(0);
#define set_dec(x) cout << fixed << setprecision(x);
#define fast_io ios_base::sync_with_stdio(false);cin.tie(0);cout.tie(0);
#define file_io freopen("input.txt", "r", stdin) ; freopen("output.txt", "w", stdout);
mt19937 rng(chrono::steady_clock::now().time_since_epoch().count());
const ll N = 109;
const ll M = 1009;
const ll Mod = 1e9 + 7;
ll n, L, a[N], dp[N][N][M][3];
int main(){
fast_io;
cin >> n >> L;
for(int i = 1; i <= n; i++) cin >> a[i];
a[n+1] = 2e4;
sort(a+1, a+n+1);
if(n == 1) kill(1);
dp[1][1][2*(a[2]-a[1])][0] = 1;
dp[1][1][a[2]-a[1]][1] = 2;
for(int i = 2; i <= n; i++){
for(int j = 1; j <= i; j++){
for(int k = 0; k <= L; k++){
for(int o = 0; o < 3; o++){
int dist = (a[i+1] - a[i]) * (2*j - o);
if(k < dist) continue;
dp[i][j][k][o] += (j-o) * dp[i-1][j-1][k-dist][o];
if(o) dp[i][j][k][o] += (3-o) * dp[i-1][j-1][k-dist][o-1];
dp[i][j][k][o] += (2*j-o) * dp[i-1][j][k-dist][o];
if(o) dp[i][j][k][o] += (3-o) * dp[i-1][j][k-dist][o-1];
dp[i][j][k][o] += j * dp[i-1][j+1][k-dist][o];
dp[i][j][k][o] %= Mod;
}
}
}
}
ll res = 0;
for(int k = 0; k <= L; k++) res += dp[n][1][k][2];
res %= Mod;
cout << res;
}
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