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;
int main(){
int n;
int t;
cin >> n >> t;
if (n==1){
cout << "1\n";
exit(0);
}
vector<vector<vector<vector<int>>>> dp(n+1,vector<vector<vector<int>>>(n+1,vector<vector<int>>(t+1,vector<int>(3,0))));
dp[0][0][0][0]=1;
vector<int> lis={};
for (int i=0;i<n;i++){
int unos;
cin >> unos;
lis.push_back(unos);
}
sort(lis.begin(),lis.end());
lis.push_back(1e9);
for (int i=1;i<=n;i++){
for (int comp=1;comp<=i;comp++){
for (int rez=0;rez<=t;rez++){
for (int pockra=0;pockra<=2;pockra++){
int prom=(2*comp-pockra)*(lis[i]-lis[i-1]);
prom%=int (1e9+7);
if (prom>rez){
// cout << "- ";
continue;
}
if (i+comp+1-pockra>n){
// cout << "- ";
continue;
}
//cout << prom << " ";
dp[i][comp][rez][pockra]+=dp[i-1][comp-1][rez-prom][pockra];
dp[i][comp][rez][pockra]%=int (1e9+7);
if (pockra==1){
dp[i][comp][rez][pockra]+=2*dp[i-1][comp-1][rez-prom][0];
dp[i][comp][rez][pockra]%=int (1e9+7);
}
if (pockra==2){
dp[i][comp][rez][pockra]+=dp[i-1][comp-1][rez-prom][1];
dp[i][comp][rez][pockra]%=int (1e9+7);
}
dp[i][comp][rez][pockra]+=(comp*2-pockra)*dp[i-1][comp][rez-prom][pockra];
dp[i][comp][rez][pockra]%=int (1e9+7);
if (pockra==1){
dp[i][comp][rez][pockra]+=(comp*2)%(int(1e9+7))*dp[i-1][comp][rez-prom][0];
dp[i][comp][rez][pockra]%=int (1e9+7);
}
if (pockra==2 && i==n){
dp[i][comp][rez][pockra]+=dp[i-1][comp][rez-prom][1];
dp[i][comp][rez][pockra]%=int (1e9+7);
}
else if (pockra==2){
dp[i][comp][rez][pockra]+=(comp-1)%(int(1e9+7))*dp[i-1][comp][rez-prom][1];
dp[i][comp][rez][pockra]%=int (1e9+7);
}
if (pockra==0){
dp[i][comp][rez][pockra]+=(comp*(comp+1))%(int(1e9+7))*dp[i-1][comp+1][rez-prom][0];
dp[i][comp][rez][pockra]%=int (1e9+7);
}
else if (pockra==1){
dp[i][comp][rez][pockra]+=(comp*comp)%(int(1e9+7))*dp[i-1][comp+1][rez-prom][1];
dp[i][comp][rez][pockra]%=int (1e9+7);
}
else if (i==n){
dp[i][comp][rez][pockra]+=dp[i-1][comp+1][rez-prom][2];
dp[i][comp][rez][pockra]%=int (1e9+7);
}
else {
dp[i][comp][rez][pockra]+=(((comp-1)*2)+(comp-1)*(comp-2))%(int(1e9+7))*dp[i-1][comp+1][rez-prom][2];
}
// cout << dp[i][comp][rez][pockra] << " ";
}
// cout << " ";
}
// cout << " ";
}
// cout << "\n";
}
int rje=0;
for (int i=0;i<=t;i++){
rje+=dp[n][1][i][2];
rje%=int(1e9+7);
}
cout << rje << "\n";
}
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