This submission is migrated from previous version of oj.uz, which used different machine for grading. This submission may have different result if resubmitted.
//resolve it
#include <bits/stdc++.h>
using namespace std;
#define ll long long
#define pb push_back
#define fr first
#define sc second
#define int ll
#define all(x) x.begin(),x.end()
#define rall(x) x.rbegin(),x.rend()
const int N=105,mod=1e9+7;
int dp[N][N][1005][3];
void solve(){
int n,l;cin>>n>>l;
vector<int> a(n);
for(int i=0;i<n;i++) cin>>a[i];
if(n==1) {
cout<<1<<endl;
return;
}
sort(all(a));
if(a[1]-a[0]<=l) dp[1][1][a[1]-a[0]][1]=2;
if(2*(a[1]-a[0])<=l) dp[1][1][2*(a[1]-a[0])][0]=1;
a.pb(10000);
for(int i=1;i<n;i++) {
int d=(a[i+1]-a[i]);
for(int j=1;j<=i;j++) {
for(int s=0;s<=l;s++) {
for(int f=0;f<3;f++) {
if(!dp[i][j][s][f]) continue;
//add to ends
if(f<2 && s+d*(2*j-f-1)<=l) {
if(i==n-1) {
dp[i+1][j][s+d*(2*j-f-1)][f+1]+=(dp[i][j][s][f]*(2-f)*j);
dp[i+1][j][s+d*(2*j-f-1)][f+1]%=mod;
}
else if(f==0 || j>1) {
dp[i+1][j][s+d*(2*j-f-1)][f+1]+=(dp[i][j][s][f]*(2-f)*(j-f));
dp[i+1][j][s+d*(2*j-f-1)][f+1]%=mod;
}
if(s+d*(2*j-f+1)<=l) {
dp[i+1][j+1][s+d*(2*j-f+1)][f+1]+=(dp[i][j][s][f]*(2-f));
dp[i+1][j+1][s+d*(2*j-f+1)][f+1]%=mod;
}
}
//create
if(s+d*(2*j-f+2)<=l) {
dp[i+1][j+1][s+d*(2*j-f+2)][f]+=dp[i][j][s][f];
dp[i+1][j+1][s+d*(2*j-f+2)][f]%=mod;
}
//add
if(s+d*(2*j-f)<=l) {//<-
dp[i+1][j][s+d*(2*j-f)][f]+=dp[i][j][s][f]*(2*j-f);
dp[i+1][j][s+d*(2*j-f)][f]%=mod;
}
//merge
if(s+d*(2*j-f-2)<=l && j>=2 && (i==n-1 || j>2 || f<2)) {
if(f==0) {
dp[i+1][j-1][s+d*(2*j-f-2)][f]+=dp[i][j][s][f]*(j-1)*j;
dp[i+1][j-1][s+d*(2*j-f-2)][f]%=mod;
}
if(f==1) {
dp[i+1][j-1][s+d*(2*j-f-2)][f]+=dp[i][j][s][f]*(j-1)*(j-1);
dp[i+1][j-1][s+d*(2*j-f-2)][f]%=mod;
}
if(f==2) {
if(i==n-1) {
dp[i+1][j-1][s+d*(2*j-f-2)][f]+=dp[i][j][s][f];
dp[i+1][j-1][s+d*(2*j-f-2)][f]%=mod;
}
else {
dp[i+1][j-1][s+d*(2*j-f-2)][f]+=dp[i][j][s][f]*(j-1)*(j-2);
dp[i+1][j-1][s+d*(2*j-f-2)][f]%=mod;
}
}
}
}
}
}
}
int ans=0;
for(int i=0;i<=l;i++) {
ans+=dp[n][1][i][2];
ans%=mod;
}
cout<<ans<<endl;
}
signed main(){
int t=1;//cin>>t;
while(t--){
solve();
}
}
//#endif
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