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;
#define ll long long
#define endl "\n"
#define fastio ios_base::sync_with_stdio(false)
#define inf LLONG_MAX
const ll mod=1e9+7;
ll dp[120][120][1020][5];
int main(){
fastio;
int n,L;
cin>>n>>L;
int a[n+1];
for(int i=1;i<=n;i++) cin>>a[i];
sort(a+1,a+n+1);
for(int open=0;open<=2;open++){
dp[1][1][0][open]=1+(open==1);
}
for(int i=1;i<n;i++){
int d=a[i+1]-a[i];
for(int j=1;j<=n;j++){
for(int cost=0;cost<=L;cost++){
for(int close=0;close<=2;close++){
int nxt=cost+(j+j-close)*d;
if(nxt<=L){
dp[i+1][j+1][nxt][close]+=dp[i][j][cost][close]*(j+1-close);
dp[i+1][j+1][nxt][close]%=mod;
dp[i+1][j][nxt][close]+=dp[i][j][cost][close]*(j+j-close);
dp[i+1][j][nxt][close]%=mod;
}
if(nxt<=L && j-1>0){
dp[i+1][j-1][nxt][close]+=dp[i][j][cost][close]*(j-1);
dp[i+1][j-1][nxt][close]%=mod;
}
if(nxt<=L && close+1<=2){
dp[i+1][j][nxt][close+1]+=dp[i][j][cost][close]*(2-close);
dp[i+1][j][nxt][close+1]%=mod;
dp[i+1][j+1][nxt][close+1]+=dp[i][j][cost][close]*(2-close);
dp[i+1][j+1][nxt][close+1]%=mod;
}
}
}
}
}
ll ans=0;
for(int cost=0;cost<=L;cost++){
ans+=dp[n][1][cost][2];
ans%=mod;
}
cout<<ans<<endl;
return 0;
}
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