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>
#define MAXN 107
#define MAXS 6007
using namespace std;
const long long mod=1e9+7;
int n,s,a[MAXN],ans,pref[2*MAXN];
int dp[MAXN][MAXN/2+7][3][3][MAXS];
bool li[MAXN][MAXN/2+7][3][3][MAXS];
bool ok(int sum){
return true;
// return sum>=-5000 and sum<=s;
}
long long even(int pos,int bal,int sum,int l,int r){
if(sum>s or bal>n/2+5)return 0;
if(sum+pref[pos+(bal-5)-2]-pref[pos-1]>s)return 0;
long long free=2*(bal-5)+(-(l==1)-(r==1)) - (-(l==2)-(r==2));
if(free<0)return 0;
if(pos==n+1 and bal==5 and l+r==3 and free==0)return 1;
else if(pos==n+1 and (bal==4 or bal==6) and l==r and l!=0 and free==0)return 1;
else if(pos==n+1)return 0;
if(free==0 and pos!=1)return 0;
if(sum>=-4000 and li[pos][bal][l][r][sum+4000])return dp[pos][bal][l][r][sum+4000];
if(sum>=-4000)li[pos][bal][l][r][sum+4000]=true;
long long curr=0;
curr+=even(pos+1,bal,sum,l,r)*free;
if(l==0){
curr+=even(pos+1,bal+1,sum-a[pos],1,r);
curr+=even(pos+1,bal-1,sum+a[pos],2,r);
}
if(r==0){
curr+=even(pos+1,bal+1,sum-a[pos],l,1);
curr+=even(pos+1,bal-1,sum+a[pos],l,2);
}
long long mult=bal-5+1-(l==1)-(r==1);
long long mult2=bal-5-1+(l==2)+(r==2);
curr+=even(pos+1,bal+1,sum-2*a[pos],l,r)*mult;
curr+=even(pos+1,bal-1,sum+2*a[pos],l,r)*mult2;
curr%=mod;
if(sum>=-4000)dp[pos][bal][l][r][sum+4000]=curr;
return curr;
}
void calc_even(){
ans+=even(1,5,0,0,0);
}
int main(){
cin>>n>>s;
int mins=1000;
if(n==1){
cout<<1<<"\n";
return 0;
}
for(int i=1;i<=n;i++){
cin>>a[i];
}
sort(a+1,a+n+1);
mins=a[1];
for(int i=1;i<=n;i++){
a[i]-=mins;
pref[i]=pref[i-1]+a[i];
}
for(int i=n+1;i<=2*n;i++){
pref[i]=pref[i-1];
}
calc_even();
cout<<ans%mod<<"\n";
return 0;
}
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