There are N children, numbered 1, 2, \ldots, N.

They have decided to share K candies among themselves. Here, for each i (1 \leq i \leq N), Child i must receive between 0 and a_i candies (inclusive). Also, no candies should be left over.

Find the number of ways for them to share candies, modulo 10^9 + 7. Here, two ways are said to be different when there exists a child who receives a different number of candies.

Constraints

* All values in input are integers.
* 1 \leq N \leq 100
* 0 \leq K \leq 10^5
* 0 \leq a_i \leq K

Input

Input is given from Standard Input in the following format:


N K
a_1 a_2 \ldots a_N


Output

Print the number of ways for the children to share candies, modulo 10^9 + 7.

Examples

Input

3 4
1 2 3


Output

5


Input

1 10
9


Output

0


Input

2 0
0 0


Output

1


Input

4 100000
100000 100000 100000 100000


Output

665683269
#include<bits/stdc++.h>
using namespace std;
typedef long long ll;

using namespace std;
#define chmax(a,b) a=max(a,b)
#define mod 1000000007
#define N 100010
ll f[N],cop[N],n,k;
int main(){
    cin>>n>>k;
    for(int i=0;i<=k;i++)f[i]=0; f[0]=1;
    while(n--){
     ll a;cin>>a;
     ll sum=0;
     for(int i=0;i<=k;i++){
         sum+=f[i];
         if(i-a-1>=0)sum-=f[i-a-1];
         sum%=mod;
         cop[i]=sum;
     }
     for(int i=0;i<=k;i++)f[i]=cop[i];
    }
    ll ans=f[k];
    if(ans<0)ans+=mod;
    cout<<ans<<endl;
 return 0;   
}