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<cstdio>
#include<algorithm>
#define mod 1000000007
using namespace std;
long long dp[101][100001]={},a[100],sum[100002]={};
int main(){
    int n,k;
    scanf("%d %d",&n,&k);
    for(int i=0;i<n;i++){
        scanf("%lld",&a[i]);
    }
    dp[0][0]=1;
    for(int i=1;i<=n;i++){
        for(int j=1;j<=k+1;j++){
            sum[j]=sum[j-1]+dp[i-1][j-1];
        }
        for(int j=0;j<=k;j++){
            dp[i][j]=sum[j+1]-sum[max(0LL,(long long)j-a[i-1])];
            dp[i][j]%=mod;
        }
    }
    printf("%lld\n",dp[n][k]);
}