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;
int N, K, a[102], mod=1e9+7; ll dp[101][100001]; 
int main(){
    scanf("%d %d", &N, &K);
    for(int i=1; i<=N; i++) scanf("%d", &a[i]);
    dp[0][0] = 1;
    for(int i=1; i<=N; i++){
        dp[i][0] = 1;
        for(int j=1; j<=K; j++){
            dp[i][j] = (dp[i-1][j] - (j>=a[i]+1? dp[i-1][j-a[i]-1]: 0) + mod) % mod;
            dp[i][j] = (dp[i][j] + dp[i][j-1]) % mod;
        }
    }
    printf("%lld\n", dp[N][K]);
}