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;

const int64_t MOD = 1e9+7;
void add(int64_t& a, int64_t b){
    a = (a+b) % MOD;
}

int64_t dp[101][100001];

int main(){
    int N, K, A[100];
    cin >> N >> K;
    for(int i=0; i<N; i++) cin >> A[i];

    dp[0][0] = 1;
    for(int i=0; i<N; i++){
        int64_t sum = 0;
        for(int j=0; j<=K; j++){
            add(sum, dp[i][j]);
            if(j-A[i]-1>=0) add(sum, MOD - dp[i][j-A[i]-1]);
            add(dp[i+1][j], sum);
        }
    }
    cout << dp[N][K] << endl;
    return 0;
}