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;

long dp[101][100010];
const int mod=1e9+7;

int main()
{
    int N, K; cin>>N>>K;
    vector<int> a(N); for(auto& e: a) cin>>e;

    dp[0][0]=1;
    for(int i=0; i<N; ++i) {
        for(int j=0; j<=K; ++j) {
            dp[i+1][j]=dp[i][j];
            if (j>=1)
                dp[i+1][j]+=dp[i+1][j-1];
            if (j-1>=a[i])
                dp[i+1][j]+=mod-dp[i][j-1-a[i]];
            dp[i+1][j]%=mod;
        }
    }
    cout<<dp[N][K]<<endl;
}
