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;
#define rep(i,n) for(int i = 0; i < (int)n; i++)
typedef long long ll;
const ll mod = 1e9+7;

int main(){
    ll n, k;
    cin >> n >> k;
    ll a[n];
    rep(i,n) cin >> a[i];
    vector<vector<ll>> dp(n+1, vector<ll>(k+2,0));
    dp[0][k] = 1;
    rep(i,n){
        for(int j = k; j >= 0; j--){
            dp[i+1][j] = (dp[i+1][j+1] + dp[i][j]) % mod;
            if(j+a[i]+1 <= k) (dp[i+1][j] += -dp[i][j+a[i]+1] + mod) %= mod ;
        }
    }
    cout << dp[n][0] << endl;
    return 0;
}