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;
const ll MOD = 1000000007;
#define REP(i, n) for (int i = 0; i < n; i++)

ll n, k, a[105], dp[105][100005];

int main() {
    cin >> n >> k;
    REP(i,n) cin >> a[i];
    dp[0][k] = 1;
    REP(i,n){
        REP(j,k+1){
            dp[i][j+1] += dp[i][j];
            dp[i][j+1] %= MOD;
        }
        REP(j,k+1){
            dp[i+1][j] += dp[i][min(k,j+a[i])] - (j>0?dp[i][j-1]:0) + MOD;
            dp[i+1][j] %= MOD;
        }
    }
    cout << dp[n][0] << endl;
    return 0;
}
