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 <iostream>
using namespace std;
typedef long long ll;
const int MOD = 1000000007; 
int n, k;
int a[110];
ll cum[100010];
ll dp[110][100010];

int main() {
    cin >> n >> k;
    for (int i = 0; i < n; i++) cin >> a[i];

    for (int j = 0; j <= a[0]; j++) dp[1][j] = 1;
    for (int i = 1; i < n; i++) {
        cum[0] = 0;
        for (int j = 0; j <= k; j++) cum[j+1] = (cum[j] + dp[i][j]) % MOD;
        for (int j = 0; j <= k; j++) dp[i+1][j] = (cum[j+1] - cum[max(0, j - a[i])] + MOD) % MOD; 
    }
    cout << dp[n][k] << endl;
}