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 long dp[105][100005];
long long MOD = 1000000007;

int main() {int n,k; scanf("%i%i", &n, &k); dp[0][0] = 1;for (int x = 1; x <= n; x++) {long long a; scanf("%lli", &a); for (int y = 0; y <= k; y++) {dp[x][y] += dp[x-1][y] - (y-a > 0 ? dp[x-1][y-a-1] : 0); if (y > 0) dp[x][y] += dp[x][y-1]; dp[x][y] %= MOD; dp[x][y] += MOD; dp[x][y] %= MOD;}}printf("%lli\n", dp[n][k] % MOD);}
