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 <cstdio>
#include <algorithm>
using namespace std;
#define ll long long
int main(){
	ll n, k, a, mod = 1000000007;
	scanf("%lld %lld", &n, &k);
	ll dp[k + 1], p[k + 2];
	for (ll i = 0; i < n; i++){
		scanf("%lld", &a);
		fill(dp, dp + k + 1, 0);
		if (i == 0) for (ll j = 0; j <= a; j++) dp[j] = 1;
		else for (ll j = 0; j <= k; j++) dp[j] = (p[j + 1] - p[max(0ll, j - a)] + mod) % mod;
		p[0] = 0;
		for (ll j = 0; j <= k; j++) p[j + 1] = (p[j] + dp[j]) % mod;
	}
	printf("%lld\n", dp[k]);
}