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;
const int mod = 1000000007;
int a[110];
long long dp[100010], s[100010], t[100010];
int main() {
	int n, k;
	scanf("%d%d", &n, &k);
	dp[0] = 1;
	for (int i = 0; i < n; i++) {
		scanf("%d", &a[i]);
		for (int j = 0; j <= k; j++) {
			s[j+1] = s[j] + dp[j];
			dp[j] = s[j+1] - s[max(j-a[i],0)];
		}
		for (int j = 0; j <= k; j++) {
			dp[j] = (dp[j] % mod + mod) % mod;
		}
	}
	printf("%lld\n", dp[k]);
	return 0;
}
