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>
#define maxn 120
#define maxk 120000
using namespace std;
typedef long long LL;
const int mod = 1000000007;
LL s[maxk];
LL f[maxk];
LL a[maxn];
int main(){
	ios::sync_with_stdio(false);
	int N, K;
	cin >> N >> K;
	for(int i = 1; i <= N; i += 1) cin >> a[i];
	f[0] = 1;
	for(int i = 1; i <= N; i += 1){
		for(int j = 0; j <= K; j += 1) s[j] = j ? (s[j - 1] + f[j]) % mod : f[j];
		for(int j = 0; j <= K; j += 1){
			int L = max(0LL, j - a[i]);
			f[j] = (s[j] - (L ? s[L - 1] : 0) + mod) % mod;
		}
	}
	cout << f[K];
}