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 K 100001
#define N 101
#define M ((ll)1e9+7)
using namespace std;
typedef long long ll;

ll n, k, a[N], dp[K], temp[K];

ll ps(int i, int j, ll *arr) {
	if (i<=0) return arr[j];
	return (arr[j]-arr[i-1]+M+M)%M;
}

int main() {
	cin>>n>>k;
	for (int i=0; i<n; i++) cin>>a[i];
	for (int j=0; j<=k; j++) dp[j]=1;
	temp[0]=1;
	for (int i=0; i<n; i++) {
		for (int j=k; j>0; j--) temp[j]=ps(j-a[i],j,dp);
		for (int j=1; j<=k; j++) dp[j]=(dp[j-1]+temp[j])%M;
	}
	cout<<ps(k,k,dp)<<endl;
}