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 int long long
#define MOD 1000000007
using namespace std;

int n,k,a[110],dp[110][100010],sum[100010];

signed main()
{
	cin>>n>>k;
	for(int i=1;i<=n;i++) cin>>a[i];
	dp[0][0]=1;
	for(int i=1;i<=n;i++){
		sum[1]=dp[i-1][0];
		for(int j=2;j<=k+1;j++){
			sum[j]=sum[j-1]+dp[i-1][j-1];
			if(sum[j]>=MOD) sum[j]-=MOD;
		}
		for(int j=0;j<=k;j++){
			dp[i][j]=(sum[j+1]-sum[max(j-a[i],0ll)]+MOD);
			if(dp[i][j]>=MOD) dp[i][j]-=MOD;
		}
	}
	cout<<dp[n][k]%MOD<<endl;
	return 0;
}