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>
using namespace std;

const int mod = 1000000007;
int n, k, i, lim;
int dp [100001];
int pre [100001];

int main ()
	{
	scanf ("%d%d",&n,&k);
	fill (pre, pre+k+1, 1);
	while (n--)
		{
		scanf ("%d",&lim);
		for (i=0; i<=k; i++)
			{
			dp[i]=pre[i];
			if (i-lim-1>=0)
				{
				dp[i]-=pre[i-lim-1];
				if (dp[i]<0)
					dp[i]+=mod;
				}
			}
		for (i=1; i<=k; i++)
			{
			pre[i]=pre[i-1]+dp[i];
			if (pre[i]>=mod)
				pre[i]-=mod;
			}
		}
	printf ("%d\n",dp[k]);
	return 0;
	}
