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;

typedef long long lli;

lli mod = 1e9 +7;
lli dp[100001], presum[100001], a[100002], n, k;
int main()
{
    ios_base::sync_with_stdio(false);cin.tie(0);cout.tie(0);
    cin >> n >> k;
    for(int i=1; i<=n; i++)cin>>a[i];
	for(int i=1; i<=k+1; i++)presum[i]=1;
    for(int i=1; i<=n; i++)
    {
    	for(lli j=0; j<=k; j++)
    		dp[j] = (presum[j+1] - presum[max(0LL, j-a[i])] + 2*mod)%mod;
    	for(int x=1; x<=k+1; x++)
    		presum[x] = (presum[x-1]+dp[x-1])%mod;
    }
    cout << dp[k];
}