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;
long long k;
int n;
long long dp[100001];
long long mod=1000000007;
int main()
{
    ios_base::sync_with_stdio(false);
    memset(dp,0,sizeof(dp));
    cin>>n>>k;
    int i,j;
    long long a;
    dp[0]=1;
    for(i=0;i<n;i++)
    {
        cin>>a;
        for(j=1;j<=k;j++)
        dp[j]=(dp[j-1]%mod+dp[j]%mod)%mod;
        for(j=k;j>=a+1;j--)
        dp[j]=(dp[j]%mod-dp[j-a-1]%mod+mod)%mod;
    }
    cout<<dp[k];
    return 0;
}
