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;
#define ll long long 
#define ull unsigned long long 
const ll mod = 1e9 + 7;
int main()
{
  ll n,k;
  cin>>n>>k;
  ll dp[n+1][k+1];
  memset(dp,0,sizeof(dp));
  ll arr[n+1];
  for(int i=1;i<=n;++i)
  cin>>arr[i];
  dp[0][0]=1;
  for(int i=1;i<=n;++i)
  {
    ll pre=0;
    for(int j=0;j<=k;++j)
    {
      pre += dp[i-1][j];
      if(j-arr[i]-1>=0) pre -= dp[i-1][j-arr[i]-1];
      pre = (pre + mod)%mod;
      dp[i][j] = pre;
    }
  }
  cout<<dp[n][k];
}