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;
using ll=long long;
ll mod=1e9+7;
int dp[101][100002];
vector<ll> v;
ll solve(int i,int j)
{
  if(dp[i][j]!=-1)
  return dp[i][j];
  if(i==0)
  return dp[i][j]=(j<=v[i]?1:0);
  if(j==0)
  return dp[i][j]=solve(i-1,j);
  ll ans=0;
  ans=(mod+solve(i,j-1)+solve(i-1,j)-((j-1-v[i]>=0)?solve(i-1,j-1-v[i]):0))%mod;
  return dp[i][j]=ans;
}
int main()
{
  memset(dp,-1,sizeof(dp));
  int n,k;
  cin>>n>>k;
  v.resize(n);
  for(ll& x:v)
  cin>>x;
  cout<<solve(n-1,k)<<endl;
  return 0;
}