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 <iostream>
using namespace std;int a[105];int d[105][100005];
#define M 1000000007
#define r(i,a,b) for(int i=a;i<=b;i++)
int main(){ios_base::sync_with_stdio(false);cin.tie(0);cout.tie(0);int n,k;cin>>n>>k;r(i,0,n-1){cin>>a[i];}r(i,0,a[0])d[0][i]=i+1;r(i,a[0]+1,k)d[0][i]=d[0][a[0]];r(i,1,n-1){d[i][0]=1;r(j,1,k){d[i][j]=d[i][j-1];d[i][j]+=(d[i-1][j]-(j-a[i]-1>=0?d[i-1][j-a[i]-1]:0))%M;d[i][j]%=M;}}cout<<(d[n-1][k]-d[n-1][k-1]+M)%M<<"\n";return 0;}