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
import java.util.*;

public class Main {
    public static long solve(int arr[],int n,int k){
        long mod = 1000000007;
        long dp[][] = new long[n+1][k+1];

        for(int j=0;j<=k;j++){
            dp[1][j] = (j > arr[1]) ? 0 : 1;
        }

        for(int i=2;i<=n;i++){
            for(int j=0;j<=k;j++){
                if(j == 0){
                    dp[i][j] = dp[i-1][j];
                }
                else{
                    dp[i][j] = (mod +  dp[i][j-1] + dp[i-1][j] - ( (j-arr[i]-1 >= 0) ? dp[i-1][j-arr[i]-1] : 0 ) )% mod;
                }
            }
        }

        return dp[n][k];
    }

    public static void main(String args[]) {
        Scanner sc = new Scanner(System.in);
        int n = sc.nextInt();
        int k = sc.nextInt();
        int arr[] = new int[n+1];
        for(int i=1;i<=n;i++) arr[i] = sc.nextInt();
        System.out.println(solve(arr,n,k));
    }
}