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.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;

public class Main {
	int mod = 1000000007;
  
  	int sub(int a, int b){
        a -= b;
        if(a < 0)a += mod;
        return a;
    }
  
    public int findNumWaysToDistributeCandies(int n, int k, int[] a) {
        int[][] prefix = new int[n+1][k+1];
        int[][] dp = new int[n+1][k+1];

        for(int i=0;i<=n;++i) {
            dp[i][0]=1;
            prefix[i][0]=1;
        }

        for(int i=1;i<=k;++i) {
            prefix[0][i]=1;
        }

        for(int i=1;i<=n;++i) {
            for(int j=1;j<=k;++j) {
                int low = (j-a[i]-1)>=0?prefix[i-1][j-a[i]-1]:0;
                int high = prefix[i-1][j];
                dp[i][j]=(sub(high,low))%mod;
                prefix[i][j]=(prefix[i][j-1]+dp[i][j])%mod;
            }
        }
        return dp[n][k];
    }

    public static void main(String[] args) {
        Main m = new Main();
        InputStreamReader r=new InputStreamReader(System.in);
        BufferedReader reader = new BufferedReader(r);
        try {
            String[] line1 = reader.readLine().split(" ");
            int n = Integer.parseInt(line1[0]);
            int k = Integer.parseInt(line1[1]);
            int[] a = new int[n+1];
            String[] line2 = reader.readLine().split(" ");
            for(int i=0;i<n;++i) {
                a[i+1]=Integer.parseInt(line2[i]);
            }
            int res = m.findNumWaysToDistributeCandies(n,k,a);
            System.out.println(res);
        } catch (IOException e) {

        }
    }
}
