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.InputStreamReader;

public class Main {
	public static void main(String[] args) throws Exception {
		BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
		String[] sa = br.readLine().split(" ");
		int n = Integer.parseInt(sa[0]);
		int k = Integer.parseInt(sa[1]);
		int[] a = new int[n + 1];
		sa = br.readLine().split(" ");
		for (int i = 0; i < n; i++) {
			a[i + 1] = Integer.parseInt(sa[i]);
		}
		br.close();

		int[] b = new int[n + 1];
		for (int i = 0; i < n; i++) {
			b[i + 1] = b[i] + a[i + 1];
		}
		
		long[][] dp = new long[n + 1][k + 1];
		dp[0][0] = 1;
		for (int i = 1; i <= n; i++) {
			dp[i][0] = dp[i - 1][0];
			for (int j = 1; j <= k; j++) {
				dp[i][j] = dp[i][j - 1] + dp[i - 1][j];
				if (j > a[i]) {
					dp[i][j] += 1000000007 - dp[i - 1][j - a[i] - 1];
				}
				dp[i][j] %= 1000000007;
			}
		}
		System.out.println(dp[n][k]);
	}
}
