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.Scanner;

public class Main {

	static Scanner sc = new Scanner(System.in);
	static long MOD = 1_000_000_007;

	public static void main(String[] args) {
		int N = sc.nextInt();
		int K = sc.nextInt();
		int[] A = new int[N];
		for (int i = 0; i < N; i++) {
			A[i] = sc.nextInt();
		}
		long[][] dp = new long[N + 1][K + 1];
		dp[0][K] = 1;
		for (int i = 0; i < N; i++) {
			long sum = 0;
			for (int j = 0; j < A[i] && j <= K; j++) {
				sum += dp[i][j];
			}
			sum %= MOD;
			for (int j = 0; j <= K; j++) {
				if (j + A[i] <= K) {
					sum += dp[i][j + A[i]];
					if (sum >= MOD) sum -= MOD;
				}
				dp[i + 1][j] = sum;
				sum += MOD - dp[i][j];
				if (sum >= MOD) sum -= MOD;
			}
		}
		System.out.println(dp[N][0]);
	}
}