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 sys
input = sys.stdin.readline
'''
allinputs = iter(input().splitlines())
input = lambda : next(allinputs)
#'''
N, K = map(int, input().split())
a = list(map(int, input().split()))
mod = 10 ** 9 + 7
dp = [[0] * (K + 1) for _ in range(N + 1)]
#dp[n][k]...n人目まででk個の飴を分ける組み合わせ
dp[0][0] = 1
	
for n in range(1, N + 1):
	#cum...累積和
	cum = [0] * (K + 2)
	for k in range(K + 1):
		cum[k + 1] = cum[k] + dp[n - 1][k]
		dp[n][k] = cum[k + 1] - cum[max(0, k - a[n - 1])]
		dp[n][k] %= mod

print(dp[-1][-1])
