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
n, k = map(int, input().split())
a = list(map(int, input().split()))
MOD = 10**9+7
dp = [[0 for _ in [0]*(k+1)] for _ in [0]*n]
sum_list = [[0] for _ in [0]*n]

def make_sum(i):
	for j in range(k+1):
		sum_list[i].append((sum_list[i][-1] + dp[i][j]) % MOD)
	return

for j in range(a[0]+1):
	dp[0][j] = 1

for i in range(1, n):
	make_sum(i-1)
	for j in range(k+1):
		dp[i][j] = (sum_list[i-1][j+1] - sum_list[i-1][max(0, j-a[i])]) % MOD

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