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())
candies = list(map(int, input().split()))

MOD = int(pow(10, 9) + 7)

dp = [[0 for i in range(K+1)] for i in range(N+1)]
dp[0] = [1 for i in range(K+1)]

for c in range(1, N+1):
    for r in range(K, -1, -1):
        lo = dp[c - 1][r]
        hi = dp[c - 1][r + candies[c - 1] + 1] if r + candies[c - 1] + 1 <= K else 0
        dp[c][r] = (lo - hi) + (dp[c][r+1] if r + 1 <= K else 0)
        dp[c][r] %= MOD

def pprint(table):
    for i, row in enumerate(table):
        print([row[j] - row[j+1] for j in range(K)] + [row[K]])

# pprint(dp)

print((dp[N][0] - (dp[N][1] if K > 0 else 0)) % MOD)
