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
sys.setrecursionlimit(2147483647)
INF = float("inf")
MOD = 10**9 + 7 # 998244353
input = lambda:sys.stdin.readline().rstrip()
def resolve():
    n, k = map(int, input().split())
    dp = [0] * (k + 1)
    dp[0] = 1
    for a in map(int, input().split()):
        # accumulate dp
        S = [0] * (k + 2)
        for i in range(k + 1):
            S[i + 1] = S[i] + dp[i]
            if S[i + 1] >= MOD:
                S[i + 1] -= MOD
        # ndp[i] = dp[i - a] + ... + dp[i]
        dp = [(S[i + 1] - S[max(0, i - a)]) % MOD for i in range(k + 1)]

    print(dp[k])
resolve()