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]*(K+1) for _ in range(N) ]
acc = [ [0]*(K+1) for _ in range(N) ]
mn = min(K,a[0])

for i in range(K+1):
    if i <= mn:
        dp[0][i] = 1
    acc[0][i] = (acc[0][i-1] + dp[0][i])%mod if i > 0 else dp[0][i]%mod

for i in range(1,N):
    dp[i][0] = dp[i-1][0]
    acc[i][0] = dp[i][0]
    for k in range(1,K+1):
        if k - a[i] <= 0:
            dp[i][k] = acc[i-1][k]  % mod 
        else:
            dp[i][k] = (acc[i-1][k] - acc[i-1][k-a[i]-1]) % mod
        acc[i][k] = (acc[i][k-1] + dp[i][k])%mod

print(dp[N-1][K]%mod)