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

N,K = map(int,input().split())
A = list(map(int,input().split()))

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

dp[0][0] = 1

cum = [0]*(K+2)

for i in range(1,N+1) :
    cum[0] = 1
    for j in range(1,K+2) :
        cum[j] = (cum[j-1] + dp[i-1][j-1]) % (10**9+7)
    for j in range(K+1) :
        dp[i][j] = (cum[j+1] - cum[max(0, j-A[i-1])] + (10**9+7)) % (10**9+7)

ans = dp[N][K]

print(ans)
#print(dp)
