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 = map(int,input().split())
MOD = 10**9 + 7

dp = [0]*(1+K)
dp[0] = 1

for a in A:
  t,dp[K] = dp[K], sum(dp[j] for j in range(K-a,K+1)) % MOD

  for i in reversed(range(K)):
    t,dp[i] = dp[i], (dp[i+1]-t+(dp[i-a] if i >= a else 0)) % MOD

print(dp[K])