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()))
mod = 10 ** 9 + 7

dp = [0] * (K + 1)
dp[K] = 1
for i in range(N):
  x = a[i]
  imos = [0] * (K + 2)
  for j in range(K + 1):
    if j - x >= 0:
      imos[j - x] += dp[j]
      imos[j - x] %= mod
    else:
      imos[0] += dp[j]
      imos[0] %= mod
    imos[j + 1] -= dp[j]
    imos[j + 1] %= mod
  for j in range(K + 1):
    imos[j + 1] += imos[j]
    imos[j + 1] %= mod
  for j in range(K + 1):
    dp[j] = imos[j]
print(dp[0])