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 = list(map(int, input().split()))
a = list(map(int, input().split()))

MOD = 10 ** 9 + 7
DP = [[0] * (K + 1) for _ in range(N)]

for i in range(a[0] + 1):
  DP[0][i] = 1

L = [0] * (K + 1)
for i in range(1, N):
  L[0] = 1
  for j in range(1, K + 1):
    L[j] = (DP[i - 1][j] + L[j - 1]) % MOD
  x = a[i]
  for j in range(K + 1):
    if j <= x:
      DP[i][j] = L[j]
    else:
      DP[i][j] = L[j] - L[j - x - 1]
      while DP[i][j] < MOD:
        DP[i][j] += MOD

print(DP[N - 1][K] % MOD)