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 = [int(x) for x in input().split()]

arr = [int(x) for x in input().split()]

# dp[i] -> number of ways to distribute i candies to n childers
MOD = 10**9 + 7
dp = [0]*(k+1)

dp[0] = 1
pref = [0] + [1]*(k+1)
for i in range(n):
    for left in range(k,0,-1):
        dp[left] += pref[left] - pref[left - min(arr[i],left)]
        dp[left] %= MOD
        # for give in range(1,min(arr[i],left)+1):
        #     dp[left] += dp[left-give]
    pref = [0]
    for e in dp:
        pref.append(pref[-1] + e)

print(dp[k]%MOD)
