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 = list(map(int,input().split()))
mod = 10**9 + 7
dp = [[0 for _ in range(k+1)] for i in range(n)]

for i in range(n):
    dp[i][0] = 1

sum_a = []
now = 0
for i in a:
    now += i
    sum_a.append(now)
#print(sum_a)
for i in range(n):
    for j in range(1,k+1):
        if sum_a[i] < j:
            dp[i][j] = 0
            break
        dp[i][j] = dp[i][j-1]
        if i > 0:
            dp[i][j] += dp[i-1][j]
            if j>a[i]:
                dp[i][j] -= dp[i-1][j-a[i]-1]

        dp[i][j] %= mod
        #print(i+1,j,dp[i][j])


print(dp[n-1][k])