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
def cumsum(inlist):
    s = 0
    outlist = [0]
    for i in inlist:
        s += i
        outlist.append(s)
    return outlist

mod = 10**9+7
n, k = [ int(v) for v in input().split() ]
a_list = [ int(v) for v in input().split() ]

dp_list = [ 0 for i in range(k+1) ]
dp_list[0] = 1

for i in range(n):
    cum_dp_list = cumsum(dp_list)

    new_dp_list = [ 0 for i in range(k+1) ]
    for j in range(k+1):
        r = min(j+1,k+1)
        l = max(0,j-a_list[i]) 
        new_dp_list[j] = cum_dp_list[r] - cum_dp_list[l]
    dp_list = [ i % mod for i in new_dp_list ]

print(dp_list[-1])