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,queue,math,copy,itertools,bisect,collections,heapq
sys.setrecursionlimit(10**7)
INF = 10**18
MOD = 10**9 + 7
LI = lambda : [int(x) for x in sys.stdin.readline().split()]
NI = lambda : int(sys.stdin.readline())

N,K = LI()
a = [0]+LI()
if K == 0:
    print(1)
    exit(0)
dp = [[1] * (K+1) for _ in range(N+1)]
ac = 0
for i in range(1,N+1):
    ac += a[i]
    s = 0
    for j in range(K+1):
        s += dp[i-1][j]
        if j-a[i]-1 >= 0: s -= dp[i-1][j-a[i]-1]
        dp[i][j] = s % MOD
print((dp[-1][K]-dp[-1][K-1])%MOD)
