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 decimal,math
from collections import Counter,defaultdict
from fractions import gcd
from bisect import bisect_right,bisect_left
decimal.getcontext().prec = 10
n,k=map(int,raw_input().split())
arr=map(int,raw_input().split())
arr = [0]+arr
mod=10**9+7
dp = [] #(n+1)*(k+1) dp
for i in range(n+1):
	ok=[]
	for j in range(k+1):
		ok.append(0)
	dp.append(ok)	
dp[0][0]=1	
for i in range(1,n+1):
	xx=0
	for j in range(k+1):
		if(j-arr[i]-1>=0):
			xx = (xx+dp[i-1][j] - dp[i-1][j-arr[i]-1])%mod
		else:
			xx=(xx+dp[i-1][j])%mod
		dp[i][j] = (xx)%mod	
	# print i,			
print (dp[n][k])%mod