233 Matrix

Time Limit: 10000/5000 MS (Java/Others)

Memory Limit: 65536/65536 K (Java/Others)

Description

In our daily life we often use 233 to express our feelings. Actually, we may say 2333, 23333, or 233333 ... in the same meaning. And here is the question: Suppose we have a matrix called 233 matrix. In the first line, it would be 233, 2333, 23333... (it means a0,1 = 233,a0,2 = 2333,a0,3 = 23333...) Besides, in 233 matrix, we got ai,j = ai-1,j +ai,j-1( i,j ≠ 0). Now you have known a1,0,a2,0,...,an,0, could you tell me an,m in the 233 matrix?

Input

There are multiple test cases. Please process till EOF.

For each case, the first line contains two postive integers n,m(n ≤ 10,m ≤ 109). The second line contains n integers, a1,0,a2,0,...,an,0(0 ≤ ai,0 < 231).

Output

For each case, output an,m mod 10000007.

Sample Input

1 1 1 2 2 0 0 3 7 23 47 16

Sample Output

234 2799 72937
Hint

Hint

hujie

Source

2014 ACM/ICPC Asia Regional Xi'an Online

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