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 $a _ {0,1} = 233$, $a_{0,2} = 2333$, $a_{0,3} = 23333$...) Besides, in 233 matrix, we got $a_{i,j} = a_{i-1,j} +a_{i,j-1}( i,j \neq 0)$. Now you have known $a_{1,0},a_{2,0},\dots,a_{n,0}$, could you tell me $a_{n,m}$ in the 233 matrix?

Input Format

There are multiple test cases. Please process till EOF.

For each case, the first line contains two postive integers $n,m(n \le 10,m \le 10^9)$. The second line contains n integers, $a_{1,0},a_{2,0},...,a_{n,0}$ ($0 \le a_{i,0} < 2^{31}$).

Output Format

For each case, output $a_{n,m}$ mod 10000007.

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

234
2799
72937

Hint