2014西安网络预选赛1009（矩阵快速幂）hdu5015

233 Matrix

Time Limit: 10000/5000 MS (Java/Others)    Memory Limit: 65536/65536 K (Java/Others)
Total Submission(s): 182    Accepted Submission(s): 116

Problem 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 ≠ 0). Now you have known a _1,0,a _2,0,...,a _n,0, could you tell me a _n,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 ≤ 10 ⁹). The second line contains n integers, a _1,0,a _2,0,...,a _n,0(0 ≤ a _i,0 < 2 ³¹).

 

Output

For each case, output a _n,m mod 10000007.

 

Sample Input

    
    
    
    

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

 

Sample Output

    
    
    
    

     
     
     
     234
2799
72937
    
    
    
    

题意：RT

思路：矩阵快速幂

            可以构造一个（n+2）*（n+2）

            假设n=3，输入的序列为23 47 16

            构造出的矩阵M（5*5）如下：                 再构造出一个(n+2)*1的矩阵A如下：

            10 0 0 0 1                                                    233

              1 1 0 0 0                                                       23

              1 1 1 0 0                                                       47

              1 1 1 1 0                                                       16

              0 0 0 0 1                                                         3

             令矩阵B=(M^m)*A

             那么答案为B的第n项