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 ≤ 10⁹). The second line contains n integers, a_1,0,a_2,0,...,a_n,0(0 ≤ a_i,0 < 2³¹).

 

Output

   For each case, output a_n,m mod 10000007.

 

Sample Input

 

Sample Output

 

Source

 

Recommend

hujie   |   We have carefully selected several similar problems for you:  5017 5016 5014 5013 5012 

1. n+2行的矩阵
2. --                      --   --  --
3. | 1  1  1  1  1  1  1  0 |   | a1 |
4. | 0  1  1  1  1  1  1  0 |   | a2 |
5. | 0  0  1  1  1  1  1  0 |   | a3 |
6. | 0  0  0  1  1  1  1  0 |   | a4 |
7. | 0  0  0  0  1  1  1  0 | * | a5 |
8. | 0  0  0  0  0  1  1  0 |   | an |
9. |  - - - - - - - - - - - |   |    |
10. | 0  0  0  0  0  0 10  1 |   | 233|
11. | 0  0  0  0  0  0  0  1 |   | 3  |
12. --                      --   --  --

 #include<iostream>

 #include<cstring>

 #include<cstdlib>

 #include<cstdio>

 #include<algorithm>

 #include<cmath>

 #include<queue>

 #include<map>

 #include<string>

 #define N 15

 #define M 15

 #define mod 10000007

 #define p 10000007

 #define mod2 100000000

 #define ll long long

 #define LL long long

 #define maxi(a,b) (a)>(b)? (a) : (b)

 #define mini(a,b) (a)<(b)? (a) : (b)

 using namespace std;

 ll nn,m;

 ll n;

 ll x[];

 //ll ans;

 struct Mat

 {

     ll mat[N][N];

 };

 Mat e,f,g;

 Mat operator * (Mat a,Mat b)

 {

     Mat c;

     memset(c.mat,,sizeof(c.mat));

     ll i,j,k;

     for(k = ; k < n ; k++)

     {

         for(i =  ; i < n ;i++)

         {

             if(a.mat[i][k]==) continue;//优化

             for(j =  ;j < n ;j++)

             {

                 if(b.mat[k][j]==) continue;//优化

                 c.mat[i][j] = (c.mat[i][j]+(a.mat[i][k]*b.mat[k][j])%mod)%mod;

             }

         }

     }

     return c;

 }

 Mat operator ^(Mat a,ll k)

 {

     Mat c;

     ll i,j;

     for(i = ; i < n ;i++)

         for(j = ; j < n ;j++)

         c.mat[i][j] = (i==j);

     for(; k ;k >>= )

     {

         if(k&) c = c*a;

         a = a*a;

     }

     return c;

 }

 void ini()

 {

     ll i,j;

     for(i=;i<=nn;i++){

         scanf("%I64d\n",&x[i]);

     }

     memset(e.mat,,sizeof(e.mat));

     memset(f.mat,,sizeof(f.mat));

     e.mat[][]=;

     e.mat[][]=;

     e.mat[][]=+x[];

     for(i=;i<=nn;i++){

         e.mat[][i+]=e.mat[][i]+x[i];

     }

     for(j=;j<nn+;j++){

         if(j!=){

             f.mat[][j]=;

         }

         f.mat[][j]=;

     }

     for(i=;i<nn+;i++){

         for(j=i;j<nn+;j++){

             f.mat[i][j]=;

         }

     }

     n=nn+;

 }

 void solve()

 {

     if(m>){

          g= e*  (f^(m-) );

     }

     else{

         g.mat[][nn+]=e.mat[][nn+];

     }

 }

 void out()

 {

     printf("%I64d\n",g.mat[][nn+]);

 }

 int main()

 {

    // freopen("data.in","r",stdin);

   //  freopen("data.out","w",stdout);

     //scanf("%d",&T);

     //for(int cnt=1;cnt<=T;cnt++)

    // while(T--)

     while(scanf("%I64d%I64d",&nn,&m)!=EOF)

     {

         ini();

         solve();

         out();

     }

     return ;

 }