test matrix %d pre eight ont nta side ide

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?

InputThere 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).OutputFor 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 

Hint

矩陣快速冪

比較裸 ，首先找到原態和現態的關系，233，2333，23333，23333， 這些數都遵循 a0=a0‘*10+3 ，

a1=a0‘*10+3+a1‘ ; a2=a0‘*10+3+a1‘+a2‘ ; a3=a0‘*10+3+a1‘+a2‘+a3‘ ;

即 an=a0‘*10+3+

代碼如下：

#include<iostream>
#include<stdio.h>
#include<cstring>
const int MOD=10000007;
using namespace std;
typedef long long LL;
const int M=15;
struct Matrix{
    LL matrix[M][M];
};
int n;//矩陣的階數
void init(Matrix &res){
    for(int i=0;i<=n;i++)
    {
        for(int j=0;j<=n;j++)
            res.matrix[i][j]=0;
        res.matrix[i][i]=1;
    }
}
Matrix multiplicative(Matrix a,Matrix b){
    Matrix res;
    memset(res.matrix,0,sizeof(res.matrix));
    for(int i = 0 ; i < n ; i++)
        for(int j = 0 ; j < n ; j++)
            for(int k = 0 ; k < n ; k++)
                res.matrix[i][j] =(res.matrix[i][j]%MOD+a.matrix[i][k]%MOD*b.matrix[k][j]%MOD)%MOD;
return res;
}
Matrix pow(Matrix mx,int m){
    Matrix res,base=mx;
    init(res); //初始為單位矩陣，即除主對角線都是1外，其他都是0
    while(m)
    {
        if(m&1)
            res=multiplicative(res,base);
        base=multiplicative(base,base);
        m>>=1;
    }
    return res;
}
void lk_init(Matrix &b)
{
    for(int i=0;i<n-1;i++)
    {
        b.matrix[i][0]=10;
        b.matrix[i][n-1]=1;
    }
    b.matrix[n-1][n-1]=1;
    for(int i=1;i<n-1;i++)
        for(int j=1;j<=i;j++)
            b.matrix[i][j]=1;
}
int main()
{

    int m,a[M];
    while(~scanf("%d%lld",&n,&m))
    {
        for(int i=1;i<=n;i++)
            scanf("%lld",&a[i]);
        a[0]=23;
        a[n+1]=3;
        n=n+2;
        Matrix base={0};
        lk_init(base);
        base=pow(base,m);
        LL ans=0;
        for(int i=0;i<n;i++)
            ans=(ans%MOD+base.matrix[n-2][i]%MOD*a[i]%MOD+MOD)%MOD;        printf("%lld\n",ans);
    }
    return 0;
}

View Code

233 Matrix