uva10689矩阵快速幂

Posted 2020-09-18 walfy

#include<map>
#include<set>
#include<cmath>
#include<queue>
#include<stack>
#include<vector>
#include<cstdio>
#include<iomanip>
#include<cstdlib>
#include<cstring>
#include<iostream>
#include<algorithm>
#define pi acos(-1)
#define ll long long
#define mod 1000000007
#define ls l,m,rt<<1
#define rs m+1,r,rt<<1|1
#pragma comment(linker, "/STACK:1024000000,1024000000")

using namespace std;

const double g=10.0,eps=1e-9;
const int N=10+5,maxn=1<<10+5,inf=0x3f3f3f3f;

ll s;
struct Node{
   ll row,col;
   ll a[N][N];
};
Node mul(Node x,Node y)
{
    Node ans;
    ans.row=x.row,ans.col=y.col;
    memset(ans.a,0,sizeof ans.a);
    for(ll i=0;i<x.row;i++)
        for(ll j=0;j<x.col;j++)
            for(ll k=0;k<y.col;k++)
                ans.a[i][k]=(ans.a[i][k]+x.a[i][j]*y.a[j][k]+s)%s;
    return ans;
}
Node quick_mul(Node x,ll n)
{
    Node ans;
    ans.row=x.row,ans.col=x.col;
    memset(ans.a,0,sizeof ans.a);
    for(ll i=0;i<ans.col;i++)ans.a[i][i]=1;
    while(n){
        if(n&1)ans=mul(ans,x);
        x=mul(x,x);
        n>>=1;
    }
    return ans;
}
int main()
{

    ios::sync_with_stdio(false);
    cin.tie(0);
 //   cout<<setiosflags(ios::fixed)<<setprecision(2);
    ll t,n,m,a,b;
    cin>>t;
    while(t--){
        cin>>a>>b>>n>>m;
        s=1;
        for(int i=1;i<=m;i++)s*=10;
        if(n==0)
        {
            cout<<a%m<<endl;
            continue;
        }
        Node A;
        A.row=2,A.col=2;
        A.a[0][0]=0,A.a[0][1]=1;
        A.a[1][0]=1,A.a[1][1]=1;
        Node B;
        B.row=2,B.col=1;
        B.a[0][0]=a,B.a[1][0]=b;
        B=mul(quick_mul(A,n),B);
        cout<<B.a[0][0]%s<<endl;
    }
    return 0;
}

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