72 lines
1.3 KiB
C++
72 lines
1.3 KiB
C++
#include <cstdio>
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#include <cmath>
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using namespace std;
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#define mod 8191
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const int maxn=5;
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typedef struct
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{
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int m[maxn][maxn];
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}Matrix;
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int N,x,y;
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void search()
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{
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y=1;
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while(1){
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x=sqrt(N*y*y+1.0);
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if(x*x-N*y*y==1) break;
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y++;
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}
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}
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Matrix per,d;
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void init()
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{
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d.m[0][0]=x%mod;
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d.m[0][1]=y*N%mod;
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d.m[1][0]=y%mod;
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d.m[1][1]=x%mod;
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for(int i=0;i<2;i++)
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for(int j=0;j<2;j++)
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per.m[i][j]= (i==j);
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}
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Matrix Multi(Matrix a,Matrix b)
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{
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Matrix c;
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for(int i=0;i<2;i++)
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for(int j=0;j<2;j++){
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c.m[i][j]=0;
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for(int k=0;k<2;k++)
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c.m[i][j]+=(a.m[i][k]*b.m[k][j])%mod;
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c.m[i][j]%=mod;
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}
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return c;
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}
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Matrix power(Matrix a,int k)
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{
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Matrix r=per;
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while(k)
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{
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if(k&1) r=Multi(r,a);
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a=Multi(a,a);
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k>>=1;
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}
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return r;
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}
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int main()
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{
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int k;
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while(~scanf("%d%d",&N,&k))
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{
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int tmp=sqrt(N+0.0);
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if(tmp*tmp==N){
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printf("No answers can meet such conditions\n");
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continue;
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}
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search();
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init();
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d=power(d,k-1);
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x=(d.m[0][0]*x%mod+d.m[0][1]*y%mod)%mod;
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printf("%d\n",x);
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}
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return 0;
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}
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