#include <stdio.h>
#include <math.h>

#define ERROR 1.0E-6

int gcd(int m,int n){
    if(m==0)return n;
    return gcd(n%m,m);
}

int m,n;
void gcd_test()
{
    int d=gcd(m,n);
    if(d!=1){
        fprintf(stderr,"Error: gcd of (%d,%d)!=1\n");
        exit(-1);
    }
}
void find_root(int k)
{
    double t0=k*(2.0*M_PI/m);
    double r,r0,x0,y0,x,y;
    r0=pow(2.0,1.0/m);
    x0=r0*cos(t0),y0=r0*sin(t0);
    do{
        double r1=pow(r0,-n);
        double r2,t2;
        x=r1*cos(-n*t0),y=-r1*sin(-n*t0);
        x=2.0-x;
        r2=sqrt(x*x+y*y);
        t2=atan2(y,x)/m;
        r2=pow(r2,1.0/m);
        t2+=k*(2.0*M_PI)/m;
        x=r2*cos(t2),y=r2*sin(t2);
        r=sqrt((x-x0)*(x-x0)+(y-y0)*(y-y0));
        x0=x;y0=y;r0=r2;t0=t2;
    }while(r>ERROR);
    printf("Find root %f+i%f\n",x0,y0);
    fflush(stdout);
}

int main()
{
    int i;
    printf("Please input positive integer m and n while m is less than n && (m,n)=1:");
    scanf("%d %d",&m, &n);
    if(m>=n||m<=0){
        fprintf(stderr,"Invalid input\n");
        return -1;
    }
    gcd_test();
    for(i=0;i<m;i++){
        find_root(i);
    }
}