#include <stdio.h>
#include <unistd.h>
#include <sys/time.h>
#include <stdlib.h>
#include <math.h>
#include <assert.h>
#include <gmp.h>

long n_iters;

unsigned long gcd(unsigned long a, unsigned long b)
{
  unsigned long temp;
  while(b) {
    temp = b;
    b = a % b;
    a = temp;
  }
  return a;
}

long time_in_usecs()
{
  struct timeval tv;
  gettimeofday(&tv, NULL);
  return tv.tv_sec * 1000000L + tv.tv_usec;
}
void child(int result_pipe)
{
  long s = 0;
  mpz_t a, b, c;
  gmp_randstate_t state;
  mpz_init(a);
  mpz_init(b);
  mpz_init(c);
  gmp_randinit_default(state);
  gmp_randseed_ui(state, time_in_usecs() * result_pipe);

  while(n_iters--) {
    mpz_urandomb(a, state, 256);
    mpz_urandomb(b, state, 256);
    mpz_gcd(c, a, b);
    s += mpz_cmp_ui(c, 1) == 0;
  }
  write(result_pipe, &s, sizeof(s));
}


double parent(int n_children)
{
  int *pipes;
  long results = 0;
  long temp;
  int pipefds[2];
  int i;
  int pid;
  double ratio;
    
  pipes = malloc(sizeof(int) * n_children);
  assert(pipes);
    
  for(i = 0; i < n_children; i++) {
    if(pipe(pipefds)) {
      perror("couldn't pipe");
      exit(1);
    }
    pipes[i] = pipefds[0];
    pid = fork(); 
    if(pid < 0) {
      perror("couldn't fork");
      exit(1);
    } else if(pid == 0) {
      child(pipefds[1]);
      exit(0);
    }
  }

  for(i = 0; i < n_children; i++) {
    read(pipes[i], &temp, sizeof(long));
    results += temp;
  }

  ratio = (double)results/(double)(n_children * n_iters);
  return sqrt(6.0/ratio);
}

int main(int argc, char **argv)
{
  assert(argc == 3);
  n_iters = atol(argv[1])/atol(argv[2]);

  printf("%.20f\n", parent(atoi(argv[2])));
  return 0;
}