Problem:
Score : 300 points

Problem Statement

You are given an integer N.

Find a triple of positive integers h, n and w such that 4/N = 1/h + 1/n + 1/w.

If there are multiple solutions, any of them will be accepted.

Constraints

It is guaranteed that, for the given integer N, there exists a solution such that h,n,w \leq 3500.

Inputs

Input is given from Standard Input in the following format:

N

Outputs

Print a triple of positive integers h, n and w that satisfies the condition, in the following format:

h n w

Sample Input 1

2

Sample Output 1

1 2 2

4/2 = 1/1 + 1/2 + 1/2.

Sample Input 2

3485

Sample Output 2

872 1012974 1539173474040

It is allowed to use an integer exceeding 3500 in a solution.

Sample Input 3

4664

Sample Output 3

3498 3498 3498

Solution in C (GCC 5.4.1) (judge verdict: Time Limit Exceeded)

#include<stdio.h>
int main()
{
    long long N,h,n,w1,w2;
    int count;
    while(~scanf("%lld",&N))
    {
        count=0;
        for(h=1;h<=3500;h++)
        {
            for(n=1;n<=5000000;n++)
            {
                w1=N*h*n;
                w2=4*h*n-n*N-h*N;
                if(w1>0&&w2>0&&w1%w2==0)
                {
                    printf("%lld %lld %lld\n",h,n,w1/w2);
                    count++;
                    break;
                }
            }
            if(count) break;
        }
    }
    return 0;
}