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: Accepted)

#include <stdio.h>

typedef long long ll;
 
int main(void) {
	
	ll N;
	
	scanf("%lld",&N);
	
	ll h,n,w;
	
	for(h=1ll;h<=3500ll;h+=1ll){
		for(n=1ll;n<=3500ll;n+=1ll){
			if(((4ll*h*n)-(N*h)-(N*n))!=0ll){
			ll div=(N*h*n)%((4ll*h*n)-(N*h)-(N*n));
			w=(N*h*n)/((4ll*h*n)-(N*h)-(N*n));
			if(w>0ll&&div==0ll){
				printf("%lld %lld %lld\n",h,n,w);
				return 0;
			}
			}
		}
	}
	
	
	return 0;
}