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: Wrong Answer)

#include <stdio.h>

int main()
{
	long long N;
	scanf("%lld", &N);

	if (N % 2 == 0) {
		printf("%lld %lld %lld\n", N/2, N, N);
		fflush(stdout);
		return 0;
	}
	
	long long h, n, w = 0, rest;
	for (h = N / 4; h <= N / 3; h++) {
		rest = h * N / (4 * h - N);
		for (n = rest + 1; n <= rest * 2 + 1; n++) {
			if ((h * n * N) % (4 * h * n - h * N - n * N) == 0) {
				w = (h * n * N) / (4 * h * n - h * N - n * N);
				break;
			}
		}
		if (w > 0) break;
	}
	printf("%lld %lld %lld\n", h, n, w);
	fflush(stdout);
	return 0;
}