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 PHP7 (7.0.15) (judge verdict: Wrong Answer)

<?php

// define('DEBUG', true);
define('DEBUG', false);

// define('MOD', 1000000007);

fscanf(STDIN, "%d", $N);

$target = 4 / $N;
$start = ceil($N / 4);

for ($i = $start; $i <= 3500; $i++) {
    $copy = $target;
    $copy -= 1 / $i;
    if ($copy == 0) continue;
    if (DEBUG) echo "i:{$i}\n";
    $start2 = ceil(1 / $copy);

    if (DEBUG) echo $copy . "-" . $start2 . PHP_EOL;
    for ($j = $start2; $j <= 3500; $j++) {
        $copy2 = $copy - 1 / $j;
        if ($copy2 == 0) continue;
        $num3 = 1 / $copy2;
        if (DEBUG) echo "i:{$i} j:{$j} test2: {$copy2}\n";
        if ((int) $num3 == $num3) {
            printf("%d %d %d\n", $i, $j, $num3);
            if (DEBUG) printf("4 / %d = 1 / %d + 1 / %d + 1 / %d\n", $N, $i, $j, $num3);
            if (DEBUG) printf("%.9f %.9f\n", 4 / $N, 1 / $i + 1 / $j + 1/ $num3);
            exit;
        }
    }
}