Problem A. Restoring Numbers

Problem A. Restoring Numbers

Pavel had two positive integers a and b. He found their sum s and greatest common divisor g,
and forgot a and b after that. Help him to restore the original numbers.

Input

A single line contains two integers s and g (1 ≤ s ≤ 10^9, 1 ≤ g ≤ 10^9) — sum and greatest common
divisor of the numbers a and b.

Output

If Pavel made a mistake and there are no such numbers a and b, output a single number - 1.
Otherwise, output two positive integers a and b on a single line, separated by a space. If there are
multiple possible solutions, output any of them.

手工翻译

Pavel 有两个正整数a和b，他发现他们的和s和最大公约数g并且在那之后忘记了a和b帮助他恢复原来的数字。

输入

一行包含s和g的数是a和b的最大公约数

输出

要是能有这个a和b就输出a和b不然就输出-1

考试时的代码

#include <iostream>
using namespace std;
 
long long gcd(long long a, long long b) {
	return b ? gcd(b, a % b) : a;
}
 
int main() {
	long long s, m;
	cin >> s >> m;
	for (long long i = 1; i <= s / 2; i++) {
		if (gcd(i, s - i) == m) {
			cout << s-i << ' ' << i;
			return 0;
		}
	}
	cout << -1;
	return 0;
}

这个代码很显然是暴力，我们对其进行时间复杂度的分析，大约是5*10^8,所以就会像考试是一样在21个点时超时。所以我们对其进行分析

#include <cstdio>
int sum, gcd;
int main () {
	scanf ("%d%d", &sum, &gcd);
	if (sum % gcd != 0 || sum == gcd) {
		printf ("-1");
		return 0;
	}
	sum /= gcd;
    printf ("%d %d", (sum - 1) * gcd, gcd);
	return 0;
}

结束