CodeForces 7 C. Line(扩展欧几里得)

C. Line

time limit per test

1 second

memory limit per test

256 megabytes

input

standard input

output

standard output

A line on the plane is described by an equation Ax + By + C = 0. You are to find any point on this line, whose coordinates are integer numbers from  - 5·10¹⁸ to 5·10¹⁸ inclusive, or to find out that such points do not exist.

Input

The first line contains three integers A, B and C ( - 2·10⁹ ≤ A, B, C ≤ 2·10⁹) — corresponding coefficients of the line equation. It is guaranteed that A² + B² > 0.

Output

If the required point exists, output its coordinates, otherwise output -1.

Sample test(s)

Input

2 5 3

Output

6 -3


就是找到这个方程的可行解


ac代码：

 
#include<stdio.h>
#include<math.h>
#include<string.h>
#include<iostream>
#include<algorithm>
#define MAXN 100010
#define LL long long
using namespace std;
LL x,y;
LL gcd(LL a,LL b)
{
	if(b==0)
	{
		x=1;
		y=0;
		return a;
	}
	else
	{
		LL ans=gcd(b,a%b);
		LL t=x;
		x=y;
		y=t-(a/b)*y;
	    return ans;
	}
}
int main()
{
	LL a,b,c,num;
	while(scanf("%lld%lld%lld",&a,&b,&c)!=EOF)
	{
		c=-c;
		num=gcd(a,b);
		if(c%num)
		{
			printf("-1\n");
			continue;
		}
		printf("%lld %lld\n",x*(c/num),y*(c/num));
	}
	return 0;
}