CodeForces 7C 【数论】

http://acm.hust.edu.cn/vjudge/contest/view.action?cid=96545#problem/B

Description

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 Input

Input

2 5 3

Output

6 -3

//求 AX+BY+C=0 的整数解（数论）

#include <stdio.h>
typedef long long ll;
ll gcd(ll a,ll b)
{
	if(b==0)
	{
		return a;
	}
	return gcd(b,a%b);
}
void extgcd(ll a,ll b,ll &d,ll &x,ll &y)
{
	if(!b)
	{
		d=a;x=1;y=0;
	}
	else
	{
		extgcd(b,a%b,d,y,x);
		y-=x*(a/b);
	}
}
int main()
{
	ll a,b,c,d,x,y,tp;
	while(~scanf("%lld%lld%lld",&a,&b,&c))
	{
		tp=gcd(a,b);c=-c;
		if(c%tp!=0)
		{
			printf("0\n");
		}
		else
		{
			extgcd(a,b,d,x,y);
			printf("%lld %lld\n",x*c/tp,y*c/tp);
		}
	}
	return 0;
}