扩展欧几里得--解一元线性方程CodeForces -7C

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

#include<stdio.h>
#include<string.h>
#include<math.h>
#include<algorithm>
using namespace std;
typedef long long LL;
LL gcd(LL a,LL b)
{
	return b ? gcd(b, a%b) : a;
}
void euclid(LL a, LL b,LL &x, LL &y)
{
	if(!b){ 
		x = 1; y = 0 ;return ;
	}
	euclid(b,a%b,y,x);
	y -= x*(a/b);
}
int main()
{
	__int64 a, b, c, x, y;
	while(scanf("%I64d%I64d%I64d",&a, &b, &c)==3)
	{
		c = -c;
		LL g = gcd(a,b);
		if(c%g)
		{
			printf("-1\n");continue;
		}
		a/=g;
		b/=g;
		c/=g;
		euclid(a,b,x,y);
		printf("%I64d %I64d\n",x*c,y*c);
	}
	return 0;
}