cf 7C. Line【拓展欧几里得】 数论模板

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

暂时不是特别明白运算的原理，不过还是要先记住...........

#include<cstdio>
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;
	while(~scanf("%lld%lld%lld",&a,&b,&c))
	{
		ll tp=gcd(a,b);
		if(c%tp!=0)//不能整除的
		{
			printf("-1\n");
		}
		else
		{
			ll x,y,d;
			extgcd(a,b,d,x,y);
			printf("%lld %lld\n",-x*c/tp,-y*c/tp);
		}
	}
	return 0;
}