CodeForces - 7C

2023-03-30

机器学习 amp ML.NET C# C Sharp the line

C.Linetimelimitpertest1secondmemorylimitpertest256megabytesinputstandardinputoutputstandardoutputAlineontheplaneisdescribedbyanequation Ax+By+C=0

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.

        Examples
      
          input
        
2 5 3

          output
        
6 -3

思路：主要运用扩展欧几里得公式。


#include<stdio.h>
__int64 extgcd(__int64 a,__int64 b,__int64 &x,__int64 &y )
{
    __int64  d=a;
    if(b!=0)
    {
        d=extgcd(b,a%b,y,x);
        y-=(a/b)*x;
    }
    else
    {
        x=1;
        y=0;
    }
    return d;
}
int main()
{
    __int64 a,b,c,x,y;
    while(~scanf("%I64d %I64d %I64d",&a,&b,&c))
    {
        __int64 k=extgcd(a,b,x,y);
        if(c%k!=0)
        {
            printf("-1\n");
        }
        else printf("%I64d %I64d\n",x*(-c/k),y*(-c/k));
    }
    return 0;
}