集训第六周 数学概念与方法 数论 线性方程 I题

Description

The Sky is Sprite. 
The Birds is Fly in the Sky. 
The Wind is Wonderful. 
Blew Throw the Trees 
Trees are Shaking, Leaves are Falling. 
Lovers Walk passing, and so are You. 
................................Write in English class by yifenfei 



Girls are clever and bright. In HDU every girl like math. Every girl like to solve math problem! 
Now tell you two nonnegative integer a and b. Find the nonnegative integer X and integer Y to satisfy X*a + Y*b = 1. If no such answer print "sorry" instead. 

 

Input

The input contains multiple test cases. 
Each case two nonnegative integer a,b (0<a, b<=2^31) 

 

Output

output nonnegative integer X and integer Y, if there are more answers than the X smaller one will be choosed. If no answer put "sorry" instead. 

 

Sample Input

77 51

10 44

34 79

 

Sample Output

2 -3

sorry

7 -3

 

给出 a1 a2

求 x1 x2 使得 a1*x1+a2*x2=1

如果不存在，输出sorry

套用扩展欧里几得算法的模版

注意输出不需要考虑最后的空格控制

注意x1要大于0

 

#include"iostream"
using namespace std;

void gcd(int a,int b,int &d,int &x,int &y)
{
    if(!b) {d=a;x=1;y=0;}
    else {gcd(b,a%b,d,y,x);y-=x*(a/b);}
}

int main()
{
    int m,n;
    while(cin>>m>>n)
    {
     int x,y,d;
     gcd(m,n,d,x,y);
     if(d!=1) cout<<"sorry"<<endl;
     else
     {
         while(x<0)
         {
             x+=n;
             y-=m;
         }
         cout<<x<<" "<<y<<endl;
     }
    }
    return 0;
}