HDU 2669 Romantic（扩展欧几里德）

Romantic

Problem 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
  
  

 

Author

yifenfei

 

Source

HDU女生专场公开赛——谁说女子不如男

 

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分析：裸的扩展欧几里德

#include<stdio.h>
#include<string.h>
long long kzgcd(long long a,long long b,long long &x,long long &y)
{
	if(b==0)
	{
		x=1;
		y=0;
		return a;
	}
	long long ans=kzgcd(b,a%b,x,y);
	long long t=x;
	x=y;
	y=t-(a/b)*y;
	return ans;
}
long long solve(long long a,long long b,long long &x,long long &y)
{
	long long gcd=kzgcd(a,b,x,y);
	if(1%gcd)
	return -1;
	b/=gcd;
	a/=gcd;
	if(a<0) a=-a;
	if(b<0) b=-b;
	x%=b;
	y%=a;
	if(x<=0)
	x+=b;
	if(y>=0)
	y-=a;
	return gcd;
}
int main()
{
	long long a,b;
	while(scanf("%lld%lld",&a,&b)==2)
	{
		long long x,y;
		long long ans=solve(a,b,x,y);
		if(ans==-1)
		printf("sorry\n");
		else
		printf("%lld %lld\n",x,y);
	}
}