hdu2669 Romantic

Romantic

Time Limit: 2000/1000 MS (Java/Others)    Memory Limit: 32768/32768 K (Java/Others)
Total Submission(s): 8837    Accepted Submission(s): 3752

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 5110 4434 79

 

Sample Output

2 -3sorry7 -3

 

Author

yifenfei

 

Source

HDU女生专场公开赛——谁说女子不如男

 

题解：

用扩展欧几里得求出x,y,x的最小非负整数即为(x%b+b)%b //想一想为什么？

然后将x代入原式得出y即可。

PS：如果gcd(a,b)不为1，则无解 //根据扩展欧几里得原理

代码：

#include<bits/stdc++.h>
using namespace std;
long long n,m;
long long gcd(long long n,long long m,long long &x,long long &y){
	if(m==0){
		x=1;y=0;
		return n;
	}
	long long ans=gcd(m,n%m,x,y);
	long long t=x;
	x=y;y=t-(n/m)*y;
	return ans;
}
int main(){
	long long x=0,y=0;
	while(~scanf("%lld%lld",&n,&m)){
		if(gcd(n,m,x,y)!=1)printf("sorry\n");
		 else{
		 	x=(x%m+m)%m;
		 	printf("%lld %lld\n",x,(1-(n*x))/m);
		 }
	}
}