HDU-5974

A Simple Math Problem

Time Limit: 2000/1000 MS (Java/Others)    Memory Limit: 65536/65536 K (Java/Others)
Total Submission(s): 3646    Accepted Submission(s): 1140

Problem Description

Given two positive integers a and b,find suitable X and Y to meet the conditions:
                                                        X+Y=a
                                              Least Common Multiple (X, Y) =b

 

 

Input

Input includes multiple sets of test data.Each test data occupies one line,including two positive integers a(1≤a≤2*10^4),b(1≤b≤10^9),and their meanings are shown in the description.Contains most of the 12W test cases.

 

 

Output

For each set of input data,output a line of two integers,representing X, Y.If you cannot find such X and Y,output one line of "No Solution"(without quotation).

 

 

Sample Input

6 8

798 10780

 

 

Sample Output

No Solution

308 490

 

 

 

AC代码：

#include<bits/stdc++.h>
using namespace std;

const int MAXX=10010;

int gcd(int a,int b){
    return (b>0)?gcd(b,a%b):a;
}

int main(){
    ios::sync_with_stdio(false);
    long long a,b,x,y;
    while(cin>>a>>b&&a&&b){
        long long temp=a;
        long long l=gcd(a,b);
        a/=l;
        b/=l;
        if(a*a-4*b<0){
            cout<<"No Solution"<<endl;
        }
        else{
            y=(a+sqrt(a*a-4*b))/2;
            y*=l;
            x=temp-y;
            if(x*y/gcd(x,y)==b*l){
                cout<<x<<" "<<y<<endl;
            }
            else{
                cout<<"No Solution"<<endl;
            } 
        }
    }
    return 0;
}