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=;

 int gcd(int a,int b){
     return (b>)?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-*b<){
             cout<<"No Solution"<<endl;
         }
         else{
             y=(a+sqrt(a*a-*b))/;
             y*=l;
             x=temp-y;
             if(x*y/gcd(x,y)==b*l){
                 cout<<x<<" "<<y<<endl;
             }
             else{
                 cout<<"No Solution"<<endl;
             }
         }
     }
     return ;
 }