POJ 2429

思路：a/n*b/n=lcm/gcd 所以这道题就是分解ans.dfs枚举每种素数情况。套Miller_Rabin和pollard_rho模板

 //#pragma comment(linker, "/STACK:167772160")//手动扩栈~~~~hdu 用c++交
 #include<cstdio>
 #include<cstring>
 #include<cstdlib>
 #include<iostream>
 #include<queue>
 #include<stack>
 #include<cmath>
 #include<set>
 #include<algorithm>
 #include<vector>
 // #include<malloc.h>
 using namespace std;
 #define clc(a,b) memset(a,b,sizeof(a))
 #define inf  (LL)1<<61
 #define LL long long
 const double eps = 1e-;
 const double pi = acos(-);
 // inline int r(){
 //     int x=0,f=1;char ch=getchar();
 //     while(ch>'9'||ch<'0'){if(ch=='-') f=-1;ch=getchar();}
 //     while(ch>='0'&&ch<='9'){x=x*10+ch-'0';ch=getchar();}
 //     return x*f;
 // }
 const int Times = ;
 const int N = ;

 LL n, m, ct, cnt;
 LL minn, mina, minb, ans;
 LL fac[N], num[N];

 LL gcd(LL a, LL b)
 {
     return b? gcd(b, a % b) : a;
 }

 LL multi(LL a, LL b, LL m)
 {
     LL ans = ;
     a %= m;
     while(b)
     {
         if(b & )
         {
             ans = (ans + a) % m;
             b--;
         }
         b >>= ;
         a = (a + a) % m;
     }
     return ans;
 }

 LL quick_mod(LL a, LL b, LL m)
 {
     LL ans = ;
     a %= m;
     while(b)
     {
         if(b & )
         {
             ans = multi(ans, a, m);
             b--;
         }
         b >>= ;
         a = multi(a, a, m);
     }
     return ans;
 }

 bool Miller_Rabin(LL n)
 {
     if(n == ) return true;
     if(n <  || !(n & )) return false;
     LL m = n - ;
     int k = ;
     while((m & ) == )
     {
         k++;
         m >>= ;
     }
     for(int i=; i<Times; i++)
     {
         LL a = rand() % (n - ) + ;
         LL x = quick_mod(a, m, n);
         LL y = ;
         for(int j=; j<k; j++)
         {
             y = multi(x, x, n);
             if(y ==  && x !=  && x != n - ) return false;
             x = y;
         }
         if(y != ) return false;
     }
     return true;
 }

 LL pollard_rho(LL n, LL c)
 {
     LL i = , k = ;
     LL x = rand() % (n - ) + ;
     LL y = x;
     while(true)
     {
         i++;
         x = (multi(x, x, n) + c) % n;
         LL d = gcd((y - x + n) % n, n);
         if( < d && d < n) return d;
         if(y == x) return n;
         if(i == k)
         {
             y = x;
             k <<= ;
         }
     }
 }

 void find(LL n, int c)
 {
     if(n == ) return;
     if(Miller_Rabin(n))
     {
         fac[ct++] = n;
         return ;
     }
     LL p = n;
     LL k = c;
     while(p >= n) p = pollard_rho(p, c--);
     find(p, k);
     find(n / p, k);
 }

 void dfs(LL dept, LL tem=)
 {
     if(dept == cnt)
     {
         LL a = tem;
         LL b = ans / a;
         if(gcd(a, b) == )
         {
             a *= n;
             b *= n;
             if(a + b < minn)
             {
                 minn = a + b;
                 mina = a;
                 minb = b;
             }
         }
         return ;
     }
     for(int i=; i<=num[dept]; i++)
     {
         if(tem > minn) return;
         dfs(dept + , tem);
         tem *= fac[dept];
     }
 }

 int main()
 {
     while(~scanf("%llu %llu", &n, &m))
     {
         if(n == m)
         {
             printf("%llu %llu\n",n,m);
             continue;
         }
         minn = inf;
         ct = cnt = ;
         ans = m / n;
         find(ans, );
         sort(fac, fac + ct);
         num[] = ;
         int k = ;
         for(int i=; i<ct; i++)
         {
             if(fac[i] == fac[i-])
                 ++num[k-];
             else
             {
                 num[k] = ;
                 fac[k++] = fac[i];
             }
         }
         cnt = k;
         dfs(, );
         if(mina > minb) swap(mina, minb);
         printf("%llu %llu\n",mina, minb);
     }
     return ;
 }