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-5;
const double pi = acos(-1);
// 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 = 10;
const int N = 5500;

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 = 0;
    a %= m;
    while(b)
    {
        if(b & 1)
        {
            ans = (ans + a) % m;
            b--;
        }
        b >>= 1;
        a = (a + a) % m;
    }
    return ans;
}

LL quick_mod(LL a, LL b, LL m)
{
    LL ans = 1;
    a %= m;
    while(b)
    {
        if(b & 1)
        {
            ans = multi(ans, a, m);
            b--;
        }
        b >>= 1;
        a = multi(a, a, m);
    }
    return ans;
}

bool Miller_Rabin(LL n)
{
    if(n == 2) return true;
    if(n < 2 || !(n & 1)) return false;
    LL m = n - 1;
    int k = 0;
    while((m & 1) == 0)
    {
        k++;
        m >>= 1;
    }
    for(int i=0; i<Times; i++)
    {
        LL a = rand() % (n - 1) + 1;
        LL x = quick_mod(a, m, n);
        LL y = 0;
        for(int j=0; j<k; j++)
        {
            y = multi(x, x, n);
            if(y == 1 && x != 1 && x != n - 1) return false;
            x = y;
        }
        if(y != 1) return false;
    }
    return true;
}

LL pollard_rho(LL n, LL c)
{
    LL i = 1, k = 2;
    LL x = rand() % (n - 1) + 1;
    LL y = x;
    while(true)
    {
        i++;
        x = (multi(x, x, n) + c) % n;
        LL d = gcd((y - x + n) % n, n);
        if(1 < d && d < n) return d;
        if(y == x) return n;
        if(i == k)
        {
            y = x;
            k <<= 1;
        }
    }
}

void find(LL n, int c)
{
    if(n == 1) 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=1)
{
    if(dept == cnt)
    {
        LL a = tem;
        LL b = ans / a;
        if(gcd(a, b) == 1)
        {
            a *= n;
            b *= n;
            if(a + b < minn)
            {
                minn = a + b;
                mina = a;
                minb = b;
            }
        }
        return ;
    }
    for(int i=0; i<=num[dept]; i++)
    {
        if(tem > minn) return;
        dfs(dept + 1, 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 = 0;
        ans = m / n;
        find(ans, 120);
        sort(fac, fac + ct);
        num[0] = 1;
        int k = 1;
        for(int i=1; i<ct; i++)
        {
            if(fac[i] == fac[i-1])
                ++num[k-1];
            else
            {
                num[k] = 1;
                fac[k++] = fac[i];
            }
        }
        cnt = k;
        dfs(0, 1);
        if(mina > minb) swap(mina, minb);
        printf("%llu %llu\n",mina, minb);
    }
    return 0;
}