19年徐州E题--大数随机质因数分解

#include <bits/stdc++.h>
using namespace std;
#define ll long long
const double eps = 1e-8;//精度
const double inf = 1e20;
const double pi = acos(-1.0);
const int mod = 998244353;
const int N = 1e5 + 10;
ll ct,cnt;
const int Times = 10;
ll fac[N],num[N];
ll a[N],times[N];
__int128 temp2[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,ll 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 fenjie(ll n)
{
    ct = 0;
    find(n,1111);
    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;
//    for(int i=0;i<cnt;i++)
//    {
//        cout << fac[i] << " " << num[i] << " ";
//    }
//    cout << "\n";
}
void sum(ll y,ll flag)
{
    for(int i=0;i<cnt;i++)
    {
        temp2[i] = fac[i];
    }
    for(int i=0;i<cnt;i++)
    {
        while(temp2[i] - y <= 0)
        {
            times[i] += flag * y / temp2[i];
            temp2[i] = temp2[i] * fac[i];
        }
    }
}
void solve()
{
    ll n,x,y;
    cin >> n >> x >> y;
    for(int i=1;i<=n;i++)
    {
        cin >> a[i];
    }
    fenjie(x);
    for(int i=0;i<cnt;i++)
    {
        //初始化
        times[i] = 0;//统计y!在fac[i]^num[i]对应的因子
    }
    sum(y,1);
    ll ans = 4e18;
    for(int i=1;i<=n;i++)
    {
        sum(a[i],-1);
    }
    for(int i=0;i<cnt;i++)
    {
        ans = min(ans,times[i]/num[i]);
    }
    cout << ans << "\n";

}
int main()
{
    ios::sync_with_stdio(false);
    cin.tie();
    cout.tie();
    int T;
    cin >> T;
    while(T--)
    {
        solve();
    }
}
/*
1
1 9 15
1
 */