C.cpp

//#pragma GCC optimize "trapv"
#pragma GCC optimize("Ofast")
#pragma GCC optimize("O3", "unroll-loops")
#pragma GCC target("avx,avx2,fma")
#include<bits/stdc++.h>
#define ll long long int
#define fab(a,b,i) for(int i=a;i<b;i++)
#define pb push_back
#define db double
#define mp make_pair
#define endl "\n"
#define f first
#define se second
#define all(x) x.begin(),x.end()
#define MOD 1000000007
#define vll vector<ll>
#define vi vector<int>
#define pii pair<int,int>
#define pll pair<ll,ll>
#define quick ios_base::sync_with_stdio(false);cin.tie(NULL);cout.tie(NULL)
ll add(ll x, ll y) {ll res = x + y; return (res >= MOD ? res - MOD : res);}
ll mul(ll x, ll y) {ll res = x * y; return (res >= MOD ? res % MOD : res);}
ll sub(ll x, ll y) {ll res = x - y; return (res < 0 ? res + MOD : res);}
ll power(ll x, ll y) {ll res = 1; x %= MOD; while (y) {if (y & 1)res = mul(res, x); y >>= 1; x = mul(x, x);} return res;}
ll mod_inv(ll x) {return power(x, MOD - 2);}

using namespace std;
map<ll,ll> m;
void fac(ll n)
{

	while(n>0 and n%2==0)
	{
		m[2]++;
		n/=2;
	}

	for( int i=3;i<sqrt(n)+1;i+=2)
	{
		while(n>0 and n%i==0)
		{
			m[i]++;
			n/=i;
		}
	}
	if(n>2)
		m[n]++;

}
ll getpow(ll a, ll b)
{
	ll res=1;
	fab(0,b,i)
	res*=a;
	return res;
}

int main()
{ quick;
#ifndef ONLINE_JUDGE
    freopen("D:/sublime/input.txt", "r", stdin);
    freopen("D:/sublime/output.txt", "w", stdout);
#endif
	int t;
	cin>>t;
	while(t--)
	{
		m.clear();
		ll p,q;
		cin>>p>>q;
		if(p%q)
		{
			cout<<p<<endl;
			continue;
		}

		fac(q);
		ll ans=1;
		for(auto i: m)
		{
			int div=i.f;
			ll w=p;
			int cnt=0;
			while(w%div==0)
			{
				cnt++;
				w/=div;
			}
			ll val=(cnt-i.se+1);
			//cout<<"i.f:"<<i.f<<" "<<cnt<<" "<<val<<endl;
			ll res=getpow(i.f,val);
			ans=max(ans,p/res);

		}
		cout<<ans<<endl;

	}
	

 cerr << "time taken : " << (float)clock() / CLOCKS_PER_SEC << " secs" << endl;
	return 0;
}