/*
    JAI JAGANNATH!
*/
//@Author : zanj0

#include <bits/stdc++.h>
#include <ext/pb_ds/assoc_container.hpp>
#include <ext/pb_ds/tree_policy.hpp>
using namespace std;
using namespace __gnu_pbds;

template <class T>
using ordered_set = __gnu_pbds::tree<T, __gnu_pbds::null_type, less<T>, __gnu_pbds::rb_tree_tag, __gnu_pbds::tree_order_statistics_node_update>;

// #define LOCAL  // ← enable locally via -DLOCAL; keep commented for OJ
#define ff first
#define ss second
#define pb push_back
#define MOD 1000000007
#define inf 1000000000000000000LL
#define ps(x, y) fixed << setprecision(y) << x
#define w(x)  \
    int x;    \
    cin >> x; \
    while (x--)
#define endl "\n"
#define timetaken cerr << "Time : " << 1000 * (long double)clock() / (long double)CLOCKS_PER_SEC << "ms\n"

typedef long long int lli;

#ifdef LOCAL
#define dbg(x) cerr << "[DBG] " << #x << " = " << (x) << '\n'
template <class A, class B>
ostream &operator<<(ostream &os, const pair<A, B> &p) { return os << '(' << p.first << ',' << p.second << ')'; }
template <class T>
ostream &operator<<(ostream &os, const vector<T> &v)
{
    os << '[';
    for (size_t i = 0; i < v.size(); ++i)
    {
        if (i)
            os << ',';
        os << v[i];
    }
    return os << ']';
}
template <class K, class V>
ostream &operator<<(ostream &os, const map<K, V> &mp)
{
    os << '{';
    bool first = true;
    for (const auto &kv : mp)
    {
        if (!first)
            os << ',';
        first = false;
        os << kv.first << ':' << kv.second;
    }
    return os << '}';
}
template <class K, class V>
ostream &operator<<(ostream &os, const unordered_map<K, V> &mp)
{
    os << '{';
    bool first = true;
    for (const auto &kv : mp)
    {
        if (!first)
            os << ',';
        first = false;
        os << kv.first << ':' << kv.second;
    }
    return os << '}';
}
#else
#define dbg(x) ((void)0)
#endif

void zanj0()
{
    ios_base::sync_with_stdio(0);
    cin.tie(0);
    cout.tie(0);
#ifdef LOCAL
    freopen("input.txt", "r", stdin);
#endif
}

/*
────────────────────────────────────────────────────────────────────────
    Problem Statement:

    Observations:
    6 = 2 * 3

    Number will always get multiplied by smallest prime.



    Claims:

────────────────────────────────────────────────────────────────────────
*/
vector<lli> GetPrimeFactors(lli x){
    vector<lli> ret;
    lli org = x;
    for(lli i = 2; i * i <= org; i++){
        while(x % i == 0){
            ret.pb(i);
            x /= i;
        }
    }
    if(x > 1) ret.pb(x);
    return ret;
}

void Solve()
{
    lli n, k;
    cin >> n >> k;

    vector<lli> v = GetPrimeFactors(n);
    lli small = v[0];
    lli cnt = 0;
    dbg(v);
    while(v.back() != v[0] && k){
        k--;
        cnt++;

        if(k){
            k--;
            
            v.pop_back();
        }
    }

    dbg(v);
    lli ret = v[0];
    cnt += (k+1)/2;
    for(int i = 1; i < v.size(); i++) ret *= v[i];

    while(cnt--) ret*= small;

    cout << ret << endl;
}

int32_t main()
{
    zanj0();
    w(t) Solve();
    timetaken;
    return 0;
}

/*
    GOLDEN RULES
    • Solutions are simple.
    • Proofs are simple.
    • Implementations are simple.
*/