Code: Divisibility Game

// #pragma GCC optimize("Ofast,unroll-loops")
#include <bits/stdc++.h>
using namespace std;
// #define int __int128
#define all(x) x.begin(), x.end()
// #define int long long
// #define double long double
using ull = unsigned long long;
using ll = long long;

void solve() {
    int n, m;
    cin >> n >> m;
    vector<int> cnta(n + m + 1), cntb(n + m + 1);
    for (int i = 0; i < n; ++i) {
        int x;
        cin >> x;
        cnta[x]++;
    }
    for (int i = 0; i < m; ++i) {
        int x;
        cin >> x;
        cntb[x]++;
    }
    vector<int> cnt(n + m + 1);
    for (int x = 1; x <= n + m; ++x) {
        for (int y = x; y <= n + m; y += x) {
            cnt[y] += cnta[x];
        }
    }
    int ca = 0, cb = 0, cc = 0;
    for (int x = 1; x <= n + m; ++x) {
        if (cnt[x] > 0 && cnt[x] < n)
            cc += cntb[x];
        else if (cnt[x] == 0)
            cb += cntb[x];
        else
            ca += cntb[x];
    }
    if (cc % 2 == 0) {
        if (ca > cb) {
            cout << "Alice\n";
        } else {
            cout << "Bob\n";
        }
    } else {
        if (ca >= cb) {
            cout << "Alice\n";
        } else {
            cout << "Bob\n";
        }
    }
}

int32_t main() {
    ios::sync_with_stdio(false);
    cin.tie(nullptr);
    cout.precision(20);

    int T = 1;
    cin >> T;
    while (T--)
        solve();

    return 0;
}