#include<bits/stdc++.h>
#define F(i, a, b) for(int i = a; i <= b; i ++)

using namespace std;

typedef long long ll;

ll hp1, hp2, atk1, atk2;
bool ck(ll l1, ll r1, ll l, ll r)
{
    
    assert(l <= r);
    if (l <= 0 && 0 <= r) return 1;
    ll L = 0, R = r1 - l1 + 1, pos = 0;
    while (L <= R)
    {
        ll Mid = (L + R) >> 1;
        ll l0 = pos * (l1 + l1 + pos - 1) / 2;
        if (l0 <= l)pos = Mid, L = Mid + 1;
        else R = Mid - 1;
    }
    // cout << "??:" << l1 << ' ' << r1 << ' ' << l << ' ' << r << " " << pos << endl;
    
    if (pos > 0)
    {
        ll tr = (r1 - pos + 1 + r1) * pos / 2;
        if (tr >= l) return 1;
    }

    
    if (pos < r1 - l1 + 1)
    {
        ll tl = (l1 + pos + l1) * (pos + 1) / 2;
        // cout << "EMM:" << tl << endl;
        if (tl <= r) return 1;
    }

    return 0;
}
pair<ll, string>sol1()
{
    ll n, m;
    for (n = 1; n * (n + 1) / 2 < hp1 + hp2; n ++);
    for (m = 1; m * (m + 1) / 2 < hp1; m ++);
    ll ans1 = n * atk2 + m * atk1;
    string ans2 = "";
    ll t1 = hp1, t2 = hp2, sum = n * (n + 1) / 2;
    
    for (int i = 1; i <= m; i ++)
    {
        // cout << "EE:" << i << ' ' << t1 << ' ' << t2 << ' ' << sum << endl;
        if (ck(i + 1, m, t1 - i, (sum - i) - t2))
        {
            t1 -= i, sum -= i;
            ans2 += 'A';
        }
        else
        {
            t2 -= i, sum -= i;
            ans2 += 'B';
        }
    }
    for (int i = m + 1; i <= n; i ++)ans2 += 'B';
    return {ans1, ans2};
}
pair<ll, string>sol2()
{
    ll n, m;
    for (n = 1; n * (n + 1) / 2 < hp1 + hp2; n ++);
    for (m = 1; m * (m + 1) / 2 < hp2; m ++);
    ll ans1 = n * atk1 + m * atk2;
    string ans2 = "";
    ll t1 = hp1, t2 = hp2, sum = n * (n + 1) / 2;
    for (int i = 1; i <= m; i ++)
    {
        // cout << "EE:" << i << ' ' << t1 << ' ' << t2 << ' ' << sum << endl;
        if (ck(i + 1, m, t2, (sum - i) - (t1 - i)))
        {
            t1 -= i, sum -= i;
            ans2 += 'A';
        }
        else
        {
            t2 -= i, sum -= i;
            ans2 += 'B';
        }
    }
    for (int i = m + 1; i <= n; i ++)ans2 += 'A';
    return {ans1, ans2};
}
void sol()
{
    cin >> hp1 >> hp2 >> atk1 >> atk2;
    auto p = sol1(), q = sol2();
    // cout << "EE:" << p.first << ' ' << p.second << ' ' << q.first << ' ' << q.second << endl;
    if (p < q) cout << p.first << ' ' << p.second << '\n';
    else cout << q.first << ' ' << q.second << '\n';
}
signed main() {
    ios::sync_with_stdio(false);
    cin.tie(0);
    int t; cin >> t;
    F(i, 1, t) sol();
    return 0;
}
/*
1
5 15 25 5

*/