#include <bits/stdc++.h>

using namespace std;

#define all(x) (x).begin(), (x).end()
#define sz(x) (int)(x).size()

mt19937 rnd(time(NULL));

double rand_d() {
    return (double)(rnd() % RAND_MAX) / RAND_MAX;
}

void rsh(vector<int> &x) {
    for (int i = 1; i < x.size(); i++) {
        swap(x[i], x[rnd() % (i + 1)]);
    }
}   

vector<int> fs = {4530, 15330, 28470, 57450, 73890, 109860, 147090, 191730, 219420};

void solve(int tc) {
    int n, t; 
    double p; cin >> n >> p >> t;
    int qtot = 0;
    int sm =0;
    for (int i = 0; i < t; i++) {
        for (int j = 0; j < n; j++) sm += (rand_d() <= p);
    }
    int exp = (sm + n - 1) / n + 5;
    for (int lol = 0; lol < t; lol++) {
        vector<int> res(n);
        for (int i = 0; i < n; i++) {
            res[i] = rand_d() <= p;
        }
        auto ask = [&](string s) -> bool {
            qtot++;
            #ifdef LOCAL 
                int ans = 0;
                for (int i = 0; i < n; i++) {
                    if (s[i] == '1') ans |= res[i];
                }
                return ans;
            #else
                cout << "Q " << s << endl;
                char c; cin >> c;
                return (c == 'P');
            #endif
        };
        auto check = [&](string ans) {
            #ifdef LOCAL 
                for (int i = 0; i < n; i++) {
                    if (ans[i] - '0' != res[i]) return false;
                }
                return true;
            #else
                cout << "A " << ans << endl;
                char c; cin >> c;
                return (c == 'C');
            #endif
        };
        vector<int> poss(n);
        iota(all(poss), 0);
        while (sz(poss) > 2 * exp) {
            double newp = (double) exp / (double) sz(poss);
            int siz = (sz(poss) - exp + 1) / 2;
            if (siz > sz(poss) - exp) siz = sz(poss) - exp;
            while (true) {
                rsh(poss);
                string S;
                for (int j = 0; j < n; j++) S += '0';
                for (int i = 0; i < siz; i++) S[poss[i]] = '1';
                if (!ask(S)) {
                    reverse(all(poss));
                    for (int j = 0; j < siz; j++) poss.pop_back();
                    break;
                }
            }
        }
        string answ;
        for (int i = 0; i < n; i++) answ += '0';
        for (int j = 0; j < sz(poss); j++) {
            string S;
            for (int i = 0; i < n; i++) S += '0';
            S[poss[j]] = '1';
            if (ask(S)) answ[poss[j]] = '1';
        }
        if (!check(answ)) return;
    }
    //cout << qtot << '\n';
    #ifdef LOCAL 
        double pts = 0;
        if (qtot <= fs[tc]) {
            pts = 90;
        } else if (qtot <= 10 * fs[tc]) {
            pts = (double)fs[tc] / (double)(fs[tc] + 4 * (qtot - fs[tc])); 
        }
        cout << "gained " << pts << '\n';
    #endif
}

signed main() {
    int tt = 1;
    #ifdef LOCAL 
        freopen("in.txt", "r", stdin);
        freopen("out.txt", "w", stdout);
        cin >> tt;
    #else 
        ios::sync_with_stdio(false); cin.tie(0); cout.tie(0);
    #endif

    for (int i = 0; i < tt; i++) {
        solve(i);
    }

    return 0;
}