#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++) {
        int cur = 0;
        for (int j = 0; j < n; j++) cur += (rand_d() <= p);
        sm= max(sm,cur);
    }
    int exp = sm+3;
    for (int lol = 0; lol < t; lol++) {
        vector<int> res(n);
        int SS=0;
        for (int i = 0; i < n; i++) {
            res[i] = rand_d() <= p;
            SS+=res[i];
        }
        int curtot = 0;
        auto ask = [&](string s) -> bool {
            qtot++;
            curtot++;
            #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
        };
        string ans, req;
        for (int i = 0; i < n; i++) {
            ans += '0';
            req += '0';
        }
        auto solve = [&](int l, int r, auto&&solve) -> void {
            for (int i = l; i < r; i++) req[i] = '1';
            bool rs = ask(req);
            for (int i = l; i < r; i++) req[i] = '0';
            if (!rs) return;
            if (l + 1 == r) {
                ans[l] = '1';
                return;
            }
            int m = (l + r) / 2;
            solve(l, m, solve);
            solve(m, r, solve);
        };

        // while (sz(poss) > 2*exp) {
        //     double newp = (double) exp / (double) sz(poss);
        //     int siz = 1;
        //     double P=1-newp;
        //     while(siz<=sz(poss)-exp&&P>=0.05){
        //         siz++;
        //         P*=(1-newp);
        //     }
        //     if(siz>sz(poss)-exp)siz=sz(poss)-exp;
        //     siz=4;
        //     int ci = 0;
        //     while (true) {
        //         ci++;
        //         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';
        // }
        solve(0, n, solve);
        assert(check(ans));
    }
    #ifdef LOCAL 
        double pts = 0;
        if (qtot <= fs[tc]) {
            pts = 90;
        } else if (qtot <= 10 * fs[tc]) {
            pts = 90 * (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;
    #endif

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

    return 0;
}