#include <bits/stdc++.h>
#define AOTSUKI
using namespace std;
constexpr bool isMultiCase = 1;
// #include "angel/math/modint.hpp"
using ll = long long;
template <class T> constexpr int len(const T &c) {
return int(std::ssize(c));
}
template <class T> using V = vector<T>;
template <class T> using RevPq = priority_queue<T, vector<T>, greater<T>>;
constexpr char eoln = '\n';
#define L(i, l, r) for (int i = (l); i < (r); ++i)
#define R(i, l, r) for (int i = (r) - 1; i >= (l); --i)
#define ALL(x) (x).begin(), (x).end()
#define fi first
#define se second
#include <cassert>
#include <cstdio>
#include <string>
#include <vector>
/// You may use:
// The number of students
int N;
// The probability any given student is positive
double P;
// This function performs a test on a subset of samples.
// Its argument is a vector of Booleans of length N,
// where the i-th element is true if the i-th sample should be added to the mix.
// It returns true if (and only if) at least one of the samples in the mix is positive.
bool test_students(std::vector<bool> mask) {
assert(mask.size() == (size_t)N);
std::string mask_str(N, ' ');
for (int i = 0; i < N; i++)
mask_str[i] = mask[i] ? '1' : '0';
printf("Q %s\n", mask_str.c_str());
fflush(stdout);
char answer;
scanf(" %c", &answer);
return answer == 'P';
}
/// You should implement:
// This function will be called once for each test instance.
// It should use test_students to determine which samples are positive.
// It must return a vector of Booleans of length N,
// where the i-th element is true if and only if the i-th sample is positive.
using Float = long double;
V<Float> opt;
V<Float> opos;
void init() {
opt.resize(N + 2, 1ll << 60);
opos.resize(N + 2, 0);
opt[0] = 0;
opt[1] = 0;
L(i, 2, N + 2) {
// split
Float ngn = pow(1 - P, i);
Float amin = 0;
L(j, 1, i) {
Float score = 1;
Float up = ((1 - pow(1 - P, j)) / (1 - ngn));
// cerr << i << ' ' << j << ' ' << up << endl;
score += opt[j] * up;
// 見つからなかったら
score += opt[i - j] * (1 - up);
if (score < opt[i]) {
opt[i] = score;
amin = j;
}
}
opos[i] = amin;
}
}
std::vector<bool> find_positive() {
V<bool> answer(N);
L(l, -1, N) {
int r = N;
Float pex = 1 - pow(1 - P, N - l - 1);
if (1 + pex * opt[r - l] < opt[r - l]) {
V<bool> mask(N);
L(i, l + 1, N) mask[i] = true;
auto res = test_students(mask);
if (not res) break;
}
while (r - l > 1) {
int m = l + 1 + opos[r - l];
// cerr << m << endl;
V<bool> mask(N);
L(i, l + 1, m) mask[i] = true;
auto res = test_students(mask);
if (res) r = m - 1;
else l = m - 1;
}
if (r == N) break;
answer[r] = true;
}
return answer;
}
int main() {
int T;
scanf("%d %lf %d", &N, &P, &T);
// You may perform any extra initialization here.
P = min(P, 0.2);
P = max(P, 0.001);
init();
/*
for (auto e : opt) cerr << e << ' ';
cerr << endl;
for (auto e : opos) cerr << e << ' ';
cerr << endl;
*/
for (int i = 0; i < T; i++) {
std::vector<bool> answer = find_positive();
assert(answer.size() == (size_t)N);
std::string answer_str(N, ' ');
for (int j = 0; j < N; j++)
answer_str[j] = answer[j] ? '1' : '0';
printf("A %s\n", answer_str.c_str());
fflush(stdout);
char verdict;
scanf(" %c", &verdict);
if (verdict == 'W')
exit(0);
}
return 0;
}
