#include <cassert>
#include <cstdio>
#include <string>
#include <vector>
#include <math.h>
#include <iostream>
#include <random>
using namespace std;
/// You may use:
// The number of students
int N;
// The probability any given student is positive
double P;
vector<pair<double, int>> f, g;
int solve(std::vector<bool>& result, int l, int r, bool containsPositive);
bool bruteforce = false;
int queryCount = 0;
vector<bool> answers;
void testAll(int num) {
bruteforce = true;
std::random_device rd;
std::mt19937 gen(rd());
std::bernoulli_distribution d(P);
answers.assign(N, false);
queryCount = 0;
for (int i = 0; i < num; i++) {
for (int j = 0; j < N; j++) {
answers[j] = d(gen);
}
std::vector<bool> answer(N);
solve(answer, 0, N, false);
if (i % (num / 100) == 0) {
cout << g[N].first << " ";
cout << double(queryCount) / double(i + 1) << endl;
}
}
bruteforce = false;
}
// 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(const std::vector<bool>& mask) {
assert(mask.size() == (size_t)N);
if (bruteforce) {
queryCount++;
for (int i = 0; i < N; i++)
if (mask[i] && answers[i])
return true;
return false;
}
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';
}
/*
f(n) = argmin(
(f(k) + g(n - k)) * (k / n + (n - k) / n * (1 - (1 - P)^k)) +
)
*/
void init() {
f.assign(N + 1, {100000.0, -1});
g.assign(N + 1, {100000.0, -1});
f[0] = {0, 0};
f[1] = {0, 0};
g[0] = {0, 0};
g[1] = {1, 1};
vector<double> pw(N + 1);
for (int i = 0; i <= N; i++)
pw[i] = pow(1.0 - P, i);
for (int n = 2; n <= N; n++) {
for (int k = 1; k < n; k++) {
double p = (1.0 - pw[k]) / (1 - pw[n]);//double(k) / double(n) + double(n - k) / double(n) * (1.0 - pw[k]);
double exp = 1.0 +
p * (f[k].first) +
(1 - p) * (f[n - k].first);
if (exp < f[n].first) {
f[n] = {exp, k};
}
}
double sumG = 0;
for (int k = 1; k <= n; k++) {
sumG += g[n - k].first * pw[k - 1] * P;
double p = 1.0 - pw[k];
double exp = 1.0 +
p * (f[k].first + sumG / (1 - pw[k])) +
(1 - p) * (g[n - k].first);
if (exp < g[n].first) {
g[n] = {exp, k};
}
}
}
}
/*
1100010010
0001
*/
int solve(std::vector<bool>& result, int l, int r, bool containsPositive) {
int n = r - l;
if (n == 0)
return -1;
if (containsPositive && n == 1) {
result[l] = true;
return l;
}
int k = containsPositive ? f[n].second : g[n].second;
vector<bool> mask(N);
for (int i = l; i < l + k; i++)
mask[i] = true;
bool res = test_students(mask);
if (containsPositive) {
if (res)
return solve(result, l, l + k, true);
else
return solve(result, l + k, r, true);
}
else {
if (res) {
int firstPositive = solve(result, l, l + k, true);
return solve(result, firstPositive + 1, r, false);
}
else {
return solve(result, l + k, r, false);
}
}
}
std::vector<bool> find_positive() {
init();
//testAll(100000);
std::vector<bool> answer(N);
//return answer;
if (P == 0.0)
return answer;
if (P == 1.0) {
for (int i = 0; i < N; i++)
answer[i] = true;
return answer;
}
//cerr << g[N].first << endl;
solve(answer, 0, N, false);
return answer;
}
int main() {
int T;
scanf("%d %lf %d", &N, &P, &T);
// You may perform any extra initialization here.
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;
}
