#include <bits/stdc++.h>
using namespace std;
#define DEBUG
/// You may use:
// The number of students
int N;
// The probability any given student is positive
double P;
vector<bool> secret;
char ask(string m) {
for (int i = 0; i < N; ++i) {
if (m[i] == '1' && secret[i]) {
return 'P';
}
}
return 'N';
}
// 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';
#ifdef DEBUG
char answer = ask(mask_str);
#endif
#ifndef DEBUG
printf("Q %s\n", mask_str.c_str());
fflush(stdout);
char answer;
scanf(" %c", &answer);
#endif
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.
bool query(int l, int r) {
vector<bool> qr(N);
for (int i = l; i <= r; ++i) {
qr[i] = 1;
}
return test_students(qr);
}
std::vector<bool> find_positive() {
std::vector<bool> answer(N);
auto dfs = [&](auto& dfs, int l, int r) -> void {
if (l == r) {
answer[l] = 1;
return;
}
int m = (l + r) / 2;
if (query(l, m)) {
dfs(dfs, l, m);
double len = r - (m + 1) + 1;
// cout << len << " = " << len * P << "\n";
if (len * P >= 5 * P * P) {
if (query(m + 1, r)) dfs(dfs, m + 1, r);
}
} else {
dfs(dfs, m + 1, r);
}
};
if (query(0, (N - 1) / 2)) dfs(dfs, 0, (N - 1) / 2);
if (query((N - 1) / 2 + 1, N - 1)) dfs(dfs, (N - 1) / 2 + 1, N - 1);
return answer;
}
void solve() {
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';
#ifndef DEBUG
printf("A %s\n", answer_str.c_str());
#endif
#ifdef DEBUG
// cout << "E ";
bool ok = true;
for (int i = 0; i < N; ++i) {
// cout << secret[i];
if (secret[i] != answer[i]) ok = false;
}
// cout << "\n";
#endif
fflush(stdout);
#ifdef DEBUG
char verdict = (ok ? 'C' : 'W');
#endif
#ifndef DEBUG
char verdict;
scanf(" %c", &verdict);
#endif
if (verdict == 'W') {
#ifdef DEBUG
cout << "WA!\n";
#endif
exit(0);
}
}
// Returns true with probability `p`, and false with probability `1 - p`
bool weighted_random_bool(double p) {
static std::random_device rd;
static std::mt19937 gen(rd());
std::bernoulli_distribution d(p);
return d(gen);
}
int main() {
int T;
scanf("%d %lf %d", &N, &P, &T);
secret = vector<bool>(N);
// You may perform any extra initialization here.
for (int i = 0; i < T; i++) {
#ifdef DEBUG
for (int j = 0; j < N; ++j) {
if (weighted_random_bool(P)) {
secret[j] = 1;
} else {
secret[j] = 0;
}
}
#endif
solve();
}
#ifdef DEBUG
cout << "AC!\n";
#endif
return 0;
}
