#include <cassert>
#include <cstdio>
#include <string>
#include <vector>
#include <random>
using namespace std;
mt19937 rnf(1234);
/// You may use:
// The number of students
int N;
// The probability any given student is positive
double P;
vector<bool> trueanswer;
// 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);
for (int i = 0; i < N; ++i)
{
if (mask[i] && trueanswer[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';
}
/// You should implement:
double dp[1003], dp1[1003];
int u[1003], u1[1003];
void rec(int l, int r, vector<bool>& answer, bool z)
{
if (z == false)
{
if (u[r - l + 1] == 0)
{
vector<bool> v(N, false);
for (int i = l; i <= r; ++i)
{
v[i] = true;
if (test_students(v))
answer[i] = true;
v[i] = false;
}
return;
}
if (u[r - l + 1] == r - l + 1)
{
vector<bool> v(N, false);
for (int i = l; i <= r; ++i)
v[i] = true;
if (!test_students(v))
return;
rec(l, r, answer, true);
return;
}
int m = l + u[r - l + 1] - 1;
rec(l, m, answer, false);
rec(m + 1, r, answer, false);
}
else
{
if (u1[r - l + 1] == 0)
{
vector<bool> v(N, false);
for (int i = l; i <= r; ++i)
{
v[i] = true;
if (test_students(v))
answer[i] = true;
v[i] = false;
}
return;
}
int m = l + u1[r - l + 1] - 1;
vector<bool> v(N, false);
for (int i = l; i <= m; ++i)
v[i] = true;
if (!test_students(v))
rec(m + 1, r, answer, true);
else
{
rec(l, m, answer, true);
rec(m + 1, r, answer, false);
}
}
}
// 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.
std::vector<bool> find_positive() {
std::vector<bool> answer(N, false);
rec(0, N - 1, answer, false);
return answer;
}
double ast[1003];
int main() {
int T;
scanf("%d %lf %d", &N, &P, &T);
trueanswer.assign(N, false);
for (int i = 0; i < N; ++i)
{
if (rnf() % 1000000000 < P * 1000000000)
trueanswer[i] = true;
}
ast[0] = 1;
for (int i = 1; i <= N; ++i)
ast[i] = (ast[i - 1] * (1 - P));
for (int n = 1; n <= N; ++n)
{
dp1[n] = n;
u1[n] = 0;
for (int i = 1; i < n; ++i)
{
double sh0 = ast[i] * (1 - ast[n - i]) / (1 - ast[n]);
double ydp = sh0 * (1 + dp1[n - i]) + (1 - sh0) * (1 + dp1[i] + dp[n - i]);
if (ydp < dp1[n])
{
dp1[n] = ydp;
u1[n] = i;
}
}
dp[n] = n;
u[n] = 0;
if (ast[n] * 1 + (1 - ast[n]) * (1 + dp1[n]) < dp[n])
{
dp[n] = ast[n] * 1 + (1 - ast[n]) * (1 + dp1[n]);
u[n] = n;
}
for (int i = 1; i < n; ++i)
{
if (dp[i] + dp[n - i] < dp[n])
{
dp[n] = dp[i] + dp[n - i];
u[n] = i;
}
}
}
// 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;
}
// 1000 0.1 1
// 1 0.001 1
// 1000 0.001 300
// 1000 0.005256 300
// 1000 0.011546 300
// 1000 0.028545 300
// 1000 0.039856 300
// 1000 0.068648 300
// 1000 0.104571 300
// 1000 0.158765 300
// 1000 0.2 300
