#include <cassert>
#include <cstdio>
#include <string>
#include <vector>
#include <bits/stdc++.h>
using namespace std;
/// 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.
const int MAX_N = 2e3;
double probAllNegative[MAX_N], expectedSteps[MAX_N];
vector<int> cuts[MAX_N];
vector<int> perm;
int expectedPositives;
int bucketSizes[] = { 1000, 300, 100, 31, 16, 15, 8, 5, 4, 1 };
bool askRange( int l, int r ) {
vector<bool> mask( N, 0 );
for ( int i = l; i <= r; i++ )
mask[perm[i]] = true;
return test_students( mask );
}
vector<int> positive;
int testCase;
void cauta() {
int pos = 0;
while ( pos < N ) {
int bs = bucketSizes[testCase];
int l = pos - 1, r = min( N, pos + bs );
if ( !askRange( pos, r - 1 ) ) {
pos += bs;
continue;
}
while ( r - l > 1 ) {
int mid = (l + r) / 2;
if ( askRange( pos, mid ) )
r = mid;
else
l = mid;
}
if ( r != N )
positive.push_back( r );
pos = r + 1;
}
}
const unsigned seed = 100;
mt19937 rnd( seed );
vector<bool> find_positive() {
positive.clear();
perm.clear();
perm.resize( N );
for ( int i = 0; i < N; i++ )
perm[i] = i;
//shuffle( perm.begin(), perm.end(), rnd );
cauta();
vector<bool> answer( N, 0 );
for ( int i: positive )
answer[i] = true;
return answer;
}
int main() {
int T;
scanf("%d %lf %d", &N, &P, &T);
if ( P < 0.002 )
testCase = 0;
else if ( P < 0.006 )
testCase = 1;
else if ( P < 0.02 )
testCase = 2;
else if ( P < 0.03 )
testCase = 3;
else if ( P < 0.05 )
testCase = 4;
else if ( P < 0.07 )
testCase = 5;
else if ( P < 0.11 )
testCase = 6;
else if ( P < 0.16 )
testCase = 7;
else if ( P < 0.22 )
testCase = 8;
else
testCase = 9;
// You may perform any extra initialization here.
probAllNegative[0] = 1;
for ( int i = 1; i <= N; i++ )
probAllNegative[i] = probAllNegative[i - 1] * (1 - P);//, cout << i << " " << probAllNegative[i] << "\n";
expectedSteps[1] = 0;
cuts[1].push_back( 1 );
for ( int i = 2; i <= N; i++ ) {
expectedSteps[i] = 2 * i;
int bestcut = 1;
for ( int j = i / 2; j >= 1; j-- ) {
double newEx = 1 + expectedSteps[i - j] * probAllNegative[j] + expectedSteps[j] * (1 - probAllNegative[j] );
//printf( "%lf %d\n", newEx, j );
if ( newEx < expectedSteps[i] ) {
expectedSteps[i] = newEx;
bestcut = j;
}
}
cuts[i].push_back( bestcut );
//printf( "%d %d %lf\n", i, bestcut, expectedSteps[i] );
}
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;
}
