#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.
vector<int>ans;
bool test(int l, int r){
vector<bool>quer(N,0);
for(int i = l;i<=r;i++){
auto it = lower_bound(ans.begin(),ans.end(),i);
if(it!=ans.end()){
if((*it)==i){
continue;
}
}
quer[i]=1;
}
return test_students(quer);
}
void solve2(int l, int r, bool shift){
//check l-r
if((r-l+1)*P>1||shift||test(l,r)){
//positive somewhere inside
if(l==r){
ans.push_back(l);
return;
}
int mid = (l+r)/2;
if(shift){
if(test(l,mid)){
solve2(l,mid,1);
}
else{
solve2(mid+1,r,1);
}
}
else{
//no shift
solve2(l,mid,0);
solve2(mid+1,r,0);
}
return;
}
return;
}
vector<int>solve(int l, int r){
//check l-r
vector<bool>quer(N);
for(int i = l;i<=r;i++){
quer[i]=1;
}
if(((r-l+1)*P>0.7&&l!=r)||test_students(quer)){
//positive somewhere inside
if(l==r){
return {l};
}
int mid = (l+r)/2;
vector<int>lef = solve(l,mid);
vector<int>rig = solve(mid+1,r);
lef.insert(lef.end(),rig.begin(),rig.end());
return lef;
}
return {};
}
std::vector<bool> find_positive2() {
std::vector<bool> answer(N);
ans.clear();
while(test(0,N-1)){
solve2(0,N-1,1);
}
vector<int>pos = ans;
for(int i : pos){
answer[i]=1;
}
return answer;
}
std::vector<bool> find_positive3() {
//30-70 to be found
//bin jump?
ans.clear();
int len = max(1,(int)floor(1.0/P));
for(int i = 0;i<N;i+=len){
int j = i+len-1;
//check here
while(test(i,j)){
solve2(i,j,1);
}
}
vector<bool>answer(N);
for(int i : ans){
answer[i]=1;
}
return answer;
}
std::vector<bool> find_positive() {
if(P<0.01){
return find_positive2();
}
else if(P<=0.2){
return find_positive3();
}
std::vector<bool> answer(N);
vector<int>pos = solve(0,N-1);
for(int i : pos){
answer[i]=1;
}
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;
}
