#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.
int calcsize(double prob){
double ans = (1.0)/prob;
ans/=1.8;
if(rand()%2){
return floor(ans);
}
return ceil(ans);
}
vector<int>ans;
bool test(int l, int r){
vector<bool>quer(N);
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);
}
const int mxn = 1005;
double pos[mxn];
double prob0(int len){
return pos[len];
}
pair<double,int> expect[mxn][mxn];
//stores: {expected num queries, preftoquery}
double finbest(int pref, int suf){
if(expect[pref][suf]!=make_pair(1e18,-1)){
return expect[pref][suf].first;
}
int len = pref+suf;
if(pref==0){
//find best
if(suf==0){
//base case
expect[pref][suf]={0,0};
}
for(int qpref = 1;qpref<=suf;qpref++){
//try querying this one
double p0 = prob0(qpref);
double curr = p0*finbest(0,suf-qpref);
curr+=(1-p0)*finbest(qpref,suf-qpref);
expect[pref][suf]=min(expect[pref][suf],{curr+1,qpref});
}
}
else if(pref==1){
//guaranteed
double curr = finbest(0,suf);
expect[pref][suf] = {curr,0};
}
else{
//only consider shorter
for(int qpref = 1;qpref<pref;qpref++){
//try querying with this one
double p0 = (prob0(qpref)-prob0(pref))/(1-prob0(pref));
double curr = p0*finbest(pref-qpref,suf);
curr+=(1-p0)*finbest(qpref,len-qpref);
expect[pref][suf]=min(expect[pref][suf],{curr+1,qpref});
}
}
return expect[pref][suf].first;
}
void pre(){
pos[0]=1;
for(int i = 1;i<mxn;i++){
pos[i]=pos[i-1]*(1-P);
}
for(int i = 0;i<mxn;i++){
for(int j = 0;j<mxn;j++){
expect[i][j]={1e18,-1};
}
}
for(int i = 0;i<mxn;i++){
for(int j = 0;j<mxn;j++){
finbest(i,j);
}
}
}
void solve(int l, int pref){
//assume there is atleast one here
if(pref==0&&l==N){
//over
return;
}
if(pref==1){
ans.push_back(l);
l++;
pref--;
solve(l,pref);
return;
}
pair<double,int>nx = expect[pref][N-l-pref];
assert(nx.second);
vector<bool>quer(N);
fill(quer.begin()+l,quer.begin()+l+nx.second,1);
if(test_students(quer)){
solve(l,nx.second);
}
else{
solve(l+nx.second,pref ? (pref-nx.second): 0);
}
}
std::vector<bool> find_positive() {
std::vector<bool> answer(N);
if(P==0){
return answer;
}
ans.clear();
solve(0,0);
for(int i : ans){
answer[i]=1;
}
return answer;
}
int main() {
int T;
scanf("%d %lf %d", &N, &P, &T);
// You may perform any extra initialization here.
pre();
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;
}
