#include <cassert>
#include <cstdio>
#include <string>
#include <vector>
#include<bits/stdc++.h>
#define pb push_back
#define all(v) v.begin(),v.end()
#define forf(i,s,e) for(int i = s; i<=e; i++)
#define forb(i,s,e) for(int i = s; i>=e; i--)
#define idx(i,v) lower_bound(all(v),i)-v.begin()
#define comp(v) v.erase(unique(all(v)),v.end())
#define sz(v) (int)v.size()
#define fs first
#define se second
#define SP << " " <<
#define LN << "\n"
#define IO cin.tie(0);cout.tie(0);ios_base::sync_with_stdio(false);
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.
double a[1001];
pair<double,int> dp[1001][2];
vector<bool> answer,v;
void findn(){
a[0] = 1;
forf(i,1,N) a[i] = a[i-1]*(1-P);
dp[1][1] = {0,0};
dp[1][0] = {1,1};
forf(i,2,N){
dp[i][1] = {1e18,0};
dp[i][0] = {1e18,0};
forf(j,1,i-1){
double p1 = max(1-a[j], ((double)j)/i); //p
double p2 = max(a[j], ((double)(i-j))/i); //n
double e = 1 + p1*(dp[j][1].fs + dp[i-j][0].fs) + p2*(dp[i-j][1].fs);
dp[i][1] = min(dp[i][1], {e,j});
}
forf(j,1,i){
double e = 1+(1-a[j])*(dp[j][1].fs + dp[i-j][0].fs) + a[j]*dp[i-j][0].fs;
dp[i][0] = min(dp[i][0], {e,j});
}
}
}
void go(vector<int> c, int d){
if(sz(c) == 1 && d == 1) {
answer[c[0]] = 1; return;
}
if(sz(c) == 0) return;
random_shuffle(all(c));
int n = sz(c); int m = dp[n][d].se;
vector<int> nc1,nc2;
forf(i,0,m-1) nc1.pb(c[i]);
forf(i,m,n-1) nc2.pb(c[i]);
for(auto i : nc1) v[i] = 1;
int f = test_students(v);
for(auto i : nc1) v[i] = 0;
if(f){
go(nc1, 1);
go(nc2,0);
}
else{
go(nc2,d);
}
}
std::vector<bool> find_positive() {
cout<<dp[N][0].fs;
forf(i,0,N-1) answer[i] = 0;
vector<int> c; forf(i,0,N-1) c.push_back(i);
go(c,0);
return answer;
}
int main() {
int T;
scanf("%d %lf %d", &N, &P, &T);
// You may perform any extra initialization here.
answer.resize(N,0);
v.resize(N,0);
findn();
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;
}
