#include <bits/stdc++.h>
using namespace std;
#define rng(i,a,b) for(int i=int(a);i<=int(b);i++)
#define rep(i,b) rng(i,0,b-1)
#define gnr(i,b,a) for(int i=int(b);i>=int(a);i--)
#define per(i,b) gnr(i,b-1,0)
#define pb push_back
#define eb emplace_back
#define fi first
#define se second
#define bg begin()
#define ed end()
#define all(x) x.bg,x.ed
#define si(x) int(x.size())
template<class t> using vc=vector<t>;
template<class t> using vvc=vc<vc<t>>;
typedef long long ll;
using pii=pair<int,int>;
using vi=vc<int>;
using uint=unsigned;
using ull=unsigned long long;
using pil=pair<int,ll>;
using pli=pair<ll,int>;
using pll=pair<ll,ll>;
using t3=tuple<int,int,int>;
#include <cassert>
#include <cstdio>
#include <string>
#include <vector>
/// You may use:
// The number of students
int N;
// The probability any given student is positive
double P;
int DEBUG = 0;
// 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.
int Z[1010];
int cnt=0;
bool test_students(std::vector<bool> mask) {
cnt++;
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';
if(!DEBUG){
printf("Q %s\n", mask_str.c_str());
fflush(stdout);
char answer;
scanf(" %c", &answer);
return answer == 'P';
}
int ss=0;
rep(i,N){
if(mask[i]) ss|=Z[i];
}
return ss;
}
std::vector<bool>answer, mask;
bool test_range(int b, int e){
rep(i,N)mask[i]=0;
rng(i,b,e)mask[i]=1;
return test_students(mask);
}
/// 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 D[1010];
int Path[1010];
void Go(int b, int e){
if(b==e){
answer[b]=1;
return;
}
int N = e-b+1;
if(Path[N]){
int c = Path[N];
if(test_range(b,b+c-1)){
Go(b,b+c-1);
if(test_range(b+c,e)) Go(b+c,e);
}
else{
Go(b+c,e);
}
}
else{
rng(i,b,e){
if(test_range(i,i))answer[i]=1;
}
}
}
std::vector<bool> find_positive() {
answer.resize(N);
mask.resize(N);
rep(i,N)answer[i]=0;
int s = 0;
if(test_range(0,N-1)){
Go(0,N-1);
}
return answer;
}
ll rand_int(ll l, ll r) { //[l, r]
#ifdef LOCAL
static mt19937_64 gen;
#else
static mt19937_64 gen(chrono::steady_clock::now().time_since_epoch().count());
#endif
return uniform_int_distribution<ll>(l, r)(gen);
}
int main() {
int T;
scanf("%d %lf %d", &N, &P, &T);
rng(i,2,N){
D[i]=i;
Path[i] = 0;
rng(j,1,i-1){
double p = (1-pow(1-P,j)) / (1-pow(1-P,i));
double q = 1-p;
double s = q * (1+D[i-j]) + p * (2 + D[j] + (1-pow(1-P,i-j)) * D[i-j] );
if(D[i]>s){
Path[i] = j;
D[i]=s;
}
}
printf("%d %f\n",i,D[i]);
}
// You may perform any extra initialization here.
for (int i = 0; i < T; i++) {
if(DEBUG){
rep(j,N){
if(rand_int(0,999) < P*1000){
Z[j]=1;
}
else Z[j]=0;
}
}
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';
if(!DEBUG){
printf("A %s\n", answer_str.c_str());
fflush(stdout);
char verdict;
scanf(" %c", &verdict);
if (verdict == 'W')
exit(0);
}
}
if(DEBUG)printf("%f\n",(double)cnt/T);
return 0;
}
