#include <bits/stdc++.h>
using namespace std;
typedef long long int ll;
typedef long double ld;
typedef pair<int,int> pii;
typedef pair<ll,ll> pll;
#define fastio ios_base::sync_with_stdio(false); cin.tie(NULL)
#define pb push_back
#define endl '\n'
#define conts continue
#define sz(a) (int)a.size()
#define ff first
#define ss second
#define all(a) a.begin(),a.end()
#define rall(a) a.rbegin(),a.rend()
#define ceil2(x,y) ((x+y-1)/(y))
#define rep(i,n) for(int i = 0; i < n; ++i)
#define rep1(i,n) for(int i = 1; i <= n; ++i)
#define rev(i,s,e) for(int i = s; i >= e; --i)
#define trav(i,a) for(auto &i : a)
template<typename T>
void amin(T &x, T y){
x = min(x,y);
}
template<typename T>
void amax(T &x, T y){
x = max(x,y);
}
template<typename A,typename B>
string to_string(pair<A,B> p);
string to_string(const string &s){
return "'"+s+"'";
}
string to_string(const char* s){
return to_string((string)s);
}
string to_string(bool b){
return b?"true":"false";
}
template<typename A>
string to_string(A v){
string res = "{";
trav(x,v){
res += to_string(x)+",";
}
if(res.back() == ',') res.pop_back();
res += "}";
return res;
}
template<typename A,typename B>
string to_string(pair<A,B> p){
return "("+to_string(p.ff)+","+to_string(p.ss)+")";
}
#define debug(x) cout << "[" << #x << "]: "; cout << to_string(x) << endl
/*
refs:
edi
*/
const int MOD = 1e9 + 7;
const int NN = 1e3 + 5;
const int inf1 = 1e9 + 5;
const ll inf2 = (ll)1e18 + 5;
bool dbg = false;
/// 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) {
if(dbg) return 'P';
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';
}
std::vector<ld> dp(NN,1e9);
std::vector<ld> dp2(NN,1e9);
std::vector<int> par(NN,-1);
std::vector<int> par2(NN,-1);
void precalc(){
int n = N;
dp[0] = dp[1] = 0;
dp2[0] = 0, dp2[1] = 1;
par2[1] = 1;
for(int i = 2; i <= n; ++i){
ld tot_neg = powl((ld)1-P, i);
for(int j = 1; j < i; j++){
ld all_neg2 = powl((ld)1-P,i-j);
ld all_neg = powl((ld)1-P,j) * (1 - all_neg2) / (1 - tot_neg);
ld val = 1+all_neg*dp[i-j];
val += (1-all_neg)*(dp[j]+dp2[i-j]);
if(val < dp[i]){
dp[i] = val;
par[i] = j;
}
}
for(int j = 1; j <= i; j++){
ld all_neg = powl((ld)1-P,j);
ld val = 1+(1-all_neg)*dp[j]+dp2[i-j];
if(val < dp2[i]){
dp2[i] = val;
par2[i] = j;
}
}
// std::cout << "at N = " << i << " got ev " << dp[i] << " and par is " << par[i] << '\n';
// std::cout << "at N = " << i << " got ev " << dp2[i] << " and par is " << par2[i] << '\n';
}
}
/// 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.
std::vector<bool> find_positive() {
// std::vector<bool> answer(N);
// return answer;
int n = N;
vector<bool> ans(n);
auto go = [&](int l, int r, int t, auto &&go) -> void{
// t = 0: positive not guaranteed (use dp2)
// t = 1: at least 1 positive (use dp)
if(l > r) return;
int len = r-l+1;
if(t){
if(len == 1){
ans[l] = 1;
return;
}
int j = par[len];
vector<bool> mask(n);
for(int k = l; k < l+j; ++k){
mask[k] = 1;
}
if(!test_students(mask)){
// no positive on left
// at least 1 positive on right
go(l+j,r,1,go);
}
else{
// at least 1 positive on left
// not guaranteed on right
go(l,l+j-1,1,go);
go(l+j,r,0,go);
}
}
else{
if(len == 1){
vector<bool> mask(n);
mask[l] = 1;
ans[l] = test_students(mask);
return;
}
int j = par2[len];
vector<bool> mask(n);
for(int k = l; k < l+j; ++k){
mask[k] = 1;
}
if(!test_students(mask)){
// no positive on left
// not guaranteed on right
go(l+j,r,0,go);
}
else{
// positive on left
// not guaranteed on right
go(l,l+j-1,1,go);
go(l+j,r,0,go);
}
}
};
go(0,n-1,0,go);
return ans;
}
int main() {
#ifdef LOCAL
dbg = true;
#endif
int T;
scanf("%d %lf %d", &N, &P, &T);
precalc();
// 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;
}
