#include <bits/stdc++.h>
#include <ext/pb_ds/assoc_container.hpp>
#include <ext/pb_ds/tree_policy.hpp>
#define ll long long
#define ld long double
#define ull unsigned long long
#define ff first
#define ss second
#define pii pair<int,int>
#define pll pair<long long, long long>
#define vi vector<int>
#define vl vector<long long>
#define pb push_back
#define rep(i, b) for(int i = 0; i < (b); ++i)
#define rep2(i,a,b) for(int i = a; i <= (b); ++i)
#define rep3(i,a,b,c) for(int i = a; i <= (b); i+=c)
#define count_bits(x) __builtin_popcountll((x))
#define all(x) (x).begin(),(x).end()
#define siz(x) (int)(x).size()
#define forall(it,x) for(auto& it:(x))
using namespace __gnu_pbds;
using namespace std;
typedef tree<int, null_type, less<int>, rb_tree_tag,tree_order_statistics_node_update> ordered_set;
mt19937 mt;void random_start(){mt.seed(chrono::time_point_cast<chrono::milliseconds>(chrono::high_resolution_clock::now()).time_since_epoch().count());}
ll los(ll a, ll b) {return a + (mt() % (b-a+1));}
const int INF = 1e9+50;
const ll INF_L = 1e18+40;
const ll MOD = 1e9+7;
int n;
ld P;
pair<ld,int> dp[1001][41];
bool test_students(vi mask)
{
string mask_str(n, '0');
forall(it,mask) mask_str[it] = '1';
printf("Q %s\n", mask_str.c_str());
fflush(stdout);
char answer;
scanf(" %c", &answer);
return answer == 'P';
}
vector<bool> solve_small()
{
vector<bool> answer(n,0);
int cur_p = 0;
int block_small_P = max(1,min(n,n/max(1,(int)(n*P))));
while((1 << __lg(block_small_P)) != block_small_P) block_small_P--;
vi elms;
rep(i,n) elms.pb(i);
shuffle(all(elms),mt);
while(cur_p < n)
{
int block = block_small_P;
block = min(block,n-cur_p);
vi b = {};
rep2(i,cur_p,cur_p+block-1) b.pb(elms[i]);
bool is = test_students(b);
if(!is)
{
cur_p += block;
continue;
}
int l = cur_p;
int r = cur_p+block-2;
int ans = cur_p+block-1;
while(l <= r)
{
int mid = (l+r)/2;
b = {};
rep2(i,cur_p,mid) b.pb(elms[i]);
if(test_students(b))
{
ans = mid;
r = mid-1;
}
else
{
l = mid+1;
}
}
answer[elms[ans]] = 1;
cur_p = ans+1;
}
return answer;
}
vector<bool> solve_big()
{
vector<bool> answer(n,0);
int cur_p = 0;
int cur_k = 0;
vi elms;
rep(i,n) elms.pb(i);
//shuffle(all(elms),mt);
while(cur_p < n)
{
if(cur_k == 1)
{
answer[cur_p] = 1;
cur_p++;
cur_k = 0;
continue;
}
int block = dp[n-cur_p][cur_k].ss;
vi x;
rep2(i,cur_p,cur_p+block-1) x.pb(elms[i]);
if(test_students(x))
{
if(cur_k == 0) cur_k = block;
cur_k = min(cur_k,block);
}
else
{
cur_k = max(0,cur_k-block);
cur_p += block;
}
}
return answer;
}
vector<bool> find_positive()
{
if(P < 0.1) return solve_small();
else return solve_big();
}
ld Pow[1001];
int main()
{
random_start();
int t;
cin >> n >> P >> t;
Pow[0] = 1;
rep2(i,1,n)
{
Pow[i] = Pow[i-1]*(1-P);
}
rep2(i,1,n)
{
dp[i][1] = dp[i-1][0];
rep2(k,2,min(i,40))
{
dp[i][k] = {1e9,0};
rep2(z,1,min(k-1,40))
{
ld ans = 1;
ld h = (Pow[z]*(1-Pow[k-z]))/(1-Pow[k]);
//jest
ans += dp[i][z].ff*(1-h);
// nie ma
ans += dp[i-z][k-z].ff*(h);
dp[i][k] = min(dp[i][k],{ans,z});
}
}
dp[i][0] = {1e9,0};
rep2(z,1,min(i,40))
{
ld ans = 1;
ld h = Pow[z];
//jest
ans += dp[i][z].ff*(1-h);
//nie ma
ans += dp[i-z][0].ff*(h);
dp[i][0] = min(dp[i][0],{ans,z});
}
}
for (int i = 0; i < t; i++)
{
vector<bool> answer = find_positive();
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);
}
}
