#include <bits/stdc++.h>
using namespace std;
#define int long long
#define doub long double
#define arr array
#define vec vector
#define fir first
#define sec second
const int N = 1e3 + 5, INF = 1e12;
int n;
doub p;
bool qry(int l, int r) {
string ans = "";
for (int i = 1; i <= n; i++)
ans += (l <= i && i <= r) ? "1" : "0";
cout << "Q " << ans << endl;
char x; cin >> x;
return (x == 'P');
}
doub prb(int x, doub e) {
return 1 - powl(1 - e, x);
}
arr<arr<pair<doub, int>, 2>, N> dp;
void dp_cmp() {
dp[0][0] = {0, -1}, dp[0][1] = {INF, -1};
dp[1][0] = {1, 1}, dp[1][1] = {0, -1};
for (int x = 2; x <= n; x++) {
dp[x][1] = {INF, -1};
for (int i = 1; i < x; i++) {
doub prb_a = prb(i, 1 / (doub) x + p);
doub a = dp[i][1].fir + dp[x - i][0].fir + 1;
doub prb_b = 1 - prb_a;
doub b = dp[x - i][1].fir + 1;
dp[x][1] = min(dp[x][1], {prb_a * a + prb_b * b, i});
}
dp[x][0] = {prb(x, p) * dp[x][1].fir + 1, x};
for (int i = 1; i < x; i++) {
doub prb_a = prb(i, p);
doub a = dp[i][1].fir + dp[x - i][0].fir + 1;
doub prb_b = 1 - prb_a;
doub b = dp[x - i][0].fir + 1;
dp[x][0] = min(dp[x][0], {prb_a * a + prb_b * b, i});
}
// cout << x << ": " << dp[x][0].fir << " " << dp[x][1].fir << '\n';
}
}
arr<bool, N> on;
void slv(int l = 1, int r = n, int b = 0) {
if (l > r) return;
int x = r - l + 1;
int i = dp[x][b].sec;
if (i == -1) { on[l] = true; return;}
i = l + i - 1;
if (qry(l, i)) {
slv(l, i, 1);
slv(i + 1, r, 0);
} else {
if (b == 0) slv(i + 1, r, 0);
else slv(i + 1, r, 1);
}
}
signed main() {
// freopen("in", "r", stdin);
int x; cin >> n >> p >> x;
dp_cmp();
for (int i = 1; i <= x; i++) {
on.fill(false);
slv();
string ans = "";
for (int j = 1; j <= n; j++)
ans += (on[j] ? "1" : "0");
cout << "A " << ans << endl;
char y; cin >> y;
}
}
