/**
 * @author n685
 * @brief
 * @date 2024-07-25 19:53:13
 *
 *
 */
#include <bits/stdc++.h>

#ifdef LOCAL
#include "dd/debug.h"
#else
#define dbg(...) 42
#define dbgP(...) 420
#define dbgRP(...) 420420
void nline() {}
void bar() {}
#endif

using db = double; // change it to double as needed
// [[maybe_unused]] const db PI = std::acos(static_cast<db>(-1.0));
[[maybe_unused]] constexpr db PI = std::numbers::pi_v<db>;
constexpr db EPS = 1e-9;
template <class T, class U> constexpr bool eq(const T &a, const U &b) {
  if constexpr (std::is_floating_point_v<std::common_type_t<T, U>>) {
    return std::abs(a - b) < EPS;
  } else {
    return a == b;
  }
}

constexpr int MX = 1000;
std::array<std::array<db, MX + 1>, MX + 1> dp;
std::array<std::array<int, MX + 1>, MX + 1> len;
std::array<db, MX + 1> ppow, ippow;
int n;

bool query(int l, int r) {
  std::string q(n, '0');
  for (int i = l - 1; i <= r - 1; ++i) {
    q[i] = '1';
  }
  std::printf("Q %s\n", q.c_str());
  std::fflush(stdout);
  char c;
  std::scanf(" %c", &c);
  return c == 'P';
}

int main() {
  db p;
  int t;
  // std::cin >> n >> p >> t;
  std::scanf("%d %lf %d", &n, &p, &t);
  if (eq(p, 0)) {
    for (int i = 0; i < t; ++i) {
      std::printf("A ");
      for (int j = 0; j < n; ++j) {
        std::printf("0");
      }
      std::printf("\n");
      std::fflush(stdout);
    }
    return 0;
  }
  if (eq(p, 1)) {
    for (int i = 0; i < t; ++i) {
      std::printf("A ");
      for (int j = 0; j < n; ++j) {
        std::printf("1");
      }
      std::printf("\n");
      std::fflush(stdout);
    }
    return 0;
  }

  ppow[0] = 1;
  for (int i = 1; i <= n; ++i) {
    ppow[i] = ppow[i - 1] * (1 - p);
  }
  for (int i = 1; i <= n; ++i) {
    ippow[i] = 1 / (1 - ppow[i]);
  }

  // std::vector dp(n + 1,
  //                std::vector(n + 1, std::numeric_limits<db>::infinity()));
  db inf = std::numeric_limits<db>::infinity();
  dp[0][0] = 0;
  for (int suf = 1; suf <= n; ++suf) {
    dp[suf][1] = dp[suf - 1][0];
    for (int pre = 2; pre <= suf; ++pre) {
      dp[suf][pre] = inf;
      for (int j = 1; j < pre; ++j) {
        db pv = (ppow[j] - ppow[pre]) * ippow[pre];
        db val = pv * dp[suf - j][pre - j] + (1 - pv) * dp[suf][j] + 1;
        if (dp[suf][pre] > val) {
          dp[suf][pre] = val;
          len[suf][pre] = j;
        }
      }
    }
    // pre = 0
    dp[suf][0] = inf;
    for (int j = 1; j <= suf; ++j) {
      db pv = ppow[j];
      db val = pv * dp[suf - j][0] + (1 - pv) * dp[suf][j] + 1;
      if (dp[suf][0] > val) {
        dp[suf][0] = val;
        len[suf][0] = j;
      }
    }
  }

  while ((t--) != 0) {
    std::string ans(n, '0');
    int suf = n, pre = 0;
    while (suf > 0) {
      // dbg(suf, pre, dp[suf][pre]);
      if (pre == 1) {
        ans[n - suf] = '1';
        --suf;
        pre = 0;
      } else {
        int j = len[suf][pre];
        if (query(n - suf + 1, n - suf + j)) {
          pre = j;
        } else {
          if (pre > 0) {
            pre -= j;
          }
          suf -= j;
        }
      }
    }
    std::printf("A %s\n", ans.c_str());
    std::fflush(stdout);
    char c;
    std::scanf(" %c", &c);
    if (c == 'W') {
      return 0;
    }
  }
}