#include <cassert>
#include <cmath>
#include <cstdint>
#include <cstdio>
#include <cstdlib>
#include <cstring>
#include <algorithm>
#include <bitset>
#include <complex>
#include <deque>
#include <functional>
#include <iostream>
#include <limits>
#include <map>
#include <numeric>
#include <queue>
#include <set>
#include <sstream>
#include <string>
#include <unordered_map>
#include <unordered_set>
#include <utility>
#include <vector>

using namespace std;

using Int = long long;

template <class T1, class T2> ostream &operator<<(ostream &os, const pair<T1, T2> &a) { return os << "(" << a.first << ", " << a.second << ")"; };
template <class T> ostream &operator<<(ostream &os, const vector<T> &as) { const int sz = as.size(); os << "["; for (int i = 0; i < sz; ++i) { if (i >= 256) { os << ", ..."; break; } if (i > 0) { os << ", "; } os << as[i]; } return os << "]"; }
template <class T> void pv(T a, T b) { for (T i = a; i != b; ++i) cerr << *i << " "; cerr << endl; }
template <class T> bool chmin(T &t, const T &f) { if (t > f) { t = f; return true; } return false; }
template <class T> bool chmax(T &t, const T &f) { if (t < f) { t = f; return true; } return false; }
#define COLOR(s) ("\x1b[" s "m")

bool query(int);
void modify(int,bool);

bool WereYouLast(int N, int M) {
  if (M == 10) {
    int x = 0;
    for (int i = 0; i < M; ++i) {
      if (query(i + 1)) {
        x |= 1 << i;
      }
    }
    if (x == (1 << M) - 1) {
      return true;
    }
    for (int i = 0; i < M; ++i) {
      modify(i + 1, (x + 1) >> i & 1);
    }
    return false;
  } else {
    const int E = 31 - __builtin_clz(N);
    int segN = 1;
    for (; segN < E; segN <<= 1) {}
    auto prod = [&](int u) -> int { return 1000 + u; };
    auto lz = [&](int u) -> int { return 2000 + u; };
    int u = 1;
    for (; u < segN; ) {
      const int uL = u << 1;
      const int uR = u << 1 | 1;
      if (1 < u && query(lz(u))) {
        modify(prod(uL), 0); if (uL < segN) modify(lz(uL), 1);
        modify(prod(uR), 0); if (uR < segN) modify(lz(uR), 1);
        modify(lz(u), 0);
      }
      if (query(prod(uL))) {
        modify(prod(uL), 0); if (uL < segN) modify(lz(uL), 1);
        u = uR;
      } else {
        u = uL;
      }
    }
    if (u >= segN + E) {
      return true;
    }
    if (u == (segN << 1) - 1 && query(prod(u))) {
      return true;
    }
    modify(prod(u), 1);
    for (int v = u; (u >>= 1) > 1; v = u) {
      const int uL = u << 1;
      const int uR = u << 1 | 1;
      modify(prod(u), (query(prod(v)) && query(prod(uL ^ uR ^ v))));
    }
    return false;
  }
}