Language: C++

#define _USE_MATH_DEFINES
#include <cassert>
#include <cstdio>
#include <cstring>
#include <iostream>
#include <string>
#include <sstream>
#include <vector>
#include <queue>
#include <stack>
#include <list>
#include <set>
#include <map>
#include <unordered_set>
#include <unordered_map>
#include <algorithm>
#include <complex>
#include <cmath>
#include <numeric>
#include <bitset>
#include <functional>
#include <random>
#include <ctime>

using namespace std;

#define trace(...) __f(#__VA_ARGS__, __VA_ARGS__)
template <typename Arg1>
void __f(const char* name, Arg1&& arg1){
  cerr << name << ": " << arg1 << endl;
}
template <typename Arg1, typename... Args>
void __f(const char* names, Arg1&& arg1, Args&&... args){
  const char* comma = strchr(names + 1, ',');
  cerr.write(names, comma - names) << ": " << arg1 << " |";
  __f(comma + 1, args...);
}

typedef long long int64;
typedef pair<int, int> ii;
const int INF = 1 << 29;
const int MOD = 1e9 + 7;

namespace {

template<typename T>
size_t make_hash(const T& v) {
  return std::hash<T>()(v);
}

// adapted from boost::hash_combine
void hash_combine(size_t& h, const size_t& v) {
  h ^= v + 0x9e3779b9 + (h << 6) + (h >> 2);
}

// hash any container
template<typename T>
struct hash_container {
  size_t operator()(const T& v) const {
    size_t h = 0;
    for (const auto& e : v) {
      hash_combine(h, make_hash(e));
    }
    return h;
  }
};

}

namespace std {

// support for pair<T,U> if T and U can be hashed
template<typename T, typename U>
struct hash<pair<T, U>> {
  size_t operator()(const pair<T,U>& v) const {
    size_t h = make_hash(v.first);
    hash_combine(h, make_hash(v.second));
    return h;
  }
};

// support for vector<T> if T is hashable
// (the T... is a required trick if the vector has a non-standard allocator)
template<typename... T>
struct hash<vector<T...>> : hash_container<vector<T...>> {};

// the same for map<T,U> if T and U are hashable
template<typename... T>
struct hash<map<T...>> : hash_container<map<T...>> {};

// simply add more containers as needed
}

const int N = (1 << 20) + 10;
char s[N];

struct Node {
  int L, R;
  int lenL, lenR;
  bool operator ==(const Node& rhs) const {
    return L == rhs.L &&
      R == rhs.R &&
      lenL == rhs.lenL &&
      lenR == rhs.lenR;
  }
};

template<>
struct hash<Node> {
  size_t operator()(const Node& v) const {
    size_t ret = make_hash(v.L);
    hash_combine(ret, make_hash(v.R));
    hash_combine(ret, make_hash(v.lenL));
    hash_combine(ret, make_hash(v.lenR));
    return ret;
  }
};

int main() {
  int n, m;
  scanf("%d%d", &n, &m);
  // n = 17; m = 10;
  vector<Node> Q;
  unordered_map<Node, int> dp;
  for (int i = 0; i <= n; ++i) {
    scanf("%s", s);
    // for (int u = 0; u < (1 << i); ++u) s[u] = '1';
    for (int j = 0; j < (1 << i); ++j) {
      if (s[j] == '1') {
        const auto& cur = Node{0, j, 0, i};
        Q.emplace_back(cur);
        dp[cur] = 1;
      }
    }
  }
  // trace(Q.size());

  unordered_map<ii, int> cnt;
  for (int i = 0; i < Q.size(); ++i) {
    const auto& cur = Q[i];
    int L = cur.L, R = cur.R;
    int lenL = cur.lenL, lenR = cur.lenR;
    // trace(i, L, R, lenL, lenR);
    if (lenR == 0) {
      while (lenL) {
        cnt[{L, lenL}] += dp[cur];
        L >>= 1;
        --lenL;
      }
      continue;
    }
    for (int k = 0; k < 2; ++k) {
      int u;
      for (u = 0; u < lenR; ++u) {
        if (((R >> (lenR - 1 - u)) & 1) == k) break;
      }
      if (u == lenR) continue;
      const auto& nxt = Node{(L << 1) | k, R & ((1 << (lenR - 1 - u)) - 1),
                             lenL + 1, lenR - 1 - u};
      if (!dp.count(nxt)) Q.emplace_back(nxt);
      dp[nxt] += dp[cur];
    }
  }

  int best = 0, ret = 0;
  for (auto& it : cnt) {
    if (it.second >= m) {
      int v = it.first.first, len = it.first.second;
      // trace(v, len, it.second);
      if (best < len || (best == len && ret > v)) {
        best = len;
        ret = v;
      }
    }
  }
  string ans;
  for (int i = 0; i < best; ++i) {
    ans += '0' + (ret & 1);
    ret >>= 1;
  }
  reverse(ans.begin(), ans.end());
  printf("%s\n", ans.c_str());

  return 0;
}


Compiler output:
a.cc:109:8: error: explicit specialization of 'template<class _Tp> struct std::hash' outside its namespace must use a nested-name-specifier [-fpermissive]
  109 | struct hash<Node> {
      |        ^~~~~~~~~~