Problem p00469 (C++)

Buggy submission (status: Time Limit Exceeded):
#include "bits/stdc++.h"
#include <unordered_map>
#include <unordered_set>
#pragma warning(disable : 4996)
using namespace std;
using ld = long double;
template <class T> using Table = vector<vector<T>>;
const ld eps = 1e-9;

template <class BidirectionalIterator>
bool next_combination(BidirectionalIterator first1, BidirectionalIterator last1,
                      BidirectionalIterator first2,
                      BidirectionalIterator last2) {
  if ((first1 == last1) || (first2 == last2)) {
    return false;
  }
  BidirectionalIterator m1 = last1;
  BidirectionalIterator m2 = last2;
  --m2;
  while (--m1 != first1 && !(*m1 < *m2)) {
  }
  bool result = (m1 == first1) && !(*first1 < *m2);
  if (!result) {
    // ???
    while (first2 != m2 && !(*m1 < *first2)) {
      ++first2;
    }
    first1 = m1;
    std::iter_swap(first1, first2);
    ++first1;
    ++first2;
  }
  if ((first1 != last1) && (first2 != last2)) {
    // ???
    m1 = last1;
    m2 = first2;
    while ((m1 != first1) && (m2 != last2)) {
      std::iter_swap(--m1, m2);
      ++m2;
    }
    // ??¢
    std::reverse(first1, m1);
    std::reverse(first1, last1);
    std::reverse(m2, last2);
    std::reverse(first2, last2);
  }
  return !result;
}

template <class BidirectionalIterator>
bool next_combination(BidirectionalIterator first, BidirectionalIterator middle,
                      BidirectionalIterator last) {
  return next_combination(first, middle, middle, last);
}

int main() {
  while (1) {
    int N;
    cin >> N;
    int K;
    cin >> K;
    if (!N)
      break;
    vector<string> sts;
    for (int i = 0; i < N; ++i) {
      string st;
      cin >> st;
      sts.emplace_back(st);
    }
    vector<int> nums(N);
    iota(nums.begin(), nums.end(), 0);
    set<string> anss;
    do {
      string ans;
      for (int i = 0; i < K; ++i) {
        ans += sts[nums[i]];
      }
      anss.emplace(ans);

    } while (next_permutation(nums.begin(), nums.end()));
    cout << anss.size() << endl;
  }
  return 0;
}

Fixed submission:
#include "bits/stdc++.h"
#include <unordered_map>
#include <unordered_set>
#pragma warning(disable : 4996)
using namespace std;
using ld = long double;
template <class T> using Table = vector<vector<T>>;
const ld eps = 1e-9;

template <class BidirectionalIterator>
bool next_combination(BidirectionalIterator first1, BidirectionalIterator last1,
                      BidirectionalIterator first2,
                      BidirectionalIterator last2) {
  if ((first1 == last1) || (first2 == last2)) {
    return false;
  }
  BidirectionalIterator m1 = last1;
  BidirectionalIterator m2 = last2;
  --m2;
  while (--m1 != first1 && !(*m1 < *m2)) {
  }
  bool result = (m1 == first1) && !(*first1 < *m2);
  if (!result) {
    // ???
    while (first2 != m2 && !(*m1 < *first2)) {
      ++first2;
    }
    first1 = m1;
    std::iter_swap(first1, first2);
    ++first1;
    ++first2;
  }
  if ((first1 != last1) && (first2 != last2)) {
    // ???
    m1 = last1;
    m2 = first2;
    while ((m1 != first1) && (m2 != last2)) {
      std::iter_swap(--m1, m2);
      ++m2;
    }
    // ??¢
    std::reverse(first1, m1);
    std::reverse(first1, last1);
    std::reverse(m2, last2);
    std::reverse(first2, last2);
  }
  return !result;
}

template <class BidirectionalIterator>
bool next_combination(BidirectionalIterator first, BidirectionalIterator middle,
                      BidirectionalIterator last) {
  return next_combination(first, middle, middle, last);
}

int main() {
  while (1) {
    int N;
    cin >> N;
    int K;
    cin >> K;
    if (!N)
      break;
    vector<string> sts;
    for (int i = 0; i < N; ++i) {
      string st;
      cin >> st;
      sts.emplace_back(st);
    }
    vector<int> nums(N);
    iota(nums.begin(), nums.end(), 0);
    set<string> anss;
    do {
      vector<int> anums(K);
      iota(anums.begin(), anums.end(), 0);
      do {
        string ans;
        for (int i = 0; i < K; ++i) {
          ans += sts[nums[anums[i]]];
        }
        anss.emplace(ans);
      } while (next_permutation(anums.begin(), anums.end()));
    } while (next_combination(nums.begin(), nums.begin() + K, nums.end()));
    cout << anss.size() << endl;
  }
  return 0;
}