Next_permutation() и Time Limit

#include <bits/stdc++.h>
using namespace std;
int main()
{
    int n, k;
    cin >> n >> k;
    vector <char> v(15);
    for (int i(0); i < n; i++)
        v[i] = (char)('a' + i);
    for (int i(0); i < k - 1; i++)
        next_permutation(v.begin(), v.begin() + n);
    for (int i(0); i < n; i++)
        cout << v[i];
}

#include <cassert>
#include <numeric>
#include <string>
#include <iostream>
 
const unsigned FACTORIALS[] = { 1, 1, 2, 6, 24, 120, 720, 5040, 40320, 362880, 3628800, 39916800, 479001600 };
 
std::string word(unsigned k, std::string &abc)
{
  assert(abc.size() < sizeof FACTORIALS / sizeof *FACTORIALS);
  assert(k < FACTORIALS[abc.size()]);
  
  if (abc.empty())
    return {};
  
  unsigned suffixes = FACTORIALS[abc.size() - 1];
  
  unsigned i = k / suffixes; 
  char a = 'a' + abc[i];
  abc.erase(i, 1);
  
  return a + word(k % suffixes, abc);
}
 
std::string word(unsigned k, unsigned N)
{
  assert(k > 0);
    
  std::string abc(N, 0);
  std::iota(abc.begin(), abc.end(), 0);
  
  return word(k - 1, abc);
}
 
int main(void) 
{
  std::cout << word(5, 4) << std::endl;
}

#include <iostream>
#include <set>
using namespace std;
 
int main()
{
    int n, k, j;
    set<char> v;
    
    cin >> n >> k;
    
    j = 'a' + n;
    for (char c = 'a'; c < j; ++c) v.insert(c);
    
    int f = 1;
    for (int i = 2; i < n; ++i) f *= i;
    
    --k;
    --n;
    while (n > 0)
    {
        set<char>::iterator it = v.begin();
        j = k / f;
        for (int i = 0; i < j; ++i) ++it;
        cout << *it;
        v.erase(it);
        k %= f;
        f /= n--;
    }
    cout << *(v.begin());
}