#include <bits/stdc++.h>
using namespace std;
int main() {
  int n, k;
  cin >> n >> k;
  int p[n], q[n];
  for (int i = 0; i < n; i++) cin >> p[i];
  for (int j = 0; j < n; j++) cin >> q[j];
  set<int> pirmas, antras;
  vector<int> ats;
  ats.push_back(-1);
  for (int i = 0; i < n; i++) {
    if (pirmas.count(q[i]))
      pirmas.erase(q[i]);
    else
      antras.insert(q[i]);
    if (antras.count(p[i]))
      antras.erase(p[i]);
    else
      pirmas.insert(p[i]);
    if ((pirmas.empty()) && (antras.empty())) ats.push_back(i);
  }
  char raides[n];
  if (ats.size() <= k)
    cout << "NO";
  else {
    cout << "YES" << endl;
    char raide = 'a';
    raide--;
    for (int i = 0; i < ats.size() - 1; i++) {
      raide++;
      raide = min(raide, 'z');
      for (int j = ats[i] + 1; j <= ats[i + 1]; j++) raides[p[j] - 1] = raide;
    }
    for (int i = 0; i < n; i++) cout << raides[i];
  }
  return 0;
}

### Prompt

Please formulate a cpp solution to the following problem:

Authors have come up with the string s consisting of n lowercase Latin letters.

You are given two permutations of its indices (not necessary equal) p and q (both of length n). Recall that the permutation is the array of length n which contains each integer from 1 to n exactly once.

For all i from 1 to n-1 the following properties hold: s[p_i] ≤ s[p_{i + 1}] and s[q_i] ≤ s[q_{i + 1}]. It means that if you will write down all characters of s in order of permutation indices, the resulting string will be sorted in the non-decreasing order.

Your task is to restore any such string s of length n consisting of at least k distinct lowercase Latin letters which suits the given permutations.

If there are multiple answers, you can print any of them.

Input

The first line of the input contains two integers n and k (1 ≤ n ≤ 2 ⋅ 10^5, 1 ≤ k ≤ 26) — the length of the string and the number of distinct characters required.

The second line of the input contains n integers p_1, p_2, ..., p_n (1 ≤ p_i ≤ n, all p_i are distinct integers from 1 to n) — the permutation p.

The third line of the input contains n integers q_1, q_2, ..., q_n (1 ≤ q_i ≤ n, all q_i are distinct integers from 1 to n) — the permutation q.

Output

If it is impossible to find the suitable string, print "NO" on the first line.

Otherwise print "YES" on the first line and string s on the second line. It should consist of n lowercase Latin letters, contain at least k distinct characters and suit the given permutations.

If there are multiple answers, you can print any of them.

Example

Input


3 2
1 2 3
1 3 2


Output


YES
abb

### Response

```cpp
#include <bits/stdc++.h>
using namespace std;
int main() {
  int n, k;
  cin >> n >> k;
  int p[n], q[n];
  for (int i = 0; i < n; i++) cin >> p[i];
  for (int j = 0; j < n; j++) cin >> q[j];
  set<int> pirmas, antras;
  vector<int> ats;
  ats.push_back(-1);
  for (int i = 0; i < n; i++) {
    if (pirmas.count(q[i]))
      pirmas.erase(q[i]);
    else
      antras.insert(q[i]);
    if (antras.count(p[i]))
      antras.erase(p[i]);
    else
      pirmas.insert(p[i]);
    if ((pirmas.empty()) && (antras.empty())) ats.push_back(i);
  }
  char raides[n];
  if (ats.size() <= k)
    cout << "NO";
  else {
    cout << "YES" << endl;
    char raide = 'a';
    raide--;
    for (int i = 0; i < ats.size() - 1; i++) {
      raide++;
      raide = min(raide, 'z');
      for (int j = ats[i] + 1; j <= ats[i + 1]; j++) raides[p[j] - 1] = raide;
    }
    for (int i = 0; i < n; i++) cout << raides[i];
  }
  return 0;
}

```