#include <bits/stdc++.h>
using namespace std;
int main() {
  int n, k, i, j = 0, m, pos = 11;
  cin >> n >> k;
  set<int> se;
  vector<char> str(n);
  string ans;
  char x;
  vector<int> res;
  int arr[n], brr[n];
  for (i = 0; i < n; i++) cin >> arr[i];
  for (i = 0; i < n; i++) cin >> brr[i];
  for (i = 0; i < n; i++) {
    if (se.find(arr[i]) != se.end())
      se.erase(arr[i]);
    else
      se.insert(arr[i]);
    if (se.find(brr[i]) != se.end())
      se.erase(brr[i]);
    else
      se.insert(brr[i]);
    if (se.size() == 0) res.push_back(i);
  }
  m = res.size();
  if (m < k)
    cout << "NO" << endl;
  else {
    k--;
    cout << "YES" << endl;
    for (i = 0; i < m; i++) {
      x = 'a' + min(k, i);
      for (; j <= res[i]; j++) str[arr[j] - 1] = x;
    }
    for (i = 0; i < n; i++) cout << str[i];
    cout << endl;
  }
  return 0;
}

### Prompt

In cpp, your task is to solve 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, i, j = 0, m, pos = 11;
  cin >> n >> k;
  set<int> se;
  vector<char> str(n);
  string ans;
  char x;
  vector<int> res;
  int arr[n], brr[n];
  for (i = 0; i < n; i++) cin >> arr[i];
  for (i = 0; i < n; i++) cin >> brr[i];
  for (i = 0; i < n; i++) {
    if (se.find(arr[i]) != se.end())
      se.erase(arr[i]);
    else
      se.insert(arr[i]);
    if (se.find(brr[i]) != se.end())
      se.erase(brr[i]);
    else
      se.insert(brr[i]);
    if (se.size() == 0) res.push_back(i);
  }
  m = res.size();
  if (m < k)
    cout << "NO" << endl;
  else {
    k--;
    cout << "YES" << endl;
    for (i = 0; i < m; i++) {
      x = 'a' + min(k, i);
      for (; j <= res[i]; j++) str[arr[j] - 1] = x;
    }
    for (i = 0; i < n; i++) cout << str[i];
    cout << endl;
  }
  return 0;
}

```