#include <bits/stdc++.h>
using namespace std;
void input(vector<int>& vec, int n) {
  for (int i = 0; i < n; i++) cin >> vec[i];
}
int main() {
  int n, k, i, j, partitions = 0, diff = 0, last_partition = 0;
  cin >> n >> k;
  char filler = 'a';
  string ret(n, '_');
  vector<bool> state(n + 1, false);
  vector<int> p(n), q(n);
  input(p, n);
  input(q, n);
  for (i = 0; i < n; i++) {
    if (state[p[i]]) {
      --diff;
      state[p[i]] = false;
    } else {
      ++diff;
      state[p[i]] = true;
    }
    if (state[q[i]]) {
      --diff;
      state[q[i]] = false;
    } else {
      ++diff;
      state[q[i]] = true;
    }
    if (!diff) {
      partitions++;
      for (j = last_partition; j <= i; j++) ret[p[j] - 1] = filler;
      if (filler < 'z') filler++;
      last_partition = i + 1;
    }
  }
  if (partitions < k)
    cout << "NO\n";
  else {
    cout << "YES\n";
    cout << ret << "\n";
  }
  return 0;
}

### Prompt

Generate 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;
void input(vector<int>& vec, int n) {
  for (int i = 0; i < n; i++) cin >> vec[i];
}
int main() {
  int n, k, i, j, partitions = 0, diff = 0, last_partition = 0;
  cin >> n >> k;
  char filler = 'a';
  string ret(n, '_');
  vector<bool> state(n + 1, false);
  vector<int> p(n), q(n);
  input(p, n);
  input(q, n);
  for (i = 0; i < n; i++) {
    if (state[p[i]]) {
      --diff;
      state[p[i]] = false;
    } else {
      ++diff;
      state[p[i]] = true;
    }
    if (state[q[i]]) {
      --diff;
      state[q[i]] = false;
    } else {
      ++diff;
      state[q[i]] = true;
    }
    if (!diff) {
      partitions++;
      for (j = last_partition; j <= i; j++) ret[p[j] - 1] = filler;
      if (filler < 'z') filler++;
      last_partition = i + 1;
    }
  }
  if (partitions < k)
    cout << "NO\n";
  else {
    cout << "YES\n";
    cout << ret << "\n";
  }
  return 0;
}

```