#include <bits/stdc++.h>
using namespace std;
int main() {
  int n, a, b, c, kk, cnt = 0;
  cin >> n >> kk;
  vector<int> p(n);
  vector<int> q(n);
  vector<int> cc(n + 1, 0);
  vector<int> ans(n + 1, -1);
  for (int i = 0; i < n; i++) cin >> p[i];
  for (int i = 0; i < n; i++) cin >> q[i];
  for (int i = 0; i < n; i++) {
    int z = 0, j;
    for (j = i; j < n; j++) {
      if (cc[p[j]] == 0) z++;
      cc[p[j]]++;
      cc[q[j]]--;
      if (cc[q[j]] == 0) z--;
      if (z == 0) break;
    }
    for (int k = i; k <= j; k++) ans[p[k]] = cnt;
    cnt++;
    i = j;
  }
  if (cnt < kk)
    cout << "NO\n";
  else {
    cout << "YES\n";
    char ch;
    for (int i = 1; i <= n; i++) {
      if (ans[i] < 26)
        ch = 'a' + ans[i];
      else
        ch = 'z';
      cout << ch;
    }
    cout << "\n";
  }
  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, a, b, c, kk, cnt = 0;
  cin >> n >> kk;
  vector<int> p(n);
  vector<int> q(n);
  vector<int> cc(n + 1, 0);
  vector<int> ans(n + 1, -1);
  for (int i = 0; i < n; i++) cin >> p[i];
  for (int i = 0; i < n; i++) cin >> q[i];
  for (int i = 0; i < n; i++) {
    int z = 0, j;
    for (j = i; j < n; j++) {
      if (cc[p[j]] == 0) z++;
      cc[p[j]]++;
      cc[q[j]]--;
      if (cc[q[j]] == 0) z--;
      if (z == 0) break;
    }
    for (int k = i; k <= j; k++) ans[p[k]] = cnt;
    cnt++;
    i = j;
  }
  if (cnt < kk)
    cout << "NO\n";
  else {
    cout << "YES\n";
    char ch;
    for (int i = 1; i <= n; i++) {
      if (ans[i] < 26)
        ch = 'a' + ans[i];
      else
        ch = 'z';
      cout << ch;
    }
    cout << "\n";
  }
  return 0;
}

```