#include <bits/stdc++.h>
using namespace std;
int main() {
  ios::sync_with_stdio(0);
  cin.tie(0);
  int n, k;
  cin >> n >> k;
  vector<int> a(n), b(n);
  for (int i = 0; i < n; i++) cin >> a[i];
  for (int i = 0; i < n; i++) cin >> b[i];
  vector<int> comp;
  set<int> rem;
  for (int i = 0; i < n; i++) {
    if (rem.count(a[i]))
      rem.erase(a[i]);
    else
      rem.insert(a[i]);
    if (rem.count(b[i]))
      rem.erase(b[i]);
    else
      rem.insert(b[i]);
    if (rem.empty()) comp.emplace_back(i);
  }
  if ((int)comp.size() < k)
    cout << "NO\n";
  else {
    cout << "YES\n";
    int pre = 0;
    string ans(n, '*');
    for (int i = 0; i < (int)comp.size(); i++) {
      char ch = char(min(i, 25) + 'a');
      for (int j = pre; j <= comp[i]; j++) {
        ans[a[j] - 1] = ch;
        ans[b[j] - 1] = ch;
      }
      pre = comp[i] + 1;
    }
    cout << ans;
  }
}

### Prompt

Your challenge is to write 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() {
  ios::sync_with_stdio(0);
  cin.tie(0);
  int n, k;
  cin >> n >> k;
  vector<int> a(n), b(n);
  for (int i = 0; i < n; i++) cin >> a[i];
  for (int i = 0; i < n; i++) cin >> b[i];
  vector<int> comp;
  set<int> rem;
  for (int i = 0; i < n; i++) {
    if (rem.count(a[i]))
      rem.erase(a[i]);
    else
      rem.insert(a[i]);
    if (rem.count(b[i]))
      rem.erase(b[i]);
    else
      rem.insert(b[i]);
    if (rem.empty()) comp.emplace_back(i);
  }
  if ((int)comp.size() < k)
    cout << "NO\n";
  else {
    cout << "YES\n";
    int pre = 0;
    string ans(n, '*');
    for (int i = 0; i < (int)comp.size(); i++) {
      char ch = char(min(i, 25) + 'a');
      for (int j = pre; j <= comp[i]; j++) {
        ans[a[j] - 1] = ch;
        ans[b[j] - 1] = ch;
      }
      pre = comp[i] + 1;
    }
    cout << ans;
  }
}

```