#include <bits/stdc++.h>
#pragma GCC optimize "03"
using namespace std;
const int N = 2e5 + 5;
const int mod = 1e9 + 7;
const int inf = 1e9 + 9;
int a[N], b[N];
map<int, int> m;
signed main() {
  ios::sync_with_stdio(false);
  cin.tie(0);
  cout.tie(0);
  int n, k;
  cin >> n >> k;
  vector<char> s(n, '\0');
  for (int i = 1; i <= n; i++) cin >> a[i];
  for (int i = 1; i <= n; i++) cin >> b[i];
  int c = 0;
  for (int i = 1; i <= n; i++) {
    if (m.find(a[i]) == m.end()) {
      m[a[i]]++;
    } else {
      m[a[i]]--;
      m.erase(a[i]);
    }
    if (m.find(b[i]) == m.end()) {
      m[b[i]]++;
    } else {
      m[b[i]]--;
      m.erase(b[i]);
    }
    if (c > 25)
      s[a[i] - 1] = 'z';
    else
      s[a[i] - 1] = char('a' + c);
    if (m.size() == 0 && c <= k - 1) c++;
  }
  if (c <= k - 1) return cout << "NO", 0;
  cout << "YES" << '\n';
  for (auto i : s) cout << i;
  return 0;
}

### Prompt

Construct a Cpp code solution to the problem outlined:

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>
#pragma GCC optimize "03"
using namespace std;
const int N = 2e5 + 5;
const int mod = 1e9 + 7;
const int inf = 1e9 + 9;
int a[N], b[N];
map<int, int> m;
signed main() {
  ios::sync_with_stdio(false);
  cin.tie(0);
  cout.tie(0);
  int n, k;
  cin >> n >> k;
  vector<char> s(n, '\0');
  for (int i = 1; i <= n; i++) cin >> a[i];
  for (int i = 1; i <= n; i++) cin >> b[i];
  int c = 0;
  for (int i = 1; i <= n; i++) {
    if (m.find(a[i]) == m.end()) {
      m[a[i]]++;
    } else {
      m[a[i]]--;
      m.erase(a[i]);
    }
    if (m.find(b[i]) == m.end()) {
      m[b[i]]++;
    } else {
      m[b[i]]--;
      m.erase(b[i]);
    }
    if (c > 25)
      s[a[i] - 1] = 'z';
    else
      s[a[i] - 1] = char('a' + c);
    if (m.size() == 0 && c <= k - 1) c++;
  }
  if (c <= k - 1) return cout << "NO", 0;
  cout << "YES" << '\n';
  for (auto i : s) cout << i;
  return 0;
}

```