#include <bits/stdc++.h>
#pragma GCC optimize("O3")
using namespace std;
mt19937 rnd(time(nullptr));
const int N = 2e5 + 5;
int p[N], q[N], pos_p[N], pos_q[N];
int mx[N];
int main() {
  ios_base::sync_with_stdio(0);
  cin.tie(0);
  cout.tie(0);
  int n, k;
  cin >> n >> k;
  for (int i = 0; i < n; ++i) {
    cin >> p[i], p[i]--;
    pos_p[p[i]] = i;
  }
  for (int i = 0; i < n; ++i) {
    cin >> q[i], q[i]--;
    pos_q[q[i]] = i, mx[i] = (i ? max(mx[i - 1], pos_p[q[i]]) : pos_p[q[i]]);
  }
  string s(n, '?');
  char c = 'a', res = 'a';
  set<pair<int, char>> last;
  for (int i = 0; i < n; ++i) {
    while (last.size() && last.begin()->first < i) last.erase(last.begin());
    if (!last.size()) {
      s[p[i]] = c, res = max(res, c);
      last.insert({mx[pos_q[p[i]]], c});
      c = min('z', char(c + 1));
    } else {
      auto cur = *last.begin();
      last.erase(last.begin());
      s[p[i]] = cur.second, res = max(res, cur.second);
      last.insert({max(mx[pos_q[p[i]]], cur.first), cur.second});
    }
  }
  if (res - 'a' + 1 >= k)
    cout << "YES\n" << s;
  else
    cout << "NO";
}

### 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>
#pragma GCC optimize("O3")
using namespace std;
mt19937 rnd(time(nullptr));
const int N = 2e5 + 5;
int p[N], q[N], pos_p[N], pos_q[N];
int mx[N];
int main() {
  ios_base::sync_with_stdio(0);
  cin.tie(0);
  cout.tie(0);
  int n, k;
  cin >> n >> k;
  for (int i = 0; i < n; ++i) {
    cin >> p[i], p[i]--;
    pos_p[p[i]] = i;
  }
  for (int i = 0; i < n; ++i) {
    cin >> q[i], q[i]--;
    pos_q[q[i]] = i, mx[i] = (i ? max(mx[i - 1], pos_p[q[i]]) : pos_p[q[i]]);
  }
  string s(n, '?');
  char c = 'a', res = 'a';
  set<pair<int, char>> last;
  for (int i = 0; i < n; ++i) {
    while (last.size() && last.begin()->first < i) last.erase(last.begin());
    if (!last.size()) {
      s[p[i]] = c, res = max(res, c);
      last.insert({mx[pos_q[p[i]]], c});
      c = min('z', char(c + 1));
    } else {
      auto cur = *last.begin();
      last.erase(last.begin());
      s[p[i]] = cur.second, res = max(res, cur.second);
      last.insert({max(mx[pos_q[p[i]]], cur.first), cur.second});
    }
  }
  if (res - 'a' + 1 >= k)
    cout << "YES\n" << s;
  else
    cout << "NO";
}

```