#include <bits/stdc++.h>
using namespace std;
int main() {
  int n, k;
  cin >> n >> k;
  vector<int> p(n, 0);
  vector<int> q(n, 0);
  for (int i = 0; i < n; i++) {
    cin >> p[i];
  }
  for (int i = 0; i < n; i++) {
    cin >> q[i];
  }
  set<int> vals1;
  set<int> vals2;
  vector<int> rights;
  for (int i = 0; i < n; i++) {
    if (vals2.count(p[i])) {
      vals2.erase(p[i]);
    } else {
      vals1.insert(p[i]);
    }
    if (vals1.count(q[i])) {
      vals1.erase(q[i]);
    } else {
      vals2.insert(q[i]);
    }
    if (vals1.empty() && vals2.empty()) {
      rights.push_back(i);
    }
  }
  if (rights.size() < k) {
    cout << "NO" << endl;
  } else {
    string s(n, ' ');
    int l = 0;
    for (int it = 0; it < rights.size(); it++) {
      int r = rights[it];
      char c = 'a' + min(it, 25);
      for (int i = l; i <= r; i++) {
        s[p[i] - 1] = c;
      }
      l = r + 1;
    }
    cout << "YES" << endl << s << endl;
  }
  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>
using namespace std;
int main() {
  int n, k;
  cin >> n >> k;
  vector<int> p(n, 0);
  vector<int> q(n, 0);
  for (int i = 0; i < n; i++) {
    cin >> p[i];
  }
  for (int i = 0; i < n; i++) {
    cin >> q[i];
  }
  set<int> vals1;
  set<int> vals2;
  vector<int> rights;
  for (int i = 0; i < n; i++) {
    if (vals2.count(p[i])) {
      vals2.erase(p[i]);
    } else {
      vals1.insert(p[i]);
    }
    if (vals1.count(q[i])) {
      vals1.erase(q[i]);
    } else {
      vals2.insert(q[i]);
    }
    if (vals1.empty() && vals2.empty()) {
      rights.push_back(i);
    }
  }
  if (rights.size() < k) {
    cout << "NO" << endl;
  } else {
    string s(n, ' ');
    int l = 0;
    for (int it = 0; it < rights.size(); it++) {
      int r = rights[it];
      char c = 'a' + min(it, 25);
      for (int i = l; i <= r; i++) {
        s[p[i] - 1] = c;
      }
      l = r + 1;
    }
    cout << "YES" << endl << s << endl;
  }
  return 0;
}

```