#include <bits/stdc++.h>
using namespace std;
int n, k;
const int dydis = 2e5 + 10;
int kur[dydis];
bool galima[dydis] = {0};
set<int> setas;
vector<int> mas;
string ans;
int main() {
  cin >> n >> k;
  ans.resize(n);
  for (int i = 0; i < n; i++) {
    int a;
    cin >> a;
    a--;
    mas.push_back(a);
    kur[a] = i;
  }
  vector<int> naujas;
  for (int i = 0; i < n; i++) {
    int a;
    cin >> a;
    a--;
    naujas.push_back(kur[a]);
  }
  set<int> setas;
  int viso = 0;
  char cur = 'a';
  for (int i = 0; i < n; i++) {
    setas.insert(naujas[i]);
    ans[mas[naujas[i]]] = cur;
    if (setas.size() == i + 1 && (*setas.rbegin()) == i) {
      viso++;
      if (cur != 'z') {
        cur++;
      }
    }
  }
  if (viso >= k) {
    cout << "YES\n" << ans;
  } else {
    cout << "NO";
  }
  return 0;
}

### 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 n, k;
const int dydis = 2e5 + 10;
int kur[dydis];
bool galima[dydis] = {0};
set<int> setas;
vector<int> mas;
string ans;
int main() {
  cin >> n >> k;
  ans.resize(n);
  for (int i = 0; i < n; i++) {
    int a;
    cin >> a;
    a--;
    mas.push_back(a);
    kur[a] = i;
  }
  vector<int> naujas;
  for (int i = 0; i < n; i++) {
    int a;
    cin >> a;
    a--;
    naujas.push_back(kur[a]);
  }
  set<int> setas;
  int viso = 0;
  char cur = 'a';
  for (int i = 0; i < n; i++) {
    setas.insert(naujas[i]);
    ans[mas[naujas[i]]] = cur;
    if (setas.size() == i + 1 && (*setas.rbegin()) == i) {
      viso++;
      if (cur != 'z') {
        cur++;
      }
    }
  }
  if (viso >= k) {
    cout << "YES\n" << ans;
  } else {
    cout << "NO";
  }
  return 0;
}

```