#include <bits/stdc++.h>
using namespace std;
int a[200007], b[200007];
char ans[200007];
int n, k;
int main() {
  cin >> n >> k;
  for (int(i) = 0; (i) < (int)(n); (i)++) {
    cin >> a[i];
    a[i]--;
  }
  for (int(i) = 0; (i) < (int)(n); (i)++) {
    cin >> b[i];
    b[i]--;
  }
  set<int> s1, s2;
  vector<int> v;
  for (int(i) = 0; (i) < (int)(n); (i)++) {
    int p = a[i], q = b[i];
    if (s2.count(p))
      s2.erase(p);
    else
      s1.insert(p);
    if (s1.count(q))
      s1.erase(q);
    else
      s2.insert(q);
    if (s1.empty() && s2.empty()) v.push_back(i);
  }
  if (v.size() < k) {
    cout << "NO" << endl;
    exit(0);
  }
  int l = 0, r = 0;
  char cur = 'a';
  for (int(i) = 0; (i) < (int)(v.size()); (i)++) {
    r = v[i];
    for (int j = l; j <= r; j++) {
      ans[a[j]] = cur;
    }
    l = r + 1;
    cur = min(char(cur + 1), 'z');
  }
  cout << "YES" << endl;
  puts(ans);
  return 0;
}

### Prompt

Please formulate 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 a[200007], b[200007];
char ans[200007];
int n, k;
int main() {
  cin >> n >> k;
  for (int(i) = 0; (i) < (int)(n); (i)++) {
    cin >> a[i];
    a[i]--;
  }
  for (int(i) = 0; (i) < (int)(n); (i)++) {
    cin >> b[i];
    b[i]--;
  }
  set<int> s1, s2;
  vector<int> v;
  for (int(i) = 0; (i) < (int)(n); (i)++) {
    int p = a[i], q = b[i];
    if (s2.count(p))
      s2.erase(p);
    else
      s1.insert(p);
    if (s1.count(q))
      s1.erase(q);
    else
      s2.insert(q);
    if (s1.empty() && s2.empty()) v.push_back(i);
  }
  if (v.size() < k) {
    cout << "NO" << endl;
    exit(0);
  }
  int l = 0, r = 0;
  char cur = 'a';
  for (int(i) = 0; (i) < (int)(v.size()); (i)++) {
    r = v[i];
    for (int j = l; j <= r; j++) {
      ans[a[j]] = cur;
    }
    l = r + 1;
    cur = min(char(cur + 1), 'z');
  }
  cout << "YES" << endl;
  puts(ans);
  return 0;
}

```