#include <bits/stdc++.h>
using namespace std;
int n, k;
int a[200005], b[200005];
int main() {
  scanf("%d%d", &n, &k);
  for (int i = 0; i < n; i++) {
    scanf("%d", a + i);
  }
  for (int i = 0; i < n; i++) {
    scanf("%d", b + i);
  }
  set<int> aa, bb;
  vector<int> ans;
  for (int i = 0; i < n; i++) {
    if (aa.count(b[i])) {
      aa.erase(b[i]);
    } else {
      bb.insert(b[i]);
    }
    if (bb.count(a[i])) {
      bb.erase(a[i]);
    } else {
      aa.insert(a[i]);
    }
    if (aa.empty() && bb.empty()) {
      ans.push_back(i);
    }
  }
  if (ans.size() >= k) {
    puts("YES");
    string s(n, ' ');
    int l = 0;
    for (int i = 0; i < ans.size(); i++) {
      int r = ans[i];
      char c = 'a' + min(i, 25);
      for (int j = l; j <= r; j++) {
        s[a[j] - 1] = c;
      }
      l = r + 1;
    }
    cout << s << '\n';
    return 0;
  }
  puts("NO");
  return 0;
}

### Prompt

Create a solution in cpp for 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;
int a[200005], b[200005];
int main() {
  scanf("%d%d", &n, &k);
  for (int i = 0; i < n; i++) {
    scanf("%d", a + i);
  }
  for (int i = 0; i < n; i++) {
    scanf("%d", b + i);
  }
  set<int> aa, bb;
  vector<int> ans;
  for (int i = 0; i < n; i++) {
    if (aa.count(b[i])) {
      aa.erase(b[i]);
    } else {
      bb.insert(b[i]);
    }
    if (bb.count(a[i])) {
      bb.erase(a[i]);
    } else {
      aa.insert(a[i]);
    }
    if (aa.empty() && bb.empty()) {
      ans.push_back(i);
    }
  }
  if (ans.size() >= k) {
    puts("YES");
    string s(n, ' ');
    int l = 0;
    for (int i = 0; i < ans.size(); i++) {
      int r = ans[i];
      char c = 'a' + min(i, 25);
      for (int j = l; j <= r; j++) {
        s[a[j] - 1] = c;
      }
      l = r + 1;
    }
    cout << s << '\n';
    return 0;
  }
  puts("NO");
  return 0;
}

```