#include <bits/stdc++.h>
using namespace std;
int tree[5000010];
void update(int node, int b, int e, int i) {
  if (b > i || e < i) return;
  if (b == i && e == i) {
    tree[node] ^= 1;
    return;
  }
  update(node * 2, b, (b + e) / 2, i),
      update(node * 2 + 1, (b + e) / 2 + 1, e, i);
  tree[node] = tree[node * 2] + tree[node * 2 + 1];
}
int main() {
  int n, k;
  cin >> n >> k;
  int a[n], b[n];
  for (int i = 0; i < n; i++) cin >> a[i];
  for (int i = 0; i < n; i++) cin >> b[i];
  int last = 0;
  char str[n + 1], c = 'a';
  for (int i = 0; i < n; i++) {
    update(1, 1, n, a[i]);
    update(1, 1, n, b[i]);
    if (!tree[1]) {
      for (int j = last; j <= i; j++) str[a[j]] = c;
      if (c != 'z') c++;
      k--;
      last = i + 1;
    }
  }
  if (k > 0) {
    cout << "NO";
    return 0;
  }
  cout << "YES\n";
  for (int i = 1; i <= n; i++) cout << str[i];
}

### Prompt

Please provide a cpp coded solution to the problem described below:

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 tree[5000010];
void update(int node, int b, int e, int i) {
  if (b > i || e < i) return;
  if (b == i && e == i) {
    tree[node] ^= 1;
    return;
  }
  update(node * 2, b, (b + e) / 2, i),
      update(node * 2 + 1, (b + e) / 2 + 1, e, i);
  tree[node] = tree[node * 2] + tree[node * 2 + 1];
}
int main() {
  int n, k;
  cin >> n >> k;
  int a[n], b[n];
  for (int i = 0; i < n; i++) cin >> a[i];
  for (int i = 0; i < n; i++) cin >> b[i];
  int last = 0;
  char str[n + 1], c = 'a';
  for (int i = 0; i < n; i++) {
    update(1, 1, n, a[i]);
    update(1, 1, n, b[i]);
    if (!tree[1]) {
      for (int j = last; j <= i; j++) str[a[j]] = c;
      if (c != 'z') c++;
      k--;
      last = i + 1;
    }
  }
  if (k > 0) {
    cout << "NO";
    return 0;
  }
  cout << "YES\n";
  for (int i = 1; i <= n; i++) cout << str[i];
}

```