#include <bits/stdc++.h>
using namespace std;
const int N = 2e5 + 5;
char ans[N];
int arr[N], inv[N], val[N];
int main() {
  int n, k;
  cin >> n >> k;
  for (int i = 1; i <= n; i++) {
    int x;
    cin >> x;
    arr[x] = i;
    inv[i] = x;
  }
  int pre = 0;
  for (int i = 1; i <= n; i++) {
    int cur;
    cin >> cur;
    cur = arr[cur];
    if (cur < pre) {
      val[cur]--;
      val[pre]++;
    }
    pre = cur;
  }
  int v = 0, inc = 0;
  for (int i = n; i > 0; i--) {
    if (inc == 0) {
      v++;
    }
    if (v == k) {
      for (int j = i; j > 0; j--) ans[j] = 'a' + 26 - v;
      break;
    }
    ans[i] = 'a' + 26 - v;
    inc += val[i];
  }
  if (v != k)
    cout << "NO" << endl;
  else {
    cout << "YES" << endl;
    for (int i = 1; i <= n; i++) cout << ans[arr[i]];
    cout << endl;
  }
}

### Prompt

Please create a solution in CPP 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;
const int N = 2e5 + 5;
char ans[N];
int arr[N], inv[N], val[N];
int main() {
  int n, k;
  cin >> n >> k;
  for (int i = 1; i <= n; i++) {
    int x;
    cin >> x;
    arr[x] = i;
    inv[i] = x;
  }
  int pre = 0;
  for (int i = 1; i <= n; i++) {
    int cur;
    cin >> cur;
    cur = arr[cur];
    if (cur < pre) {
      val[cur]--;
      val[pre]++;
    }
    pre = cur;
  }
  int v = 0, inc = 0;
  for (int i = n; i > 0; i--) {
    if (inc == 0) {
      v++;
    }
    if (v == k) {
      for (int j = i; j > 0; j--) ans[j] = 'a' + 26 - v;
      break;
    }
    ans[i] = 'a' + 26 - v;
    inc += val[i];
  }
  if (v != k)
    cout << "NO" << endl;
  else {
    cout << "YES" << endl;
    for (int i = 1; i <= n; i++) cout << ans[arr[i]];
    cout << endl;
  }
}

```