#include <bits/stdc++.h>
using namespace std;
int n, k, a[200001], b[200001], F[200001], Cnt[200001], d, dem = 0;
char Ch[200001], u = 'a';
int main() {
  ios_base::sync_with_stdio(0);
  cin >> n >> k;
  for (int i = 1; i <= n; i++) cin >> a[i];
  for (int i = 1; i <= n; i++) cin >> b[i];
  int x = 0;
  for (int i = 1; i <= n; i++) {
    F[a[i]]++;
    F[b[i]]--;
    if (F[a[i]] == 0) d++;
    if (F[b[i]] == 0 && b[i] != a[i]) d++;
    if (d == i - x) {
      Cnt[++dem] = i;
      x = i;
      d = 0;
    }
  }
  if (dem < k) {
    cout << "NO";
    return 0;
  }
  int j = 1;
  for (int i = 1; i <= n; i++) {
    Ch[a[i]] = u;
    if (i == Cnt[j] && j < 26) u = char(u + 1), j++;
  }
  cout << "YES" << endl;
  for (int i = 1; i <= n; i++) cout << Ch[i];
}

### 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;
int n, k, a[200001], b[200001], F[200001], Cnt[200001], d, dem = 0;
char Ch[200001], u = 'a';
int main() {
  ios_base::sync_with_stdio(0);
  cin >> n >> k;
  for (int i = 1; i <= n; i++) cin >> a[i];
  for (int i = 1; i <= n; i++) cin >> b[i];
  int x = 0;
  for (int i = 1; i <= n; i++) {
    F[a[i]]++;
    F[b[i]]--;
    if (F[a[i]] == 0) d++;
    if (F[b[i]] == 0 && b[i] != a[i]) d++;
    if (d == i - x) {
      Cnt[++dem] = i;
      x = i;
      d = 0;
    }
  }
  if (dem < k) {
    cout << "NO";
    return 0;
  }
  int j = 1;
  for (int i = 1; i <= n; i++) {
    Ch[a[i]] = u;
    if (i == Cnt[j] && j < 26) u = char(u + 1), j++;
  }
  cout << "YES" << endl;
  for (int i = 1; i <= n; i++) cout << Ch[i];
}

```