#include <bits/stdc++.h>
using namespace std;
int n, k, x[200005], y[200005], z[200005], w[200005];
char ans[200005];
int main() {
  scanf("%d%d", &n, &k);
  for (int i = 0; i < n; i++) {
    int tmp;
    scanf("%d", &tmp);
    x[tmp] = i;
    w[i] = tmp - 1;
  }
  for (int i = 0; i < n; i++) {
    int tmp;
    scanf("%d", &tmp);
    y[tmp] = i;
  }
  for (int i = 1; i <= n; i++) {
    int ta = min(x[i], y[i]);
    int tb = max(x[i], y[i]);
    z[ta + 1]++;
    z[tb + 1]--;
  }
  ans[w[0]] = 'a';
  k = 'a' + k - 1;
  for (int i = 1; i < n; i++) {
    z[i] += z[i - 1];
    if (z[i] == 0 && ans[w[i - 1]] != k)
      ans[w[i]] = ans[w[i - 1]] + 1;
    else
      ans[w[i]] = ans[w[i - 1]];
  }
  if (ans[w[n - 1]] == k)
    printf("YES\n%s\n", ans);
  else
    puts("NO");
}

### Prompt

In Cpp, your task is to solve 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, x[200005], y[200005], z[200005], w[200005];
char ans[200005];
int main() {
  scanf("%d%d", &n, &k);
  for (int i = 0; i < n; i++) {
    int tmp;
    scanf("%d", &tmp);
    x[tmp] = i;
    w[i] = tmp - 1;
  }
  for (int i = 0; i < n; i++) {
    int tmp;
    scanf("%d", &tmp);
    y[tmp] = i;
  }
  for (int i = 1; i <= n; i++) {
    int ta = min(x[i], y[i]);
    int tb = max(x[i], y[i]);
    z[ta + 1]++;
    z[tb + 1]--;
  }
  ans[w[0]] = 'a';
  k = 'a' + k - 1;
  for (int i = 1; i < n; i++) {
    z[i] += z[i - 1];
    if (z[i] == 0 && ans[w[i - 1]] != k)
      ans[w[i]] = ans[w[i - 1]] + 1;
    else
      ans[w[i]] = ans[w[i - 1]];
  }
  if (ans[w[n - 1]] == k)
    printf("YES\n%s\n", ans);
  else
    puts("NO");
}

```