#include <bits/stdc++.h>
using namespace std;
const int N = 2e5 + 10;
int p[N], q[N], id[N], m[N];
char s[N];
int main() {
  int n, k;
  cin >> n >> k;
  for (int i = 1; i <= n; i++) {
    scanf("%d", p + i);
    id[p[i]] = i;
  }
  for (int i = 1; i <= n; i++) m[i] = i;
  for (int i = 1; i <= n; i++) {
    scanf("%d", q + i);
    if (id[q[i]] > i)
      m[i] = max(m[i], id[q[i]]);
    else
      m[id[q[i]]] = max(m[id[q[i]]], i);
  }
  char c = 'a';
  for (int i = 1, j = 1; i <= n; i++) {
    if (i > j) {
      j = i;
      if (c != 'a' + k - 1) c++;
    }
    s[p[i]] = c;
    j = max(j, m[i]);
  }
  if (c == 'a' + k - 1)
    printf("YES\n%s\n", s + 1);
  else
    printf("NO\n");
}

### Prompt

Your task is to create a CPP solution 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 + 10;
int p[N], q[N], id[N], m[N];
char s[N];
int main() {
  int n, k;
  cin >> n >> k;
  for (int i = 1; i <= n; i++) {
    scanf("%d", p + i);
    id[p[i]] = i;
  }
  for (int i = 1; i <= n; i++) m[i] = i;
  for (int i = 1; i <= n; i++) {
    scanf("%d", q + i);
    if (id[q[i]] > i)
      m[i] = max(m[i], id[q[i]]);
    else
      m[id[q[i]]] = max(m[id[q[i]]], i);
  }
  char c = 'a';
  for (int i = 1, j = 1; i <= n; i++) {
    if (i > j) {
      j = i;
      if (c != 'a' + k - 1) c++;
    }
    s[p[i]] = c;
    j = max(j, m[i]);
  }
  if (c == 'a' + k - 1)
    printf("YES\n%s\n", s + 1);
  else
    printf("NO\n");
}

```