#include <bits/stdc++.h>
const int K = 30, N = 200100;
int s[K], a[N], b[N], p[N], q[N], n, k;
char ans[N];
inline int max(int x, int y) { return x > y ? x : y; }
int main() {
  register int i, j;
  scanf("%d%d", &n, &k);
  for (i = 1; i <= n; i++) scanf("%d", &p[i]), a[p[i]] = i;
  for (i = 1; i <= n; i++) scanf("%d", &q[i]), b[q[i]] = i;
  for (i = 1; i <= k; i++) {
    if (s[i - 1] >= n)
      return !printf("NO");
    else if (i == k)
      break;
    s[i] = s[i - 1] + 1;
    for (j = s[i]; j <= s[i]; j++)
      ans[p[j]] = i + 96, s[i] = max(s[i], max(b[p[j]], a[q[j]]));
  }
  for (i = s[k - 1] + 1; i <= n; i++) ans[p[i]] = k + 96;
  printf("YES\n");
  for (i = 1; i <= n; i++) putchar(ans[i]);
  return 0;
}

### Prompt

Your challenge is to write 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>
const int K = 30, N = 200100;
int s[K], a[N], b[N], p[N], q[N], n, k;
char ans[N];
inline int max(int x, int y) { return x > y ? x : y; }
int main() {
  register int i, j;
  scanf("%d%d", &n, &k);
  for (i = 1; i <= n; i++) scanf("%d", &p[i]), a[p[i]] = i;
  for (i = 1; i <= n; i++) scanf("%d", &q[i]), b[q[i]] = i;
  for (i = 1; i <= k; i++) {
    if (s[i - 1] >= n)
      return !printf("NO");
    else if (i == k)
      break;
    s[i] = s[i - 1] + 1;
    for (j = s[i]; j <= s[i]; j++)
      ans[p[j]] = i + 96, s[i] = max(s[i], max(b[p[j]], a[q[j]]));
  }
  for (i = s[k - 1] + 1; i <= n; i++) ans[p[i]] = k + 96;
  printf("YES\n");
  for (i = 1; i <= n; i++) putchar(ans[i]);
  return 0;
}

```