#include <bits/stdc++.h>
using namespace std;
template <typename T>
void read(T &x) {
  x = 0;
  char ch = getchar();
  int fh = 1;
  while (ch < '0' || ch > '9') {
    if (ch == '-') fh = -1;
    ch = getchar();
  }
  while (ch >= '0' && ch <= '9') x = x * 10 + ch - '0', ch = getchar();
  x *= fh;
}
int n, k, a[200010], no, b[200010], an, f[200010];
char ans[200010];
int main() {
  read(n);
  read(k);
  for (int i = 1; i <= n; i++) read(a[i]);
  for (int i = 1; i <= n; i++) read(b[i]);
  for (int i = 1; i <= n; i++) {
    f[a[i]]++;
    if (f[a[i]] == 1) no++;
    if (f[b[i]] == 1) no--;
    f[b[i]]--;
    ans[a[i]] = (char)(an + 'a');
    if (no == 0 && i != n) an = min(an + 1, k - 1);
  }
  if (an == k - 1) {
    puts("YES");
    for (int i = 1; i <= n; i++) cout << ans[i];
  } else
    puts("NO");
  return 0;
}

### Prompt

Create a solution in CPP for 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;
template <typename T>
void read(T &x) {
  x = 0;
  char ch = getchar();
  int fh = 1;
  while (ch < '0' || ch > '9') {
    if (ch == '-') fh = -1;
    ch = getchar();
  }
  while (ch >= '0' && ch <= '9') x = x * 10 + ch - '0', ch = getchar();
  x *= fh;
}
int n, k, a[200010], no, b[200010], an, f[200010];
char ans[200010];
int main() {
  read(n);
  read(k);
  for (int i = 1; i <= n; i++) read(a[i]);
  for (int i = 1; i <= n; i++) read(b[i]);
  for (int i = 1; i <= n; i++) {
    f[a[i]]++;
    if (f[a[i]] == 1) no++;
    if (f[b[i]] == 1) no--;
    f[b[i]]--;
    ans[a[i]] = (char)(an + 'a');
    if (no == 0 && i != n) an = min(an + 1, k - 1);
  }
  if (an == k - 1) {
    puts("YES");
    for (int i = 1; i <= n; i++) cout << ans[i];
  } else
    puts("NO");
  return 0;
}

```