#include <bits/stdc++.h>
using namespace std;
int n, k, P[(200010)], Q[(200010)], ret[(200010)], C[(200010)], ans[(200010)];
inline int read() {
  int x = 0, f = 1;
  char ch = getchar();
  while (ch < '0' || ch > '9')
    ch == '-' ? f = -1, ch = getchar() : ch = getchar();
  while (ch >= '0' && ch <= '9')
    x = (x << 1) + (x << 3) + (ch ^ 48), ch = getchar();
  return x * f;
}
signed main() {
  n = read(), k = read();
  for (int i = 1; i <= n; ++i) P[i] = read();
  for (int i = 1; i <= n; ++i) Q[i] = read();
  for (int i = 1; i <= n; ++i) ret[P[i]] = i;
  for (int i = 2; i <= n; ++i)
    if (ret[Q[i]] < ret[Q[i - 1]])
      C[ret[Q[i]]] += ret[Q[i - 1]] - ret[Q[i]],
          C[ret[Q[i - 1]]] -= ret[Q[i - 1]] - ret[Q[i]];
  int sum = 0;
  for (int i = 1; i <= n; ++i) {
    if (sum)
      ans[i] = ans[i - 1];
    else
      ans[i] = ans[i - 1] + 1;
    sum += C[i];
  }
  if (ans[n] < k)
    puts("NO");
  else {
    puts("YES");
    for (int i = 1; i <= n; ++i) printf("%c", min(ans[ret[i]], k) + 'a' - 1);
    puts("");
  }
  return 0;
}

### 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, P[(200010)], Q[(200010)], ret[(200010)], C[(200010)], ans[(200010)];
inline int read() {
  int x = 0, f = 1;
  char ch = getchar();
  while (ch < '0' || ch > '9')
    ch == '-' ? f = -1, ch = getchar() : ch = getchar();
  while (ch >= '0' && ch <= '9')
    x = (x << 1) + (x << 3) + (ch ^ 48), ch = getchar();
  return x * f;
}
signed main() {
  n = read(), k = read();
  for (int i = 1; i <= n; ++i) P[i] = read();
  for (int i = 1; i <= n; ++i) Q[i] = read();
  for (int i = 1; i <= n; ++i) ret[P[i]] = i;
  for (int i = 2; i <= n; ++i)
    if (ret[Q[i]] < ret[Q[i - 1]])
      C[ret[Q[i]]] += ret[Q[i - 1]] - ret[Q[i]],
          C[ret[Q[i - 1]]] -= ret[Q[i - 1]] - ret[Q[i]];
  int sum = 0;
  for (int i = 1; i <= n; ++i) {
    if (sum)
      ans[i] = ans[i - 1];
    else
      ans[i] = ans[i - 1] + 1;
    sum += C[i];
  }
  if (ans[n] < k)
    puts("NO");
  else {
    puts("YES");
    for (int i = 1; i <= n; ++i) printf("%c", min(ans[ret[i]], k) + 'a' - 1);
    puts("");
  }
  return 0;
}

```