#include <bits/stdc++.h>
using namespace std;
int N, K;
char ans[200020];
struct Node {
  int idx;
  int p1;
  int p2;
} nodes[200020];
bool cmp1(Node x, Node y) { return x.p1 < y.p1; }
int main() {
  cin >> N >> K;
  int temp;
  for (int i = 1; i <= N; i++) {
    nodes[i].idx = i;
    cin >> temp;
    nodes[temp].p1 = i;
  }
  for (int i = 1; i <= N; i++) {
    cin >> temp;
    nodes[temp].p2 = i;
  }
  sort(nodes + 1, nodes + N + 1, cmp1);
  int cnt = 0, m = 0;
  for (int i = 1; i <= N; i++) {
    m = max(nodes[i].p2, m);
    ans[nodes[i].idx] = 'a' + min(K - 1, cnt);
    ;
    if (m == i) {
      cnt++;
    }
  }
  if (cnt >= K) {
    cout << "YES" << endl;
    for (int i = 1; i <= N; i++) cout << ans[i];
  } else {
    cout << "NO" << endl;
  }
}

### Prompt

Please formulate 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;
int N, K;
char ans[200020];
struct Node {
  int idx;
  int p1;
  int p2;
} nodes[200020];
bool cmp1(Node x, Node y) { return x.p1 < y.p1; }
int main() {
  cin >> N >> K;
  int temp;
  for (int i = 1; i <= N; i++) {
    nodes[i].idx = i;
    cin >> temp;
    nodes[temp].p1 = i;
  }
  for (int i = 1; i <= N; i++) {
    cin >> temp;
    nodes[temp].p2 = i;
  }
  sort(nodes + 1, nodes + N + 1, cmp1);
  int cnt = 0, m = 0;
  for (int i = 1; i <= N; i++) {
    m = max(nodes[i].p2, m);
    ans[nodes[i].idx] = 'a' + min(K - 1, cnt);
    ;
    if (m == i) {
      cnt++;
    }
  }
  if (cnt >= K) {
    cout << "YES" << endl;
    for (int i = 1; i <= N; i++) cout << ans[i];
  } else {
    cout << "NO" << endl;
  }
}

```