#include <bits/stdc++.h>
using namespace std;
const int N = 2e5 + 5;
int n, k, p[2][N], vis[N], cnt, ans[N];
vector<int> go[N], to[N];
void read_input() {
  cin >> n >> k;
  for (int i = 0; i < 2; i++)
    for (int j = 0; j < n; j++) {
      cin >> p[i][j];
      p[i][j]--;
      if (j > 0) {
        go[p[i][j]].push_back(p[i][j - 1]);
        to[p[i][j - 1]].push_back(p[i][j]);
      }
    }
}
void dfs(int u, vector<int> *adj, vector<int> &vec) {
  vis[u] = 1;
  for (int v : adj[u])
    if (vis[v] == false) dfs(v, adj, vec);
  vec.push_back(u);
}
void kosaraju() {
  vector<int> ord;
  for (int u = 0; u < n; u++)
    if (vis[u] == false) dfs(u, go, ord);
  memset(vis, 0, sizeof vis);
  reverse(ord.begin(), ord.end());
  for (int u : ord)
    if (vis[u] == false) {
      vector<int> comp;
      dfs(u, to, comp);
      for (int u : comp) ans[u] = cnt;
      cnt++;
    }
}
void write_output() {
  if (cnt < k) {
    cout << "NO" << endl;
    return;
  }
  cout << "YES" << endl;
  for (int i = 0; i < n; i++) cout << char(min(cnt - ans[i], k) - 1 + 'a');
  cout << endl;
}
int main() {
  ios_base::sync_with_stdio(0), cin.tie(0);
  read_input(), kosaraju(), write_output();
}

### 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;
const int N = 2e5 + 5;
int n, k, p[2][N], vis[N], cnt, ans[N];
vector<int> go[N], to[N];
void read_input() {
  cin >> n >> k;
  for (int i = 0; i < 2; i++)
    for (int j = 0; j < n; j++) {
      cin >> p[i][j];
      p[i][j]--;
      if (j > 0) {
        go[p[i][j]].push_back(p[i][j - 1]);
        to[p[i][j - 1]].push_back(p[i][j]);
      }
    }
}
void dfs(int u, vector<int> *adj, vector<int> &vec) {
  vis[u] = 1;
  for (int v : adj[u])
    if (vis[v] == false) dfs(v, adj, vec);
  vec.push_back(u);
}
void kosaraju() {
  vector<int> ord;
  for (int u = 0; u < n; u++)
    if (vis[u] == false) dfs(u, go, ord);
  memset(vis, 0, sizeof vis);
  reverse(ord.begin(), ord.end());
  for (int u : ord)
    if (vis[u] == false) {
      vector<int> comp;
      dfs(u, to, comp);
      for (int u : comp) ans[u] = cnt;
      cnt++;
    }
}
void write_output() {
  if (cnt < k) {
    cout << "NO" << endl;
    return;
  }
  cout << "YES" << endl;
  for (int i = 0; i < n; i++) cout << char(min(cnt - ans[i], k) - 1 + 'a');
  cout << endl;
}
int main() {
  ios_base::sync_with_stdio(0), cin.tie(0);
  read_input(), kosaraju(), write_output();
}

```