#include <bits/stdc++.h>
using namespace std;
const long long inf = 1e18;
const int mod = 1e9 + 7;
const int N = 1e7 + 1;
const int L = 29;
void solve() {
  int n, k;
  cin >> n >> k;
  vector<int> p(n + 1), ppos(n + 1), q(n + 1), qpos(n + 1), ans(n + 1, -1);
  for (int i = 1; i <= n; i++) {
    cin >> p[i];
    ppos[p[i]] = i;
  }
  for (int i = 1; i <= n; i++) {
    cin >> q[i];
    qpos[q[i]] = i;
  }
  int ptr = 1, curr = 0;
  while (ptr <= n) {
    int last = ppos[p[ptr]];
    while (ptr <= last) {
      last = max({last, ppos[p[ptr]], qpos[p[ptr]]});
      ans[p[ptr]] = curr;
      ans[q[ptr]] = curr;
      ptr++;
    }
    curr++;
  }
  if (curr < k) {
    cout << "NO\n";
    return;
  }
  cout << "YES\n";
  for (int i = 1; i <= n; i++) {
    char alpa = min(25, ans[i]) + 'a';
    cout << alpa;
  }
  cout << "\n";
}
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(NULL);
  cout.tie(NULL);
  ;
  std::cout << std::fixed << std::setprecision(20);
  ;
  int t = 1;
  for (int i = 1; i <= t; i++) {
    solve();
  }
}

### Prompt

Generate 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;
const long long inf = 1e18;
const int mod = 1e9 + 7;
const int N = 1e7 + 1;
const int L = 29;
void solve() {
  int n, k;
  cin >> n >> k;
  vector<int> p(n + 1), ppos(n + 1), q(n + 1), qpos(n + 1), ans(n + 1, -1);
  for (int i = 1; i <= n; i++) {
    cin >> p[i];
    ppos[p[i]] = i;
  }
  for (int i = 1; i <= n; i++) {
    cin >> q[i];
    qpos[q[i]] = i;
  }
  int ptr = 1, curr = 0;
  while (ptr <= n) {
    int last = ppos[p[ptr]];
    while (ptr <= last) {
      last = max({last, ppos[p[ptr]], qpos[p[ptr]]});
      ans[p[ptr]] = curr;
      ans[q[ptr]] = curr;
      ptr++;
    }
    curr++;
  }
  if (curr < k) {
    cout << "NO\n";
    return;
  }
  cout << "YES\n";
  for (int i = 1; i <= n; i++) {
    char alpa = min(25, ans[i]) + 'a';
    cout << alpa;
  }
  cout << "\n";
}
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(NULL);
  cout.tie(NULL);
  ;
  std::cout << std::fixed << std::setprecision(20);
  ;
  int t = 1;
  for (int i = 1; i <= t; i++) {
    solve();
  }
}

```