#include <bits/stdc++.h>
using namespace std;
long long n, k;
long long t[200002], v[200002];
set<long long> a, b;
vector<long long> w;
int main() {
  cin >> n >> k;
  w.push_back(0);
  k++;
  for (int i = 0; i < n; i++) cin >> t[i];
  for (int i = 0; i < n; i++) cin >> v[i];
  for (int i = 0; i < n; i++) {
    if (a.count(v[i]))
      a.erase(v[i]);
    else
      b.insert(v[i]);
    if (b.count(t[i]))
      b.erase(t[i]);
    else
      a.insert(t[i]);
    if (a.empty() && b.empty()) w.push_back(i + 1);
    if (w.size() == k) break;
  }
  w[k - 1] = n;
  if (w.size() < k) return cout << "NO", 0;
  cout << "YES\n";
  string res(n, ' ');
  for (int i = 1; i < k; i++)
    for (int j = w[i - 1]; j < w[i]; j++) res[t[j] - 1] = 'a' + i - 1;
  cout << res;
  return 0;
}

### Prompt

In Cpp, your task is to solve 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;
long long n, k;
long long t[200002], v[200002];
set<long long> a, b;
vector<long long> w;
int main() {
  cin >> n >> k;
  w.push_back(0);
  k++;
  for (int i = 0; i < n; i++) cin >> t[i];
  for (int i = 0; i < n; i++) cin >> v[i];
  for (int i = 0; i < n; i++) {
    if (a.count(v[i]))
      a.erase(v[i]);
    else
      b.insert(v[i]);
    if (b.count(t[i]))
      b.erase(t[i]);
    else
      a.insert(t[i]);
    if (a.empty() && b.empty()) w.push_back(i + 1);
    if (w.size() == k) break;
  }
  w[k - 1] = n;
  if (w.size() < k) return cout << "NO", 0;
  cout << "YES\n";
  string res(n, ' ');
  for (int i = 1; i < k; i++)
    for (int j = w[i - 1]; j < w[i]; j++) res[t[j] - 1] = 'a' + i - 1;
  cout << res;
  return 0;
}

```