#include <bits/stdc++.h>
using namespace std;
const long long INF = 1e9 + 8;
const long long maxn = 1e6 + 5;
const long long mo_num = 1e9 + 7;
long long n, m, a[maxn], b[maxn], ans;
set<long long> qian, hou;
vector<long long> Ans;
int32_t main() {
  ios::sync_with_stdio(0);
  cin.tie(0);
  cout.tie(0);
  cin >> n >> m;
  for (long long i = 1; i <= n; i++) cin >> a[i];
  for (long long i = 1; i <= n; i++) cin >> b[i];
  for (long long i = 1; i <= n; i++) {
    if (hou.count(a[i])) {
      hou.erase(a[i]);
    } else
      qian.insert(a[i]);
    if (qian.count(b[i])) {
      qian.erase(b[i]);
    } else
      hou.insert(b[i]);
    if (qian.empty() && hou.empty()) Ans.push_back(i);
  }
  if (Ans.size() < m) {
    cout << "NO";
  } else {
    string t = string(n + 2, ' ');
    long long cnt = 0, have = 1;
    for (auto i : Ans) {
      char now = min('a' + cnt, (long long)'z');
      while (have <= i) {
        t[a[have++]] = (char)now;
      }
      cnt++;
    }
    cout << ("YES") << '\n';
    for (long long i = 1; i <= n; i++) cout << t[i];
    cout << '\n';
  }
  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;
const long long INF = 1e9 + 8;
const long long maxn = 1e6 + 5;
const long long mo_num = 1e9 + 7;
long long n, m, a[maxn], b[maxn], ans;
set<long long> qian, hou;
vector<long long> Ans;
int32_t main() {
  ios::sync_with_stdio(0);
  cin.tie(0);
  cout.tie(0);
  cin >> n >> m;
  for (long long i = 1; i <= n; i++) cin >> a[i];
  for (long long i = 1; i <= n; i++) cin >> b[i];
  for (long long i = 1; i <= n; i++) {
    if (hou.count(a[i])) {
      hou.erase(a[i]);
    } else
      qian.insert(a[i]);
    if (qian.count(b[i])) {
      qian.erase(b[i]);
    } else
      hou.insert(b[i]);
    if (qian.empty() && hou.empty()) Ans.push_back(i);
  }
  if (Ans.size() < m) {
    cout << "NO";
  } else {
    string t = string(n + 2, ' ');
    long long cnt = 0, have = 1;
    for (auto i : Ans) {
      char now = min('a' + cnt, (long long)'z');
      while (have <= i) {
        t[a[have++]] = (char)now;
      }
      cnt++;
    }
    cout << ("YES") << '\n';
    for (long long i = 1; i <= n; i++) cout << t[i];
    cout << '\n';
  }
  return 0;
}

```