#include <bits/stdc++.h>
using namespace std;
template <class T>
bool uin(T &a, T b) {
  return a > b ? (a = b, true) : false;
}
template <class T>
bool uax(T &a, T b) {
  return a < b ? (a = b, true) : false;
}
int main() {
  long long n, k, cn = 0;
  cin >> n >> k;
  vector<long long> v1, v2, v;
  for (long long i = 0; i < (long long)(n); ++i) {
    long long a;
    cin >> a;
    v1.push_back(a);
  }
  for (long long i = 0; i < (long long)(n); ++i) {
    long long a;
    cin >> a;
    v2.push_back(a);
  }
  set<long long> s1, s2;
  for (long long i = 0; i < n; i++) {
    if (s1.count(v2[i]))
      s1.erase(v2[i]);
    else
      s2.insert(v2[i]);
    if (s2.count(v1[i]))
      s2.erase(v1[i]);
    else
      s1.insert(v1[i]);
    if (s1.empty() && s2.empty()) {
      v.push_back(i);
      cn++;
    }
  }
  if (cn < k) {
    cout << "NO\n";
    return 0;
  }
  cout << "YES\n";
  string ss(n, ' ');
  long long j = 0, c = 0;
  for (long long i = 0; i < cn; i++) {
    while (j <= v[i]) {
      char ch = 'a' + min(c, (long long)25);
      ss[v1[j] - 1] = ch;
      j++;
    }
    c++;
  }
  cout << ss;
}

### Prompt

Your challenge is to write 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;
template <class T>
bool uin(T &a, T b) {
  return a > b ? (a = b, true) : false;
}
template <class T>
bool uax(T &a, T b) {
  return a < b ? (a = b, true) : false;
}
int main() {
  long long n, k, cn = 0;
  cin >> n >> k;
  vector<long long> v1, v2, v;
  for (long long i = 0; i < (long long)(n); ++i) {
    long long a;
    cin >> a;
    v1.push_back(a);
  }
  for (long long i = 0; i < (long long)(n); ++i) {
    long long a;
    cin >> a;
    v2.push_back(a);
  }
  set<long long> s1, s2;
  for (long long i = 0; i < n; i++) {
    if (s1.count(v2[i]))
      s1.erase(v2[i]);
    else
      s2.insert(v2[i]);
    if (s2.count(v1[i]))
      s2.erase(v1[i]);
    else
      s1.insert(v1[i]);
    if (s1.empty() && s2.empty()) {
      v.push_back(i);
      cn++;
    }
  }
  if (cn < k) {
    cout << "NO\n";
    return 0;
  }
  cout << "YES\n";
  string ss(n, ' ');
  long long j = 0, c = 0;
  for (long long i = 0; i < cn; i++) {
    while (j <= v[i]) {
      char ch = 'a' + min(c, (long long)25);
      ss[v1[j] - 1] = ch;
      j++;
    }
    c++;
  }
  cout << ss;
}

```