#include <bits/stdc++.h>
using namespace std;
const long long oo = 1e18;
const long long MAXN = 2e5 + 100;
long long N, K;
vector<long long> v1, v2;
long long cont = 0;
long long arr[MAXN];
int32_t main() {
  ios_base::sync_with_stdio(0);
  cin.tie(0);
  cout.tie(0);
  cin >> N >> K;
  K--;
  string cad;
  long long temp = 0;
  for (long long i = 0; i < N; i++) {
    long long n;
    cin >> n;
    v1.push_back(n);
  }
  for (long long i = 0; i < N; i++) {
    long long n;
    cin >> n;
    v2.push_back(n);
  }
  bool band = false;
  for (long long i = 0; i < N; i++) {
    cad += 'a' + temp;
    if (temp == K) band = true;
    if (!arr[v1[i]]) {
      arr[v1[i]]++;
      cont++;
    } else {
      arr[v1[i]]--;
      cont--;
    }
    if (!arr[v2[i]]) {
      arr[v2[i]]++;
      cont++;
    } else {
      arr[v2[i]]--;
      cont--;
    }
    if (!cont) temp++;
    if (temp > K) temp = K;
  }
  if (!band) {
    cout << "NO" << '\n';
  } else {
    cout << "YES" << '\n';
    string temp;
    for (long long i = 0; i < N; i++) temp += " ";
    for (long long i = 0; i < N; i++) {
      temp[v2[i] - 1] = cad[i];
    }
    cout << temp << '\n';
  }
  return 0;
}

### 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 oo = 1e18;
const long long MAXN = 2e5 + 100;
long long N, K;
vector<long long> v1, v2;
long long cont = 0;
long long arr[MAXN];
int32_t main() {
  ios_base::sync_with_stdio(0);
  cin.tie(0);
  cout.tie(0);
  cin >> N >> K;
  K--;
  string cad;
  long long temp = 0;
  for (long long i = 0; i < N; i++) {
    long long n;
    cin >> n;
    v1.push_back(n);
  }
  for (long long i = 0; i < N; i++) {
    long long n;
    cin >> n;
    v2.push_back(n);
  }
  bool band = false;
  for (long long i = 0; i < N; i++) {
    cad += 'a' + temp;
    if (temp == K) band = true;
    if (!arr[v1[i]]) {
      arr[v1[i]]++;
      cont++;
    } else {
      arr[v1[i]]--;
      cont--;
    }
    if (!arr[v2[i]]) {
      arr[v2[i]]++;
      cont++;
    } else {
      arr[v2[i]]--;
      cont--;
    }
    if (!cont) temp++;
    if (temp > K) temp = K;
  }
  if (!band) {
    cout << "NO" << '\n';
  } else {
    cout << "YES" << '\n';
    string temp;
    for (long long i = 0; i < N; i++) temp += " ";
    for (long long i = 0; i < N; i++) {
      temp[v2[i] - 1] = cad[i];
    }
    cout << temp << '\n';
  }
  return 0;
}

```