#include <bits/stdc++.h>
const long long mod = 1e9 + 7;
using namespace std;
long long gcd(long long a, long long b) { return b == 0 ? a : gcd(b, a % b); }
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(NULL);
  cout.tie(NULL);
  long long n, k;
  cin >> n >> k;
  vector<long long> a(n + 1), b(n + 1), m(n + 1), m2(n + 1);
  for (long long i = 1; i <= n; i++) {
    cin >> a[i];
    m[a[i]] = i;
  }
  for (long long j = 1; j <= n; j++) {
    cin >> b[j];
    m2[b[j]] = j;
  }
  long long cnt = 0;
  vector<long long> v(n + 1);
  for (long long i = 1; i <= n; i++) {
    long long x = i;
    while (i <= x) {
      v[a[i]] = cnt;
      x = max(x, m[b[i]]);
      x = max(x, m2[a[i]]);
      i++;
    }
    i--;
    cnt++;
  }
  if (cnt < k)
    cout << "NO\n";
  else {
    char c = 'a';
    k--;
    map<long long, char> val;
    for (long long i = 1; i <= n; i++) {
      if (val[v[a[i]]]) continue;
      val[v[a[i]]] = c;
      if (k) {
        k--;
        c++;
      }
    }
    cout << "YES\n";
    for (long long i = 1; i <= n; i++) cout << val[v[i]];
  }
}

### Prompt

Please formulate 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>
const long long mod = 1e9 + 7;
using namespace std;
long long gcd(long long a, long long b) { return b == 0 ? a : gcd(b, a % b); }
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(NULL);
  cout.tie(NULL);
  long long n, k;
  cin >> n >> k;
  vector<long long> a(n + 1), b(n + 1), m(n + 1), m2(n + 1);
  for (long long i = 1; i <= n; i++) {
    cin >> a[i];
    m[a[i]] = i;
  }
  for (long long j = 1; j <= n; j++) {
    cin >> b[j];
    m2[b[j]] = j;
  }
  long long cnt = 0;
  vector<long long> v(n + 1);
  for (long long i = 1; i <= n; i++) {
    long long x = i;
    while (i <= x) {
      v[a[i]] = cnt;
      x = max(x, m[b[i]]);
      x = max(x, m2[a[i]]);
      i++;
    }
    i--;
    cnt++;
  }
  if (cnt < k)
    cout << "NO\n";
  else {
    char c = 'a';
    k--;
    map<long long, char> val;
    for (long long i = 1; i <= n; i++) {
      if (val[v[a[i]]]) continue;
      val[v[a[i]]] = c;
      if (k) {
        k--;
        c++;
      }
    }
    cout << "YES\n";
    for (long long i = 1; i <= n; i++) cout << val[v[i]];
  }
}

```