#include <bits/stdc++.h>
using namespace std;
int n, k, p[200005], q[200005], d[200005], mn[200005], mx[200005], val[200005];
vector<char> str(200005);
void assign(int x, int v) {
  for (int i = x; i <= n; ++i) val[i] = v;
}
int main() {
  ios::sync_with_stdio(0);
  cin.tie(0);
  cin >> n >> k;
  for (int i = 1; i <= n; ++i) {
    cin >> p[i];
    d[p[i]] = i;
  }
  for (int i = 1; i <= n; ++i) {
    cin >> q[i];
  }
  mn[n + 1] = 200005;
  for (int i = 1; i <= n; ++i) mx[i] = max(mx[i - 1], d[q[i]]);
  for (int i = n; i; --i) mn[i] = min(mn[i + 1], d[q[i]]);
  int i = 1, cnt = 0;
  while (i <= n) {
    if (cnt == 26) break;
    if (mx[i - 1] < mn[i]) assign(i, cnt++);
    ++i;
  }
  if (cnt < k) {
    cout << "NO";
    return 0;
  }
  cout << "YES\n";
  for (int i = 1; i <= n; ++i) str[q[i]] = val[i] + 'a';
  for (int i = 1; i <= n; ++i) cout << str[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>
using namespace std;
int n, k, p[200005], q[200005], d[200005], mn[200005], mx[200005], val[200005];
vector<char> str(200005);
void assign(int x, int v) {
  for (int i = x; i <= n; ++i) val[i] = v;
}
int main() {
  ios::sync_with_stdio(0);
  cin.tie(0);
  cin >> n >> k;
  for (int i = 1; i <= n; ++i) {
    cin >> p[i];
    d[p[i]] = i;
  }
  for (int i = 1; i <= n; ++i) {
    cin >> q[i];
  }
  mn[n + 1] = 200005;
  for (int i = 1; i <= n; ++i) mx[i] = max(mx[i - 1], d[q[i]]);
  for (int i = n; i; --i) mn[i] = min(mn[i + 1], d[q[i]]);
  int i = 1, cnt = 0;
  while (i <= n) {
    if (cnt == 26) break;
    if (mx[i - 1] < mn[i]) assign(i, cnt++);
    ++i;
  }
  if (cnt < k) {
    cout << "NO";
    return 0;
  }
  cout << "YES\n";
  for (int i = 1; i <= n; ++i) str[q[i]] = val[i] + 'a';
  for (int i = 1; i <= n; ++i) cout << str[i];
}

```