#include <bits/stdc++.h>
using namespace std;
const int maxN = 2e5 + 1;
int n, k;
int p[maxN], q[maxN];
int mapp[maxN], Right[maxN];
int res[maxN], finalres[maxN];
void ReadInput() {
  cin >> n >> k;
  for (int i = 1; i <= n; ++i) {
    cin >> p[i];
    mapp[p[i]] = i;
  }
  for (int i = 1; i <= n; ++i) cin >> q[i];
}
void Solve() {
  fill(Right + 1, Right + n + 1, 0);
  for (int i = 1; i < n; ++i) {
    int a = mapp[q[i]], b = mapp[q[i + 1]];
    if (a > b) Right[b] = a;
  }
  int cnt = 0, maxR = -1;
  for (int i = 1; i <= n; ++i) {
    if (i > maxR) ++cnt;
    if (Right[i] > maxR) maxR = Right[i];
    res[i] = cnt;
  }
  if (cnt < k) {
    cout << "NO";
    return;
  }
  cout << "YES\n";
  for (int i = 1; i <= n; ++i) finalres[p[i]] = min(res[i], k);
  for (int i = 1; i <= n; ++i) cout << (char)(finalres[i] - 1 + 'a');
}
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(nullptr);
  ReadInput();
  Solve();
}

### 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;
const int maxN = 2e5 + 1;
int n, k;
int p[maxN], q[maxN];
int mapp[maxN], Right[maxN];
int res[maxN], finalres[maxN];
void ReadInput() {
  cin >> n >> k;
  for (int i = 1; i <= n; ++i) {
    cin >> p[i];
    mapp[p[i]] = i;
  }
  for (int i = 1; i <= n; ++i) cin >> q[i];
}
void Solve() {
  fill(Right + 1, Right + n + 1, 0);
  for (int i = 1; i < n; ++i) {
    int a = mapp[q[i]], b = mapp[q[i + 1]];
    if (a > b) Right[b] = a;
  }
  int cnt = 0, maxR = -1;
  for (int i = 1; i <= n; ++i) {
    if (i > maxR) ++cnt;
    if (Right[i] > maxR) maxR = Right[i];
    res[i] = cnt;
  }
  if (cnt < k) {
    cout << "NO";
    return;
  }
  cout << "YES\n";
  for (int i = 1; i <= n; ++i) finalres[p[i]] = min(res[i], k);
  for (int i = 1; i <= n; ++i) cout << (char)(finalres[i] - 1 + 'a');
}
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(nullptr);
  ReadInput();
  Solve();
}

```