#include <bits/stdc++.h>
using namespace std;
const int maxn = 3e6 + 555;
int p[maxn];
int ppos[maxn];
int q[maxn];
int qpos[maxn];
char ans[maxn];
void solve() {
  int n, m;
  scanf("%d %d", &n, &m);
  for (int i = 1; i <= n; i++) {
    scanf("%d", &p[i]);
    ppos[p[i]] = i;
  }
  for (int i = 1; i <= n; i++) {
    scanf("%d", &q[i]);
    qpos[q[i]] = i;
  }
  vector<pair<int, int> > v;
  int L = 1;
  int r = 1;
  for (int i = 1; i <= n; i++) {
    r = max(r, qpos[p[i]]);
    r = max(r, ppos[q[i]]);
    if (r == i) {
      v.push_back(make_pair(L, r));
      L = i + 1;
      r = i + 1;
    }
  }
  if (int(v.size()) < m)
    puts("NO");
  else {
    for (int i = 0; i < v.size(); i++) {
      for (int j = v[i].first; j <= v[i].second; j++) {
        ans[p[j]] = min((int)'z', 'a' + i);
      }
    }
    puts("YES");
    for (int i = 1; i <= n; i++) printf("%c", ans[i]);
  }
}
signed main() { solve(); }

### Prompt

Your task is to create 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 = 3e6 + 555;
int p[maxn];
int ppos[maxn];
int q[maxn];
int qpos[maxn];
char ans[maxn];
void solve() {
  int n, m;
  scanf("%d %d", &n, &m);
  for (int i = 1; i <= n; i++) {
    scanf("%d", &p[i]);
    ppos[p[i]] = i;
  }
  for (int i = 1; i <= n; i++) {
    scanf("%d", &q[i]);
    qpos[q[i]] = i;
  }
  vector<pair<int, int> > v;
  int L = 1;
  int r = 1;
  for (int i = 1; i <= n; i++) {
    r = max(r, qpos[p[i]]);
    r = max(r, ppos[q[i]]);
    if (r == i) {
      v.push_back(make_pair(L, r));
      L = i + 1;
      r = i + 1;
    }
  }
  if (int(v.size()) < m)
    puts("NO");
  else {
    for (int i = 0; i < v.size(); i++) {
      for (int j = v[i].first; j <= v[i].second; j++) {
        ans[p[j]] = min((int)'z', 'a' + i);
      }
    }
    puts("YES");
    for (int i = 1; i <= n; i++) printf("%c", ans[i]);
  }
}
signed main() { solve(); }

```