#include <bits/stdc++.h>
using namespace std;
const int INF = 0x3f3f3f3f;
const long long LINF = 0x3f3f3f3f3f3f3f3f;
const int MOD = (int)1e9 + 7;
const int N = (int)2e5 + 7;
int p[N], q[N], pre[N], pos[N];
char ans[N], c[N];
int main() {
  int n, k;
  scanf("%d%d", &n, &k);
  for (int i = (1); i < (n + 1); ++i) scanf("%d", &p[i]);
  for (int i = (1); i < (n + 1); ++i) scanf("%d", &q[i]);
  for (int i = (1); i < (n + 1); ++i) pos[p[i]] = i;
  for (int i = (1); i < (n); ++i) {
    pre[pos[q[i]]] = pos[q[i + 1]];
  }
  pre[pos[q[n]]] = n + 1;
  int mn = n + 1;
  c[n + 1] = 'z' + 1;
  for (int i = (n + 1) - 1; i >= (1); --i) {
    if (i >= mn)
      c[i] = c[i + 1];
    else
      c[i] = max((int)'a', c[i + 1] - 1);
    mn = min(mn, pre[i]);
  }
  for (int i = (1); i < (n + 1); ++i) {
    ans[p[i]] = c[i];
  }
  if ('z' - c[1] + 1 >= k) {
    printf("YES\n");
    printf("%s\n", ans + 1);
  } else {
    printf("NO\n");
  }
  return 0;
}

### Prompt

Please create a solution in cpp 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 INF = 0x3f3f3f3f;
const long long LINF = 0x3f3f3f3f3f3f3f3f;
const int MOD = (int)1e9 + 7;
const int N = (int)2e5 + 7;
int p[N], q[N], pre[N], pos[N];
char ans[N], c[N];
int main() {
  int n, k;
  scanf("%d%d", &n, &k);
  for (int i = (1); i < (n + 1); ++i) scanf("%d", &p[i]);
  for (int i = (1); i < (n + 1); ++i) scanf("%d", &q[i]);
  for (int i = (1); i < (n + 1); ++i) pos[p[i]] = i;
  for (int i = (1); i < (n); ++i) {
    pre[pos[q[i]]] = pos[q[i + 1]];
  }
  pre[pos[q[n]]] = n + 1;
  int mn = n + 1;
  c[n + 1] = 'z' + 1;
  for (int i = (n + 1) - 1; i >= (1); --i) {
    if (i >= mn)
      c[i] = c[i + 1];
    else
      c[i] = max((int)'a', c[i + 1] - 1);
    mn = min(mn, pre[i]);
  }
  for (int i = (1); i < (n + 1); ++i) {
    ans[p[i]] = c[i];
  }
  if ('z' - c[1] + 1 >= k) {
    printf("YES\n");
    printf("%s\n", ans + 1);
  } else {
    printf("NO\n");
  }
  return 0;
}

```