#include <bits/stdc++.h>
using namespace std;
long long n, d, a[200069], pst[200069], pr[200069], z[200069];
long long fd(long long x) {
  if (pr[x] != x) {
    pr[x] = fd(pr[x]);
  }
  return pr[x];
}
int main() {
  long long i, k, l = -1, j, c = 0;
  scanf("%lld%lld", &n, &d);
  for (i = 1; i <= n; i++) {
    scanf("%lld", a + i);
    pst[a[i]] = i;
    pr[i] = i;
  }
  for (i = 1; i <= n; i++) {
    scanf("%lld", &k);
    if (l != -1) {
      for (j = pst[l]; j > pst[k]; j = pst[pr[a[j - 1]]]) {
        pr[fd(a[j])] = fd(a[j - 1]);
      }
    }
    l = k;
  }
  for (i = 1; i <= n; i++) {
    if (fd(a[i]) == a[i]) {
      c++;
    }
    z[a[i]] = c;
  }
  if (c < d) {
    printf("NO\n");
  } else {
    printf("YES\n");
    for (i = 1; i <= n; i++) {
      printf("%c", (char)min(z[i], (long long)26) - 1 + 'a');
    }
    printf("\n");
  }
}

### Prompt

Generate 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;
long long n, d, a[200069], pst[200069], pr[200069], z[200069];
long long fd(long long x) {
  if (pr[x] != x) {
    pr[x] = fd(pr[x]);
  }
  return pr[x];
}
int main() {
  long long i, k, l = -1, j, c = 0;
  scanf("%lld%lld", &n, &d);
  for (i = 1; i <= n; i++) {
    scanf("%lld", a + i);
    pst[a[i]] = i;
    pr[i] = i;
  }
  for (i = 1; i <= n; i++) {
    scanf("%lld", &k);
    if (l != -1) {
      for (j = pst[l]; j > pst[k]; j = pst[pr[a[j - 1]]]) {
        pr[fd(a[j])] = fd(a[j - 1]);
      }
    }
    l = k;
  }
  for (i = 1; i <= n; i++) {
    if (fd(a[i]) == a[i]) {
      c++;
    }
    z[a[i]] = c;
  }
  if (c < d) {
    printf("NO\n");
  } else {
    printf("YES\n");
    for (i = 1; i <= n; i++) {
      printf("%c", (char)min(z[i], (long long)26) - 1 + 'a');
    }
    printf("\n");
  }
}

```