#include <bits/stdc++.h>
using namespace std;
long long read() {
  long long sum = 0;
  char c = getchar();
  bool f = 0;
  while (c < '0' || c > '9') {
    if (c == '-') f = 1;
    c = getchar();
  }
  while (c >= '0' && c <= '9') {
    sum = sum * 10 + c - '0';
    c = getchar();
  }
  if (f) return -sum;
  return sum;
}
const int N = 200005;
int n, m, P[N], Q[N], pos[N], L[N], bel[N];
char ans[N];
int main() {
  int i, j, k;
  n = read();
  m = read();
  for (i = 1; i <= n; i++) P[i] = read(), pos[P[i]] = i;
  for (i = 1; i <= n; i++) Q[i] = read();
  for (k = n, i = n; i >= 1; i--) j = pos[Q[i]], k = min(k, j), L[j] = k;
  for (j = 1, k = n, i = n; i >= 1; i--) {
    k = min(k, L[i]);
    bel[i] = j;
    if (k == i) j++;
  }
  if (bel[1] < m) {
    puts("NO");
    return 0;
  }
  puts("YES");
  for (j = -1, i = 1; i <= n; i++) {
    if (bel[i] != bel[i - 1]) j++;
    ans[P[i]] = 'a' + min(25, j);
  }
  for (i = 1; i <= n; i++) printf("%c", ans[i]);
  return 0;
}

### Prompt

Create a solution in CPP for 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 read() {
  long long sum = 0;
  char c = getchar();
  bool f = 0;
  while (c < '0' || c > '9') {
    if (c == '-') f = 1;
    c = getchar();
  }
  while (c >= '0' && c <= '9') {
    sum = sum * 10 + c - '0';
    c = getchar();
  }
  if (f) return -sum;
  return sum;
}
const int N = 200005;
int n, m, P[N], Q[N], pos[N], L[N], bel[N];
char ans[N];
int main() {
  int i, j, k;
  n = read();
  m = read();
  for (i = 1; i <= n; i++) P[i] = read(), pos[P[i]] = i;
  for (i = 1; i <= n; i++) Q[i] = read();
  for (k = n, i = n; i >= 1; i--) j = pos[Q[i]], k = min(k, j), L[j] = k;
  for (j = 1, k = n, i = n; i >= 1; i--) {
    k = min(k, L[i]);
    bel[i] = j;
    if (k == i) j++;
  }
  if (bel[1] < m) {
    puts("NO");
    return 0;
  }
  puts("YES");
  for (j = -1, i = 1; i <= n; i++) {
    if (bel[i] != bel[i - 1]) j++;
    ans[P[i]] = 'a' + min(25, j);
  }
  for (i = 1; i <= n; i++) printf("%c", ans[i]);
  return 0;
}

```