#include <bits/stdc++.h>
const int N = 200010;
int n, k, sa, sb, cnt;
char c[N];
int a[N], b[N], va[N], vb[N], blk[N];
inline int min(int x, int y) { return (x < y ? x : y); }
int main() {
  scanf("%d%d", &n, &k);
  for (int i = 1; i <= n; ++i) scanf("%d", a + i);
  for (int i = 1; i <= n; ++i) scanf("%d", b + i);
  for (int i = 1; i <= n; ++i) {
    vb[a[i]] ? (vb[a[i]] = 0, --sb) : (va[a[i]] = 1, ++sa);
    va[b[i]] ? (va[b[i]] = 0, --sa) : (vb[b[i]] = 1, ++sb);
    sa || sb || (blk[++cnt] = i);
  }
  if (cnt < k) return puts("NO"), 0;
  int l = 1, r = 0;
  char ch;
  for (int i = 1; i <= cnt; ++i, l = r + 1) {
    r = blk[i];
    ch = 'a' + min(i, 26) - 1;
    for (int j = l; j <= r; ++j) c[a[j]] = ch;
  }
  printf("YES\n%s", c + 1);
  return 0;
}

### Prompt

Please formulate 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>
const int N = 200010;
int n, k, sa, sb, cnt;
char c[N];
int a[N], b[N], va[N], vb[N], blk[N];
inline int min(int x, int y) { return (x < y ? x : y); }
int main() {
  scanf("%d%d", &n, &k);
  for (int i = 1; i <= n; ++i) scanf("%d", a + i);
  for (int i = 1; i <= n; ++i) scanf("%d", b + i);
  for (int i = 1; i <= n; ++i) {
    vb[a[i]] ? (vb[a[i]] = 0, --sb) : (va[a[i]] = 1, ++sa);
    va[b[i]] ? (va[b[i]] = 0, --sa) : (vb[b[i]] = 1, ++sb);
    sa || sb || (blk[++cnt] = i);
  }
  if (cnt < k) return puts("NO"), 0;
  int l = 1, r = 0;
  char ch;
  for (int i = 1; i <= cnt; ++i, l = r + 1) {
    r = blk[i];
    ch = 'a' + min(i, 26) - 1;
    for (int j = l; j <= r; ++j) c[a[j]] = ch;
  }
  printf("YES\n%s", c + 1);
  return 0;
}

```