Unstable String Sort
Description
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: $s[p_i] \le s[p_{i + 1}]$ and $s[q_i] \le s[q_{i + 1}]$. 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.
The first line of the input contains two integers $n$ and $k$ ($1 \le n \le 2 \cdot 10^5, 1 \le k \le 26$) — the length of the string and the number of distinct characters required.
The second line of the input contains $n$ integers $p_1, p_2, \dots, p_n$ ($1 \le p_i \le n$, all $p_i$ are distinct integers from $1$ to $n$) — the permutation $p$.
The third line of the input contains $n$ integers $q_1, q_2, \dots, q_n$ ($1 \le q_i \le n$, all $q_i$ are distinct integers from $1$ to $n$) — the permutation $q$.
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.
Input
The first line of the input contains two integers $n$ and $k$ ($1 \le n \le 2 \cdot 10^5, 1 \le k \le 26$) — the length of the string and the number of distinct characters required.
The second line of the input contains $n$ integers $p_1, p_2, \dots, p_n$ ($1 \le p_i \le n$, all $p_i$ are distinct integers from $1$ to $n$) — the permutation $p$.
The third line of the input contains $n$ integers $q_1, q_2, \dots, q_n$ ($1 \le q_i \le n$, 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.
Samples
3 2
1 2 3
1 3 2
YES
abb