F. Unstable String Sorttime limit per test2 secondsmemory limit per test256 megabytesinputstandard inputoutputstandard outputAuthors 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.InputThe 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.OutputIf 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.ExampleInput
3 2
1 2 3
1 3 2
Output
YES
abb

3 2
1 2 3
1 3 2

YES abb 
['data structures', 'dfs and similar', 'dsu', 'graphs', 'greedy', 'implementation', 'strings', '*2100']