F. AB Treetime limit per test2 secondsmemory limit per test256 megabytesinputstandard inputoutputstandard outputKilani and Abd are neighbors for 3000 years, but then the day came and Kilani decided to move to another house. As a farewell gift, Kilani is going to challenge Abd with a problem written by their other neighbor with the same name Abd.  The problem is:You are given a connected tree rooted at node 1.You should assign a character a or b to every node in the tree so that the total number of a's is equal to x and the total number of b's is equal to n - x.Let's define a string for each node v of the tree as follows:   if v is root then the string is just one character assigned to v:  otherwise, let's take a string defined for the v's parent p_v and add to the end of it a character assigned to v. You should assign every node a character in a way that minimizes the number of distinct strings among the strings of all nodes.InputThe first line contains two integers n and x (1 \leq n \leq 10^5; 0 \leq x \leq n) — the number of vertices in the tree the number of a's.The second line contains n - 1 integers p_2, p_3, \dots, p_{n} (1 \leq p_i \leq n; p_i \neq i), where p_i is the parent of node i.It is guaranteed that the input describes a connected tree.OutputIn the first line, print the minimum possible total number of distinct strings.In the second line, print n characters, where all characters are either a or b and the i-th character is the character assigned to the i-th node.Make sure that the total number of a's is equal to x and the total number of b's is equal to n - x.If there is more than one answer you can print any of them.ExampleInput
9 3
1 2 2 4 4 4 3 1
Output
4
aabbbbbba
NoteThe tree from the sample is shown below:  The tree after assigning characters to every node (according to the output) is the following:  Strings for all nodes are the following:   string of node 1 is: a  string of node 2 is: aa  string of node 3 is: aab  string of node 4 is: aab  string of node 5 is: aabb  string of node 6 is: aabb  string of node 7 is: aabb  string of node 8 is: aabb  string of node 9 is: aa The set of unique strings is \{\text{a}, \text{aa}, \text{aab}, \text{aabb}\}, so the number of distinct strings is 4.
9 3
1 2 2 4 4 4 3 1

4 aabbbbbba 
['dp', 'greedy', 'trees', '*3100']