B"Kilani 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: You should assign every node a character in a way that minimizes the number of distinct strings among the strings of all nodes. The first line contains two integers n and x ( 1 <= q n <= q 10^5 ; 0 <= q x <= q n ) -- the number of vertices in the tree the number of a's. The second line contains n - 1 integers p_2, p_3, ... , p_{n} ( 1 <= q p_i <= q n ; p_i neq i ), where p_i is the parent of node i . It is guaranteed that the input describes a connected tree. In 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. The 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: The set of unique strings is { text{a}, text{aa}, text{aab}, text{aabb} } , so the number of distinct strings is 4 . "...