Count Palindromic Word Sequences

A palindrome is a string that reads the same from left to right and from right to left. In this problem, all spaces are ignored when deciding whether a string is a palindrome.

You are given N distinct words. You may choose words and arrange them in order to make a string S. A word may be used multiple times, and some words may be unused. Exactly one space must be placed between adjacent words, including between two equal consecutive words. S may not start or end with a space.

Count the strings S that can be made this way such that, after ignoring spaces, S is a palindrome and the total length of S is at most K. Spaces between words are included in the length. The empty string is not counted.

The first line contains the number of words N and the length limit K. Both are positive integers, with N <= 50 and K <= 100.

Each of the next N lines contains one word. Every word consists only of lowercase English letters, has length at most 15, and no word appears more than once.

Print the number of valid strings S, modulo 835454957.

In the first public test case, exactly 5 strings satisfy the conditions within the length limit.