Aligned Typesetting

In this problem, a sentence with $n$ words is a sequence of $n$ non-empty strings $[w_1, w_2, \ldots, w_n]$. Given a sentence, a valid typesetting of length $L$ is a string of length exactly $L$ formed by concatenating all the words in the sentence in order and inserting a positive number of spaces between each adjacent pair of words.

An aligned typesetting is a valid typesetting in which the number of spaces between each adjacent pair of words is the same.

For example, given the sentence $[\text{harry}, \text{ron}, \text{hermione}]$ and using _ to indicate a space:

• the string __harry_ronhermione is not a valid typesetting;
• the string harry_ron_____hermione is a valid typesetting of length 22, but it is not an aligned typesetting;
• the string harry___ron___hermione is an aligned typesetting of length 22.

Darcy was given a sentence of $n$ words and the desired length of typesetting $L$. Can you help him figure out whether an aligned typesetting of the desired length exists?

The first line contains two integers $n$ ($1 \le n \le 10^6$), the number of words, and $L$ ($0 \le L \le 10^6$), the desired length of typesetting.

The next $n$ lines describe the words. Each of these lines contains a single string $w_i$, the $i$-th word in the sentence. The word contains only lowercase letters and has length between 1 and $10^6$.

The total length of all the words in the sentence is at most $10^6$.

Display whether the sentence has an aligned typesetting of the given length $L$.