Hash

A HAIKU is a string that consists of at most 50 lowercase English letters. For a HAIKU $s$, you can compute the hash $h$ as follows:

h = 0
for i=0,...|s|-1
    h = (h * a + (s[i] - 'a' + 1)) % b

You are given two integers $a$ and $b$. Construct 100 distinct HAIKUs that have the same hash.

You are given two space-separated integers $a$ and $b$ ($b \le 10^9$, $26 \le a < b$).

Print 100 HAIKUs with the same hash, one per line.

Several HAIKUs are omitted in the printed version of statements; the full version is published in the contest system.