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≤109, 26≤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.