http://codeforces.net/blog/entry/14256 in D2-C.

I understood that for each x there is exactly 1 k. But how can I prove that for each K in [1, a] there always exists nice numbers for all remainders [1, b-1]? For instance if a = 3, b = 5. How to be so sure that for Each k {1, 2, 3} there will always be nice numbers with remainder values [1, b-1]