Here's the problem (IMO 2013 Problem 1): Assume that k and n are two positive integers. Prove that there exist positive integers m1, ... , mk such that 
Think:
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Here's a generalization, which is much easier once you've found the segtree solution to the above problem. Assume that k and n are two positive integers. Prove that there exist positive integers m1, ... , mk such that
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is an integer and l < = log2(k) + 1.
