RU-ALLRUSSIAN 1978 Problem 5

Two players play a game. There is a heap of m tokens and a heap of $\mathrm{n}< \mathrm{m}$ tokens. Each player in turn takes one or more tokens from the heap which is larger. The number he takes must be a multiple of the number in the smaller heap. For example, if the heaps are 15 and 4, the first player may take 4, 8 or 12 from the larger heap. The first player to clear a heap wins. Show that if $\mathrm{m} > 2\mathrm{n}$ , then the first player can always win. Find all k such that if $\mathrm{m} > \mathrm{k}\mathrm{n}$ , then the first player can always win.