I think this is (so far) the most efficient solution for large m. It requires at most log(4*m)/log(5) iterations; while the smaller sized solutions that have been suggested require at least 0.8*m iterations (or a very large array). For example, for m = 10^5, this solution takes at most 8 iterations while the other solutions of smaller size require at least 80,000 iterations.
Flip the main diagonal of a matrix
Is the Point in a Circle?
Convert from Base 10 to base 5
Divisible by 3
Number of paths on a n-dimensional grid
Under the sea: Snell's law & total internal reflection
Number of paths on a 3d grid
The last non-zero digit of a factorial
Fractal: area and perimeter of Koch snowflake
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