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(Any number as sum of powers)
Here is the core idea: any number k can be written as a sum of powers of 2. For example, 13=8+4+1=23+22+20. To jump up 13 steps, you could jump 8 steps, then 4, then 1. That is only 3 jumps instead of 13. This works because every number has at most logk bits in its binary representation.
So you need at most logk jumps. For k up to 105, that is at most 17 jumps per query.
