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Can anyone tell me the logic of the code from AtCoder?

By into_the_world, history, 23 months ago, In English

In yesterday's AtCoder Beginner Contest 280 I didn't able to solve D. Then I was looking for solution and after seeing this submission I was shocked. Can anyone tell me how the logic work for this problem submission?

D — Factorial and Multiple

Submission

Thanks.

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23 months ago, # |
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Here is an alternative approach. Suppose k is 1792. Convert 1792 into 2^8 * 7^1. It is clear that n needs to be at least 7 in order to cover the 7, but what is the n required to provide eight 2s? Let's count: 2 provides one 2. 4 provides two 2s. 6 provides one 2. 8 provides three 2s. Now we have (1+2+1+3 = 7) 2s. We still need one more. 10 provides one 2. Now we have eight 2s. This means n==10 is the max n needed. The other factor found earlier is n==7 but 7 is less than 10. So, the answer is 10.

Edit: Just realized OP was referring to a particular submission.

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