Carving Tiny Fractions

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Points: 25 (partial)
Time limit: 2.0s
Memory limit: 256M

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Problem type

You are walking alone in the woods one night when out of the corner of your eye you see something moving. You turn and see a Large Russian Bear moving towards you.

It turns out this bear is writing a contest problem, and requires a list of Egyptian Fractions (reciprocals of positive integers) whose sum is extremely close to, but not exactly, equal to 1.

Input Format

You are given a single integer v{1,1}

Output Format

On the first line, output a single integer n, 1n1000.

On the second line, output n integers, 1xi1018.

Scoring

If your output is improperly formatted you will receive 0 points.

Otherwise, let S=i=1n1xi. If v=1 then you must have S>1 or you will receive 0 points. Similarly, if v=1 then you must have S<1 or you will recieve 0 points.

If you have a valid submission, then you receive points according to the following table, where T=log10(|1S|)

TScore
T<300
30T<503(T30)
50T<10060+2(T50)5
100T<50080+T10020
T500100

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