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Exercise

USACO · 2020 · US Open · gold-3

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number-theory · combinatorics

The organizer’s problem statement is available at the official source link.

sample trace

Exercise: number theory walkthrough

Exercise: use the linked editorial?s number theory, combinatorics idea on the published sample, then verify the displayed output.

Published input5 1000000007modelAlgorithm ideaUse divisibility or residue structure to reduce the numeric search to the factors or remainders relevant to the task.task resultExpected output21
  1. 1

    Factor

    Identify the divisor, prime, or modulus conditions that characterize valid values.
  2. 2

    Count

    Combine the valid cases without enumerating the full numeric range.
  3. 3

    Finish

    Apply the task?s bounds and report the resulting count or value.
  4. 4

    Verify the sample

    Use the published sample output to check the result of this idea on the displayed input.
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