Stupid people P45462


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The current pandemic has proven (once again) how many stupid people there are. Consider, for instance, the use of face masks, under this simplified model: The length of a face is ℓ, with the bottom of the chin at position 0 and the top of the front at position ℓ. The bottom of the mouth is at position m, and the top of the nostrils is at position n, with 0 < m < n < ℓ.

Let us consider that a placement of a mask is defined by two real numbers: its bottom position b ≥ 0 and its upper position u ≤ ℓ, where b < u. We say that a placement is reasonable if it completely covers the mouth and the nostrils, that is, if bm and un.

A stupid person just choses any possible placement such that 0 ≤ b < u ≤ ℓ uniformly at random. Note that b and u are real numbers with an arbitrary (or infinite) number of decimals. What is the probability that a stupid person wears a mask in a reasonable way?


Input consists of several cases, each with three real numbers m, n and ℓ. You can assume 0 < m < n < ℓ ≤ 106.


For every case, print the probability that a stupid person wears a mask in a reasonable way. Print four digits after the decimal point. The input cases do not have precision issues.

Public test cases
  • Input

    10 15 20
    1.62 2.72 3.14
    1 2 3


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    Salvador Roura
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