Kata

In an infinite array with two rows, the numbers in the top row are denoted

. . . , A[−2], A[−1], A[0], A[1], A[2], . . .

and the numbers in the bottom row are denoted

. . . , B[−2], B[−1], B[0], B[1], B[2], . . .

For each integer k, the entry A[k] is directly above the entry B[k] in the array, as shown:

...

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A[-2]

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A[-1]

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A[0]

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A[1]

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A[2]

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...

...

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B[-2]

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B[-1]

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B[0]

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B[1]

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B[2]

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...

For each integer k, A[k] is the average of the entry to its left, the entry to its right, and the entry below it; similarly, each entry B[k] is the average of the entry to its left, the entry to its right, and the entry above it.

Given A[0], A[1], A[2] and A[3], determine the value of A[n]. (Where range of n is -1000<n<1000)

Test Cases are called as an array of ([A[0], A[1], A[2], A[3]], n)

Hint: Calculate B[k]

FOR JS Node v10.x -> Inputs and Outputs in BigInt!

Adapted from 2018 Euclid Mathematics Contest. https://www.cemc.uwaterloo.ca/contests/past_contests/2018/2018EuclidContest.pdf