Pies With Nothing Left Over

Medium

A bakery makes two kinds of pies: - a large pie takes 4 apples and 1 crust; - a small pie takes 2 apples and 1 crust. The storeroom has apples apples and crusts crusts. The goal is to bake pies that use up every last apple and crust. Return [large, small], the number of large and small pies to bake. If there is no way to use everything up exactly, return an empty list.

Example 1

apples=10, crusts=3 → [2, 1]

Two large pies (8 apples, 2 crusts) and one small pie (2 apples, 1 crust) use exactly 10 apples and 3 crusts.

Example 2

apples=9, crusts=3 → []

Every pie takes an even number of apples and 9 is odd, so nothing works.

Example 3

apples=2, crusts=3 → []

Three crusts need at least 6 apples, and there are only 2.

Constraints

0 ≤ apples ≤ 10⁸
0 ≤ crusts ≤ 10⁸

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Topics

Math

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Input

apples=10, crusts=3

Expected

[2, 1]

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