Code by Its Position

Medium

List every string made of the characters 0 and 1 in this order: first by length (shortest first), and strings of the same length in increasing order as binary numbers. The empty string comes first: "", "0", "1", "00", "01", "10", "11", "000", ... Positions start at zero. Given num, return the string at position num.

Example 1

num=5 → '10'

The list starts "" (0), "0" (1), "1" (2), "00" (3), "01" (4), "10" (5).

Example 2

num=0 → ''

The very first code is the empty one.

Example 3

num=13 → '110'

There are 7 codes of length at most 2 (numbers 0–6), then eight codes of length 3: "000" is number 7, and "110" is number 13.

Constraints

0 ≤ num < 2⁶²

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Topics

Bit Manipulation Math String

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Input

num=5

Expected

'10'

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