581. Generate Binary Numbers from 1 to N

Given an integer n, generate the binary representations of the numbers from 1 to n in order and return them as a list of strings. A queue-based approach appends '0' and '1' to previously generated numbers. The input is JSON {n}.

Input: JSON {n}.

Output: Array — binary strings for 1..n.

Examples

Input: {"n":5}
Output: ["1","10","11","100","101"]
Explanation: Binary of 1 through 5.

Input: {"n":1}
Output: ["1"]
Explanation: Just 1.

Input: {"n":3}
Output: ["1","10","11"]
Explanation: Binary of 1,2,3.

Constraints

• 1<=n<=10^4

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