A head librarian is implementing a new system to organize incoming book shipments onto shelves. There are numShelves shelves numbered from 0 to numShelves - 1, and initially, every shelf is empty (0 books).

The library receives a batch of books to be shelved one by one. For the $i^{\text{th}}$ book in the sequence, there is a restriction limit[i]. This book must be placed on the shelf with the minimum number of books currently on it, considering only the shelves from index 0 to limit[i] - 1.

If there are multiple shelves within that range having the same minimum number of books, the librarian chooses the shelf with the smallest index.

Given numShelves and the array limit, find the shelf index assigned to every book in the shipment.

Input: numShelves = 5, limit = [3, 2, 3, 2, 4] Output: [0, 1, 2, 0, 3] Explanation:

Book Limit	Shelf Counts (Current)	Assigned To	Remarks
3	[0, 0, 0, 0, 0]	0	Look at shelves 0 to 2. All have 0 books. Tie-break: choose the lowest index 0.
2	[1, 0, 0, 0, 0]	1	Look at shelves 0 to 1. Shelf 1 has 0 books (min). Shelf 0 has 1. Choose 1.
3	[1, 1, 0, 0, 0]	2	Look at shelves 0 to 2. Shelf 2 has 0 books. Choose 2.
2	[1, 1, 1, 0, 0]	0	Look at shelves 0 to 1. Both have 1 book. Tie-break: choose the lowest index 0.
4	[2, 1, 1, 0, 0]	3	Look at shelves 0 to 3. Shelf 3 has 0 books. Choose 3.

Example 2

Input: numShelves = 3, limit = [2, 1, 3, 2, 2] Output: [0, 0, 1, 1, 0]

Example 3

Input: numShelves = 5, limit = [4, 3, 5, 1, 4, 5] Output: [0, 1, 2, 0, 3, 4]

Constraints:

• 1 ≤ numShelves ≤ $10^5$
• 1 ≤ limit.length ≤ $10^5$
• 1 ≤ limit[i] ≤ numShelves