Simulated Memory Heap Manager

You are tasked with simulating a simplified memory heap manager. The memory heap is represented as an array of n cells (numbered from 1 to n), each initially free.

You need to process m commands. Each command is one of the following:

• ALLOC x: Allocate a contiguous block of x free cells. If such a block exists, choose the block with the smallest starting index, mark it as allocated, and output the starting index of the allocation (1-indexed). If no such block exists, output \( -1 \).
• FREE i: Free the memory block that was allocated starting at index i. If the block exists (i.e. i is a valid starting index of an allocated block), free the block (mark the cells as free) and output \( 0 \). Otherwise, output \( -1 \).

Input and Output: Read input from stdin and write output to stdout. The input format is described below.

Note: Ensure your solution maintains the memory state across operations and that it passes all test cases.

inputFormat

The first line contains two integers \( n \) and \( m \) separated by a space, where \( n \) is the number of cells in the memory heap, and \( m \) is the number of commands.

The next \( m \) lines each contain one command. Each command is either of the form ALLOC x or FREE i.

outputFormat

For each command, output a single line containing the result of the operation:

• For ALLOC commands, output the starting index (1-indexed) of the allocated block, or \( -1 \) if allocation fails.
• For FREE commands, output \( 0 \) if the block is successfully freed, or \( -1 \) if the specified index does not correspond to an allocated block.

## sample

10 6
ALLOC 5
ALLOC 4
FREE 1
ALLOC 6
ALLOC 1
FREE 5

1
6
0
-1
1
-1

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