Longest Valid Substring after Toggle Operations

You are given a sequence \( a \) of length \( n \), where initially every element is the character L. There are \( q \) operations. In each operation, you are given an index \( x \) (1-indexed). If \( a_x = L \), change it to R, otherwise change it to L (i.e. toggle it).

A string \( s \), consisting only of the characters L and R, is said to satisfy the condition if it does not contain two consecutive characters that are different. Equivalently, every two adjacent characters in \( s \) must be identical.

After each operation, output the length of the longest contiguous substring (subarray) of \( a \) that satisfies the condition.

Note: The positions are 1-indexed.

inputFormat

The first line contains two integers \( n \) and \( q \) — the length of the sequence and the number of operations.

The next \( q \) lines each contain an integer \( x \) (1-indexed) indicating the position to toggle.

outputFormat

After each operation, output one integer — the length of the longest contiguous substring that satisfies the condition.

sample

5 3
3
1
5

2
2
1