Dynamic Range GCD Queries

You are given a sequence of \( n \) integers and must perform \( m \) operations on this sequence. The operations are of two types:

• GCD Query: Given indices \( L \) and \( R \) (1-indexed), compute the greatest common divisor (GCD) of the subarray from \( L \) to \( R \).
• Update: Given an index \( i \) (1-indexed) and a value \( x \), update the \( i^{th} \) element of the sequence to \( x \).

Your task is to process these operations efficiently and output the result for each GCD query.

inputFormat

The first line contains two integers \( n \) and \( m \), where \( n \) is the number of elements in the sequence and \( m \) is the number of operations.

The second line contains \( n \) space-separated integers representing the initial sequence.

Each of the next \( m \) lines describes an operation in one of the following formats:

• 1 L R: A GCD query for the subarray between indices \( L \) and \( R \) (inclusive).
• 2 i x: An update operation, setting the \( i^{th} \) element to \( x \).

outputFormat

For each GCD query, output the computed GCD on a new line.

## sample

5 4
2 4 6 8 10
1 1 5
2 3 12
1 2 4
1 1 5

2
4
2

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