Dynamic Array Range Minimum Query

You are given an array of N integers and Q operations to perform on the array. There are two types of operations:

• Update Operation: Given in the form 1 x y, update the element at index x in the array to the value y.
• Query Operation: Given in the form 2 l r, output the minimum value in the subarray from index l to r (inclusive).

You are required to perform these operations in the given order and output the result for each query operation.

Note: The queries and updates are performed on a 0-indexed array.

The solution must process the operations efficiently. A segment tree is a typical data structure to achieve this in \(O(\log N)\) time per operation.

inputFormat

The input is given from standard input (stdin) and has the following format:

N Q
a0 a1 ... aN-1
op1
op2
...
opQ

Here:

• N is the number of elements in the array.
• Q is the number of operations to perform.
• The next line contains N space-separated integers, which are the elements of the array.
• Each of the following Q lines represents an operation in one of two forms:
  • 1 x y — update the element at index x to the value y.
  • 2 l r — output the minimum element in the subarray from index l to r (inclusive).

outputFormat

For each query operation (of the form 2 l r), print the corresponding minimum value from the specified subarray on a new line to standard output (stdout).

## sample

5 5
1 3 2 7 9
2 1 3
1 2 6
2 1 3
2 0 4
1 4 1

2
3
1

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