Show Ratings Management

You are given a list of shows with their user ratings. There are two types of operations (queries) you can perform on these ratings:

• Update the rating of a show.
• Query the average rating of a range of shows.

For an update query, you are provided with type 1, an index i and a new rating j. For a range query, the query type is 2, and you are provided with two indices i and j, and you need to compute the average of the ratings from the i^th show to the j^th show (both inclusive). The average must be output with exactly two decimal places.

Note: The indices are 1-based.

You are required to handle multiple test cases from the standard input.

The formula for the average of a sequence of numbers \(a_i\) from index \(i\) to \(j\) is given by:

[ \text{average} = \frac{\sum_{k=i}^{j} a_k}{j-i+1} ]

Your task is to update and query ratings as described, and output the query results to the standard output.

inputFormat

The input begins with an integer T (\(1 \le T \le 10\)) representing the number of test cases. Each test case is described as follows:

1. The first line contains two integers \(N\) and \(Q\) (\(1 \le N, Q \le 10^5\)), representing the number of shows and the number of queries respectively.
2. The second line contains \(N\) space-separated integers, representing the initial ratings of the shows.
3. The next \(Q\) lines each contain three integers type i j where:
   • if type == 1: update the rating of the i^th show to j.
   • if type == 2: compute the average rating for shows in the range \([i, j]\).

It is guaranteed that the indices are valid and all ratings are integers.

outputFormat

For each query of type 2 in every test case, output the computed average rating on a new line, formatted to exactly two decimal places.

## sample

1
5 3
10 20 30 40 50
1 3 35
2 2 4
2 1 5

31.67
31.00

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