Taco Queries

You are given a 0-indexed integer array \(A\) of size \(N\) and \(T\) queries. There are two types of queries:

• 1 X: Add the integer \(X\) to every element in \(A\).
• 2 L R: Compute the sum of the subarray from index \(L\) to \(R\) (inclusive), taking into account all previous additions.

Mathematically, for a query of type 2, you must output:

\(\sum_{i=L}^{R} (A_i + c)\), where \(c\) is the cumulative addition from all type 1 queries executed so far.

Process the queries sequentially and output the result for each type 2 query on a new line.

inputFormat

The input is given via standard input (stdin) in the following format:

1. The first line contains two integers \(N\) and \(T\) separated by a space.
2. The second line contains \(N\) space-separated integers representing the array \(A\).
3. The next \(T\) lines each contain a query in one of the following formats: "1 X" or "2 L R".

outputFormat

For each query of type 2, output the corresponding sum on a separate line to standard output (stdout).

## sample

5 5
1 2 3 4 5
1 5
2 0 2
2 1 3
1 -2
2 2 4

21
24
21

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