- Time limit: 1.00 s
- Memory limit: 512 MB
Your task is to maintain an array of n values and efficiently process the following types of queries:
- Increase the first value in range [a,b] by 1, the second value by 2, the third value by 3, and so on.
- Calculate the sum of values in range [a,b].
Input
The first input line has two integers n and q: the size of the array and the number of queries.
The next line has n values t_1,t_2,\dots,t_n: the initial contents of the array.
Finally, there are q lines describing the queries. The format of each line is either "1 a b" or "2 a b".
Output
Print the answer to each sum query.
Constraints
- 1 \le n, q \le 2 \cdot 10^5
- 1 \le t_i \le 10^6
- 1 \le a \le b \le n
Example
Input:
5 3 4 2 3 1 7 2 1 5 1 1 5 2 1 5
Output:
17 32