Polynomial Queries

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