Polynomial Queries

• 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:

1. Increase the first value in range $[a,b]$ by $1$, the second value by $2$, the third value by $3$, and so on.
   
2. 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