Reversals and Sums

Given an array of n integers, you have to process following operations:

reverse a subarray

calculate the sum of values in a subarray

Input

The first input line has two integers n and m: the size of the array and the number of operations. The array elements are numbered 1,2,\dots,n. The next line as n integers x_1,x_2,\dots,x_n: the contents of the array. Finally, there are m lines that describe the operations. Each line has three integers t, a and b. If t=1, you should reverse a subarray from a to b. If t=2, you should calculate the sum of values from a to b.

Output

Print the answer to each operation where t=2.

Constraints

$1 \le n \le 2$ \cdot 10^5$

$1 \le m \le 10^5$

$0 \le x_i \le 10^9$

$1 \le a \le b \le n$

Example

Input

8 3
2 1 3 4 5 3 4 4
2 2 4
1 3 6
2 2 4

Output

8
9