Range Updates and Sums

Your task is to maintain an array of n values and efficiently process the following types of queries:

Increase each value in range [a,b] by x.

Set each value in range [a,b] to x.

Calculate the sum of values in range [a,b].

Input

The first input line has two integers n and q: the array size 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 one of the following: "1 a b x", "2 a b x", or "3 a b".

Output

Print the answer to each sum query.

Constraints

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

$1 \le t_i, x \le 10^6$

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

Example

Input

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

Output

7
11
15