CSES - Range Updates and Sums
  • Time limit: 1.00 s
  • Memory limit: 512 MB

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

  1. Increase each value in range [a,b][a,b] by xx.
  2. Set each value in range [a,b][a,b] to xx.
  3. Calculate the sum of values in range [a,b][a,b].

Input

The first input line has two integers nn and qq: the array size and the number of queries.

The next line has nn values t1,t2,,tnt_1,t_2,\dots,t_n: the initial contents of the array.

Finally, there are qq lines describing the queries. The format of each line is one of the following: "1 aa bb xx", "2 aa bb xx", or "3 aa bb".

Output

Print the answer to each sum query.

Constraints

  • 1n,q21051 \le n, q \le 2 \cdot 10^5
  • 1ti,x1061 \le t_i, x \le 10^6
  • 1abn1 \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