Range Updates and Sums

• 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 each value in range $[a,b]$ by $x$.
   
2. Set each value in range $[a,b]$ to $x$.
   
3. 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