CSES - 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