**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:

- 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