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