**Time limit:**1.00 s**Memory limit:**512 MB

- 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