Please write a program that maintains a sequence, supporting the following operations:

Operation	Input Format	Description
1. Modify	MAKE-SAME posi tot c	Starting at the ~posi~-th number in the current sequence, change all the values of ~tot~ consecutive numbers to ~c~.
2. Get Sum	GET-SUM posi tot	Starting at the ~posi~-th number in the current sequence, output the sum of ~tot~ consecutive numbers.
3. Max Sum	MAX-SUM	Output the largest sum of any (non-empty) consecutive subsequence of the current sequence.

Input Specification

The first line of input contains two integers ~N~ and ~M~, where ~N~ is the initial length of the sequence and ~M~ is the number of operations.

The second line of input contains ~N~ integers, describing the initial sequence.

For the next ~M~ lines, each line will contain a command in one of the formats described above.

Output Specification

For each GET-SUM or MAX-SUM operation in the input, output the result of the query on a separate line.

Sample Input

9 8
2 -6 3 5 1 -5 -3 6 3
GET-SUM 5 4
MAX-SUM
MAKE-SAME 3 3 2
GET-SUM 5 4
MAX-SUM
MAKE-SAME 2 1 12
MAX-SUM
GET-SUM 8 2

Sample Output

-1
10
0
9
21
9

Constraints

The data in the input is guaranteed to be valid, and will always refer to existing positions in the sequence.

In test data worth ~40\%~ of the points, ~N \le 100~.
In test data worth ~100\%~ of the points, ~N \le 100~ ~000~.

In test data worth ~100\%~ of the points, the value of any number in the sequence will be in the range ~[-10~ ~000, 10~ ~000]~.
In test data worth ~100\%~ of the points, ~M \le 100~ ~000~.