Maintaining a Sequence

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Points: 40 (partial)
Time limit: 2.0s
Memory limit: 256M

Problem type

Please write a program that maintains a sequence, supporting the following 6 operations:

Operation Input Format Description
1. Insert INSERT posi tot c1 c2 ... ctot After the posi-th number in the current sequence, insert a total of tot numbers: c_1, c_2, \ldots, c_{tot}. Insertion to the beginning of the sequence will have posi equal to 0.
2. Delete DELETE posi tot Starting at the posi-th number in the current sequence, delete a total of tot consecutive numbers.
3. 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.
4. Reverse REVERSE posi tot Starting at the posi-th number in the current sequence, reverse the order of tot consecutive numbers.
5. Get Sum GET-SUM posi tot Starting at the posi-th number in the current sequence, output the sum of tot consecutive numbers.
6. 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
INSERT 8 3 -5 7 2
DELETE 12 1
MAKE-SAME 3 3 2
REVERSE 3 6
GET-SUM 5 4
MAX-SUM

Sample Output

-1
10
1
10

Constraints

You may assume that at any given time, the sequence will contain at least 1 number.
The data in the input is guaranteed to be valid, and will always refer to existing positions in the sequence.

In test data worth 50\% of the points, the sequence may contain up to 30\,000 numbers at any given moment.
In test data worth 100\% of the points, the sequence may contain up to 500\,000 numbers at any given moment.

In test data worth 100\% of the points, the value of any number in the sequence will be in the range [-1\,000, 1\,000].
In test data worth 100\% of the points, M \le 20\,000, the sum of all inserted values will not exceed 4\,000\,000, and the input will not exceed 20MB.


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