MULTQ3 - Multiples of 3

There are N numbers a[0], a[1] ... a[N - 1]. Initially all are 0. You have to perform two types of operations :

  1. Increase the numbers between indices A and B (inclusive) by 1. This is represented by the command "0 A B"
  2. Answer how many numbers between indices A and B (inclusive) are divisible by 3. This is represented by the command "1 A B".

Input

The first line contains two integers, N and Q. Each of the next Q lines are either of the form "0 A B" or "1 A B" as mentioned above.

Output

Output 1 line for each of the queries of the form "1 A B" containing the required answer for the corresponding query.

Sample

Input:
4 7
1 0 3
0 1 2
0 1 3
1 0 0
0 0 3
1 3 3
1 0 3

Output:
4
1
0
2

Constraints

1 ≤ N ≤ 100000
1 ≤ Q ≤ 100000
0 ≤ A ≤ B ≤ N - 1


Added by:Varun Jalan
Date:2010-09-12
Time limit:1s
Source limit:50000B
Memory limit:1536MB
Cluster: Cube (Intel G860)
Languages:All except: NODEJS OBJC VB.NET
Resource:own problem

hide comments
2020-05-19 19:04:35
AC in one go
2020-04-25 17:36:58
guys there is nothing tricky in 9th test case, you may have done any small mistake if you are getting WA,, took me 4 hours to debug,,,, but finally AC :D, my 20th.
2020-04-14 10:16:36
naive solution with optimization,AC in one go
2020-04-02 12:23:53
Test cases upto case 9 are simple sum queries without any updates, so even a wrong code may pass cases till 9. Just use Segment Trees + lazy propagation as mentioned below. No need to even use Fast IO
2020-03-31 10:03:49
got wa on 9th test case .can someone help ?
2020-02-21 02:43:05
I constantly get WA in test case 9. Is there anyone with the same issue?
Is there any common mistakes in lazy prop that beginners usually make?
Edit: It is just a stupid typo. Cost me a day :((

Last edit: 2020-02-21 04:31:32
2019-11-15 06:24:49
segment tree + Lazy +Fast I/O only
2019-09-20 19:47:30
Can it be solved without lazy propagation?
2019-08-08 06:03:48
badihi jat
2019-07-28 05:31:57
A good problem to learn lazy propogation.
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