HORRIBLE  Horrible Queries
World is getting more evil and it's getting tougher to get into the Evil League of Evil. Since the legendary Bad Horse has retired, now you have to correctly answer the evil questions of Dr. Horrible, who has a PhD in horribleness (but not in Computer Science). You are given an array of N elements, which are initially all 0. After that you will be given C commands. They are 
* 0 p q v  you have to add v to all numbers in the range of p to q (inclusive), where p and q are two indexes of the array.
* 1 p q  output a line containing a single integer which is the sum of all the array elements between p and q (inclusive)
Input
In the first line you'll be given T, number of test cases.
Each test case will start with N (N <= 100 000) and C (C <= 100 000). After that you'll be given C commands in the format as mentioned above. 1 <= p, q <= N and 1 <= v <= 10^7.
Output
Print the answers of the queries.
Example
Input:
1
8 6
0 2 4 26
0 4 8 80
0 4 5 20
1 8 8
0 5 7 14
1 4 8
Output:
80
508
hide comments
prabodh prakash:
20170514 07:35:21
Super recommended to learn segment tree. I would urge problem solvers to also solve this question for maximum over a range. The whole concept of segment tree and lazy propagation will become clear. 

zubayer_sust:
20170423 07:12:32
At last AC!


zubayer_sust:
20170423 06:55:02
Can someone provide me some critical testcases? 

flyingduchman_:
20170329 11:55:03
BITrange update + range query


sucide:
20170324 19:50:26
Solved in few attempts using lazy.


nikhil_ankam:
20170324 13:20:38
overflow caused me three WA, take care.Have fun! 

jeelapamy:
20170322 19:09:47
learnt alot 

pbd:
20170306 04:27:44
MAX = 1e+5  4 WAs


free__bird:
20170304 18:03:04
Those who have done this with Segment tree, study about Binary Indexed Tree(bit)


nilabja16180:
20170227 21:44:14
AC in 2nd Go!

Added by:  Iqram Mahmud 
Date:  20101204 
Time limit:  2.329s 
Source limit:  50000B 
Memory limit:  1536MB 
Cluster:  Cube (Intel G860) 
Languages:  All except: ASM64 
Resource:  Own. Thanks to Emir Habul. 