RANGESUM  Range Sum
Problem Statement
You are initially given an array of N integers ( 1<=N<=10^{5} ). Given this array, you have to perform 2 kinds of operations :
(i) Operation 1 : Op1( l, r )
You are given 2 integers l and r. ( 1 <= l <= r <= current size of the array ). You need to return the sum of all the elements with indices between l and r ( both inclusive ). That is, if the elements currently in the array are a_{1}, a_{2}, a_{3}.... a_{n}, you need to return the following sum : a_{l} + a_{l+1} + a_{l+2} ... + a_{r}.
(ii) Operation 2 : Op2( x )
You are given a single integer x ( x <= 10^{9} ). Add this element to the beginning of the array. After this operation, x will now become a_{1}, the old a_{1} will now become a_{2}, and so on. The size of the array will increase by 1.
Input
The first line contains a single integer N ( 1 <= N <= 10^{5} ), the number of elements initially in the array.
This is followed by a line containing N space separated integers, a_{1} a_{2} .... a_{N}. ( a_{i} <= 10^{9} )
The next line contains a single integer Q, the number of operations you will be asked to perform. ( 1 <= Q <= 10^{5} )
Q lines of input follow. Each such line starts with either the number 1 or the number 2. This indicates the type of operation that you are required to perform. The format of these queries are as follows :
1 l r : Carry out operation 1 with arguments l and r. ( 1 <= l <= r <= current size of the array )
That is, return the sum of the following array elements : a_{l} + a_{l+1} ... + a_{r}
2 x : Carry out operation 2 with the argument x. ( x <= 10^{9} )
That is, add the value x at the beginning of the array.
Output
For each query of type 1, output the return value on a new line. No output needs to be printed for queries of type 2.
Example
Input #1: 10
1 2 3 4 5 6 7 8 9 10
4
1 1 10
1 1 1
1 10 10
1 2 7
Output #1:
55
1
10
27
Input #2:
5
6 7 8 9 10
9
2 5
2 4
1 2 7
2 3
2 2
2 1
1 1 10
1 1 1
1 10 10
Output #2:
45
55
1
10
hide comments
anantct7:
20170730 10:23:08
Really Nice question...Prefix sum would do it :p 

jaykay12:
20170617 08:40:49
Nice Question. Use Prefix Sum. O(1) for both Queries. :) Finally AC. 

sas1905:
20170606 01:51:20
O(1) query processing..!! No need of BIT..!! 

nky_007:
20170531 10:50:45
nice one!! 

vengatesh15:
20170311 14:10:03
easy one ... use long long O(1) for both query. 

chandan pandey:
20170116 18:30:52
Did it using BIT.


hugewarriors:
20161228 13:31:19


Madhukar Reddy:
20160818 08:44:17
It is given that numbers array is input in the second line, is it possible to spread over multiple lines? Please check this, I am getting NZEC error in python. And also I don't see any accepted submissions in python yet


square1001:
20160816 02:08:28
Easy. No Binary Search Tree. Only Prefix Sum :) 

yuk_96:
20160622 13:38:48
Last edit: 20160622 13:39:01 
Added by:  Gowri Sundaram 
Date:  20130411 
Time limit:  2s 
Source limit:  50000B 
Memory limit:  1536MB 
Cluster:  Cube (Intel G860) 
Languages:  All except: ASM64 