RANGESUM - Range Sum


Problem Statement

You are initially given an array of N integers ( 1<=N<=105 ). 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 a1, a2, a3.... an, you need to return the following sum : al + al+1 + al+2 ... + ar.

(ii) Operation 2 : Op2( x )

You are given a single integer x ( |x| <= 109 ). Add this element to the beginning of the array. After this operation, x will now become a1, the old a1 will now become a2, and so on. The size of the array will increase by 1.

 

Input

The first line contains a single integer N ( 1 <= N <= 105 ), the number of elements initially in the array.

This is followed by a line containing N space separated integers, a1 a2 .... aN. ( |ai| <= 109 )

The next line contains a single integer Q, the number of operations you will be asked to perform. ( 1 <= Q <= 105 )

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 : al + al+1 ... + ar

2 x : Carry out operation 2 with the argument x. ( |x| <= 109 )
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
karthik_vg: 2017-11-03 05:23:07

never use accumalate in c++ it costed me 3 WA.

amulyagaur: 2017-08-16 07:30:10

AC in 1 go!

anantct7: 2017-07-30 10:23:08

Really Nice question...Prefix sum would do it :p

jaykay12: 2017-06-17 08:40:49

Nice Question. Use Prefix Sum. O(1) for both Queries. :) Finally AC.

sas1905: 2017-06-06 01:51:20

O(1) query processing..!! No need of BIT..!!

nky_007: 2017-05-31 10:50:45

nice one!!

vengatesh15: 2017-03-11 14:10:03

easy one ... use long long O(1) for both query.

chandan pandey: 2017-01-16 18:30:52

Did it using BIT.
BIT rocks!!!
Any other ideas guys ?

hugewarriors: 2016-12-28 13:31:19



Last edit: 2016-12-28 13:32:16
Madhukar Reddy: 2016-08-18 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
Got accepted after below edit

Edit:
Accept r more than size of the array + extra numbers

Last edit: 2016-08-18 10:41:39

Added by:Gowri Sundaram
Date:2013-04-11
Time limit:2s
Source limit:50000B
Memory limit:1536MB
Cluster: Cube (Intel G860)
Languages:All except: ASM64