OPMODULO - "Operation - Modulo"


Mahmud solved some easy math problems from SPOJ and called himself king of number theory. GodFather GodMATHer Rashad heard it and got angry, so he kidnapped Mahmud. Rashad gave him a task called "Operation - Modulo". Mahmud must solve this task, you know what will happen otherwise ;(. In the Operation - Modulo, we define a function f(n) = (n mod 1) + (n mod 2) + (n mod 3) + ... + (n mod n), where n mod x donates the remainder when dividing n by x. Rashad interests with integers n such that f(n)=f(n-1), so he gave Mahmud two numbers L and R, and demands him to find the sum of all integers n such that L ≤ n ≤ R and f(n)=f(n-1).

Input

First and the only line of input contains two positive integers, L and R (1 ≤ L ≤ R ≤ 1018).

Output

Print the demanded sum in one line.

Example

Input:

1 3

Output:

3

Note:

I hope you proved your solution before submitting it :)


hide comments
hodobox: 2019-05-26 03:19:35

@drdrunkenstein, so you see that f(1)=f(0) and f(2)=f(1), so both n=1 and n=2 satisfy f(n)=f(n-1), and the answer is the sum of all such numbers, in this case 1+2 = 3.

drdrunkenstein: 2019-04-24 16:58:39

Can someone explain me the test cases?
f(0)=0
f(1)=1%1=0
f(2)=2%1 + 2%2=0
f(3)=3%1 + 3%2 + 3%3=1

So in range 1 to 3 there are only two values of n for which f(n)=f(n-1) i.e. n=1 & n=2.
So how does the test case has answer 3?

sandeep48: 2018-12-25 15:01:15

try to figure out the sequence of no.
nice problem ,+1

kushagrasri: 2018-11-13 08:04:20

once you get the idea, the problem is super easy.
plus, everything fits in long long int. a very interesting problem.
ac in one go!

abhishak69: 2018-10-06 13:59:40

can you give more testcase

prakash1108: 2018-03-17 14:22:10

nice problem @barishnamazov

Re: Thanks

Last edit: 2018-03-18 16:29:18
julkas: 2018-03-17 10:58:21

@barishnamazov Good problem, Успехов!

Re: Thanks :)

Last edit: 2018-03-17 13:28:39
mahmud2690: 2018-03-15 19:50:30

nice problem bratan. +1

Re: Thanks bratan <3

Last edit: 2018-03-15 19:56:59

Added by:Barish
Date:2018-03-15
Time limit:1s
Source limit:50000B
Memory limit:1536MB
Cluster: Cube (Intel G860)
Languages:All
Resource:Deep places of my brain