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 denotes 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 :)


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

hide comments
2018-03-17 14:22:10
nice problem @barishnamazov

Re: Thanks

Last edit: 2018-03-18 16:29:18
2018-03-17 10:58:21
@barishnamazov Good problem, Успехов!

Re: Thanks :)

Last edit: 2018-03-17 13:28:39
2018-03-15 19:50:30
nice problem bratan. +1

Re: Thanks bratan <3

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