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 :)