A number is perfect if it is equal to the sum of its divisors that are smaller than it. For example, number ~28~ is perfect because ~28 = 1 + 2 + 4 + 7 + 14~.

Motivated by this definition, we introduce the metric of imperfection of number ~N~, denoted with ~f(N)~, as the absolute difference between ~N~ and the sum of its divisors less than ~N~. It follows that perfect numbers' imperfection score is ~0~, and the rest of natural numbers have a higher imperfection score. For example:

• ~f(6) = |6 - 1 - 2 - 3| = 0~,
• ~f(11) = |11 - 1| = 10~,
• ~f(24) = |24 - 1 - 2 - 3 - 4 - 6 - 8 - 12| = |{-12}| = 12~.

Write a programme that, for positive integers ~A~ and ~B~, calculates the sum of imperfections of all numbers between ~A~ and ~B~: ~f(A) + f(A+1) + \dots + f(B)~.

Input Specification

The first line of input contains the positive integers ~A~ and ~B~ ~(1 \leq A \leq B \leq 10^7)~.

Output Specification

The first and only line of output must contain the required sum.

Sample Input 1

1 9

Sample Output 1

21

Explanation for Sample Output 1

~1 + 1 + 2 + 1 + 4 + 0 + 6 + 1 + 5 = 21~.

Sample Input 2

24 24

Sample Output 2

12