Let us begin with a positive integer ~N~ and find the smallest positive integer which doesn't divide ~N~. If we repeat the procedure with the resulting number, then again with the new result and so on, we will eventually obtain the number ~2~. Let us define ~\text{strength}(N)~ as the length of the resulting sequence.

For example, for ~N = 6~ we obtain the sequence ~6, 4, 3, 2~ which consists of ~4~ numbers, thus ~\text{strength}(6) = 4~.

Given two positive integers ~A < B~, calculate the sum of strengths of all integers between ~A~ and ~B~ (inclusive), that is,

$$\displaystyle \text{strength}(A) + \text{strength}(A + 1) + \dots + \text{strength}(B)$$

Input Specification

The first and only line of input contains two positive integers, ~A~ and ~B~ ~(3 \leq A < B < 10^{17})~.

Output Specification

The first and only line of output should contain the requested sum of strengths.

Sample Input 1

3 6

Sample Output 1

11

Sample Input 2

100 200

Sample Output 2

262