SNAGA

문제

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 (two). Let us define 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 strength(6) = 4.

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

strength(A) + strength(A + 1) + ... + strength(B)

입력

The first and only line of input contains two positive integers, A and B (3 ≤ A < B < 10¹⁷).

 

출력

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

 

3 6

11

100 200

262