Number Strength

For a positive integer N, find the smallest positive integer that does not divide N. Replace N with that value and repeat the same process. Stop as soon as N becomes 2.

For example, when N = 6, the number 6 is divisible by 1, 2, and 3, but not by 4, so the next value is 4. Then 4 changes to 3, and 3 changes to 2, producing the sequence 6, 4, 3, 2.

Define strength(N) as the length of the sequence produced by this process. Therefore, strength(6) = 4.

Given two positive integers A < B, compute the sum of number strengths for every integer from A through B, inclusive.

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

The first line contains two integers A and B. (3 <= A < B < 10^17)

Print the sum of number strengths for all integers from A through B, inclusive.