Maniacal Midsummer Marathon 2014 by AL, TL, JJ

"What do we make them do for problem A?"
"Uh… make them prime factorize a number."
"Isn't that a bit too easy?"
"Fine, make them prime factorize a BIG number."
"Like with GNFS? Isn't that a bit too hard?"
"Fine, let's make them prime factorize a lot of numbers."
"Just how many are you thinking?"
"All of them."
"wat."
"k screw this, let's slap on some bounds and call it a day."

Given two integers ~A~ and ~B~ ~(2 \le A \le B \le 1\,000\,000)~, determine the number of distinct prime factors for each integer between ~A~ and ~B~, inclusive.

Input Specification

The input consists of two lines. The first line will contain the integer ~A~, and the second line will contain the integer ~B~.

Output Specification

The output should contain ~B-A+1~ lines. Each line should contain a single integer, the number of distinct prime factors of ~A, A+1, \dots, B~.

Sample Input

20
30

Sample Output

2
2
2
1
2
1
2
1
2
1
3