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 $B$ $(2\le A\le B\le 1000000)$, 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