Namit's girlfriend birthday is coming next week.He went to a gift shop and saw (N) gifts are arranged in a single row in such a way that the position at which the gift is placed is equal to its price.(Position starts from 1.)

Namit's girlfriend being a maths student like those numbers which have exactly 3 divisors, so Namit  decide to buy only those gifts which are placed at a position which have only 3 divisors, but Namit's girlfriend likes gifts whose price are above a certain amount(K).

Now Namit wants to know total choices he have and how many gifts his girlfriend like for a given value of N.

Input

Input starts with 1<=T<=1000 (number of test cases). Then T lines follows each containing two integer 1<=N<10^10 (number of gifts at gift shop) and 1<=K<=10^10.

Output

You program should output two values indicating total number of choices and the number of gifts Namit's girlfriend like.

Example

Input:
3

10 2

20 7

10 4

Output:
2 2

2 1

2 1