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The same number of divisors

The same number of divisors

Time limit 1 second
Memory limit 128 MiB

During his math lesson, Kostya fell in love with looking for divisors in numbers. And the more numbers with the same number of divisors, the better Kostya's mood was.

Help Kostya have a good mood.

In the range from a to b, find the largest amount of numbers with the same number of divisors. Print the number of divisors and the amount of such numbers. If there are several answers, then output the one with more divisors.

Input data

Two numbers a and b (1ab10^5).

Output data

Print two numbers: the number of divisors and amount of such numbers.


On a segment from 1 to 10:

  • number 1 has 1 divisor;

  • number 2 has 2 divisors;

  • number 3 has 2 divisors;

  • number 4 has 3 divisors;

  • number 5 has 2 divisors;

  • number 6 has 4 divisors;

  • number 7 has 2 divisors;

  • number 8 has 4 divisors;

  • number 9 has 3 divisors;

  • number 10 has 4 divisors.

The largest amount of numbers have 2 divisors, and their amount is 4.


Input example #1
1 10
Output example #1
2 4
Source 2020 ІІ stage All Ukrainian Olympiad in Informatics, Zhitomir