The same number of divisors#10218

The same number of divisors

1 second

128 megabytes

Very easy

Kostya loves finding divisors of numbers during his math lessons. The more numbers with the same number of divisors he finds, the better his mood becomes.

Help Kostya to have a good mood!

Find, in the range from $a$ to $b$ , the largest count of numbers with the same number of divisors. Output the number of divisors and the count of such numbers. If there are several possible answers, output the one with a greater number of divisors.

Input

Two integers $a$ and $b$ ( $1 \leq a \leq b \leq 1 0^{5}$ 1 \leq a \leq b \leq 10^5).

Output

Print two integers: the number of divisors and the count of such numbers.

Examples

On the 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 group is those with $2$ divisors and their count is $4$ .

Example 1

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1 \leq a \leq b \leq 1 0^{5}