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A3. Heidi Learns Hashing (Hard)
time limit per test
5 seconds
memory limit per test
256 megabytes
input
standard input
output
standard output

Now Heidi is ready to crack Madame Kovarian's hashing function.

Madame Kovarian has a very strict set of rules for name changes. Two names can be interchanged only if using the following hashing function on them results in a collision. However, the hashing function is parametrized, so one can always find a set of parameters that causes such a collision. Heidi decided to exploit this to her advantage.

Given two strings $$$w_1$$$, $$$w_2$$$ of equal length $$$n$$$ consisting of lowercase English letters and an integer $$$m$$$.

Consider the standard polynomial hashing function:

$$$H_p(w) := \left( \sum_{i=0}^{|w|-1} w_i r^i \right) \mbox{mod}(p)$$$

where $$$p$$$ is some prime, and $$$r$$$ is some number such that $$$2\leq r \leq p-2$$$.

The goal is to find $$$r$$$ and a prime $$$p$$$ ($$$m \leq p \leq 10^9$$$) such that $$$H_p(w_1) = H_p(w_2)$$$.

Strings $$$w_1$$$ and $$$w_2$$$ are sampled independently at random from all strings of length $$$n$$$ over lowercase English letters.

Input

The first line contains two integers $$$n$$$ and $$$m$$$ ($$$10 \le n \le 10^5$$$, $$$2 \le m \le 10^5$$$).

The second and the third line, respectively, contain the words $$$w_1$$$, $$$w_2$$$ that were sampled independently at random from all strings of length $$$n$$$ over lowercase English letters.

Output

Output integers $$$p, r$$$.

$$$p$$$ should be a prime in the range $$$[m, 10^9]$$$ and $$$r$$$ should be an integer satisfying $$$r\in [2,p-2]$$$.

At least one solution is guaranteed to exist. In case multiple solutions exist, print any of them.

Examples
Input
10 5
bgcbaaaaaa
cccaaaaaaa
Output
5 2
Input
10 100
melodypond
riversongg
Output
118219 79724
Note

In the first example, note that even though $$$p=3$$$ and $$$r=2$$$ also causes a colision of hashes, it is not a correct solution, since $$$m$$$ is $$$5$$$ and thus we want $$$p\geq 5$$$.

In the second example, we are aware of the extra 'g' at the end. We just didn't realize that "River Song" and "Melody Pond" have different lengths...