Mimi is taking both art and computer science this semester! Inspired, she decides to make an art piece based on the binary representation of two positive integers, ~N~ and ~M~.

Mimi takes a strip of paper and draws ~K~ stripes on it. The ~i^\text{th}~ stripe is blue if ~2^{i-1}~ appears in the binary representation of either ~N~ or ~M~, but not both. Otherwise, it is painted purple.

Can you tell Mimi how many blue and purple stripes there are?

Constraints

~1 \le N, M \le 10^9~
~1 \le K \le 30~

Input Specification

The first and only line of input will contain 3 space separated integers: ~N~, ~M~, and ~K~.

Output Specification

The output should contain two space-separated integers: the number of stripes that are painted blue, and the number of stripes that are painted purple, respectively.

Sample Input

3 1 2

Sample Output

1 1

Explanation for Sample Output

The binary representation of ~3~ is ~2^1 + 2^0~, and the binary representation of ~1~ is ~2^0~.
Both representations have ~2^0~, so the first stripe is painted purple.
Since only ~3~ has ~2^1~ in its binary representation, the second stripe is painted blue.