National Olympiad in Informatics, China, 2013

The inner product (a.k.a. dot product) of two ~d~-dimensional vectors ~A = [a_1, a_2, \dots, a_d]~ and ~B = [b_1, b_2, \dots, b_d]~ is equal to the sum of products of their corresponding components. Specifically:

$$\displaystyle (A,B) = \sum_{i=1}^d a_i b_i = a_1 b_1+a_2 b_2+\dots+a_d b_d$$

Given ~n~ such ~d~-dimensional vectors, ~x_1, \dots, x_n~, Little Meow-Meow would like to know if there exist two vectors whose inner product is a multiple of ~k~. Please help her solve this problem.

Input Specification

The first line of input contains ~3~ positive integers ~n~, ~d~, and ~k~, respectively representing the number of vectors, the number of dimensions, and the number of which an inner product could be a multiple.
The next ~n~ lines each contains ~d~ nonnegative integers. On the ~i~-th of these lines, the ~j~-th integer represents ~x_{i,j}~, the ~j~-th component of vector ~x_i~.

Output Specification

Output two integers, separated by a space.
If there exist two vectors ~x_p~ and ~x_q~ whose inner product is an integer multiple of ~k~, then output their indices ~p~ and ~q~ ~(p < q)~. If there are multiple answers, output any one of them.
If an answer does not exist, then output -1 -1.

Sample Input

3 5 2
1 0 1 0 1
1 1 0 1 0
0 1 0 1 1

Sample Output

2 3

Explanation

~(x_1, x_2) = 1~
~(x_1, x_3) = 1~
~(x_2, x_3) = 2~

Constraints

Test Case	~n~	~d~	~k~	~x_{i,j}~
~1~	~2~	~20~	~2~	~\le 10~
~2~	~5~	~20~	~2~	~\le 10~
~3~	~10~	~20~	~3~	~\le 10~
~4~	~20~	~20~	~2~	~\le 100~
~5~	~50~	~20~	~3~	~\le 100~
~6~	~50~	~50~	~2~	~\le 1\,000~
~7~	~50~	~50~	~3~	~\le 3\,000\,000~
~8~	~80~	~80~	~2~	~\le 2\,000\,000~
~9~	~100~	~100~	~3~	~\le 3\,000\,000~
~10~	~500~	~100~	~3~	~\le 3\,000\,000~
~11~	~1\,000~	~100~	~2~	~\le 2\,000\,000~
~12~	~1\,000~	~100~	~3~	~\le 3\,000\,000~
~13~	~10\,000~	~100~	~2~	~< 10~
~14~	~10\,000~	~100~	~3~	~< 10~
~15~	~15\,000~	~100~	~2~	~< 10~
~16~	~18\,000~	~100~	~2~	~< 10~
~17~	~20\,000~	~100~	~2~	~< 10~
~18~	~50\,000~	~30~	~3~	~< 10~
~19~	~80\,000~	~30~	~3~	~< 10~
~20~	~100\,000~	~30~	~3~	~< 10~

Problem translated to English by Alex.