17313번 - Inner Product 스페셜 저지다국어

문제

The inner product (a.k.a. dot product) of two d-dimensional vectors A = [a₁, a₂, …, a_d] and B = [b₁, b₂, …, b_d] is equal to the sum of products of their corresponding components. Given n such d-dimensional vectors, x₁, …, x_n, Little Meow-Meow would like to know if there exists two vectors whose inner product is a multiple of k. Please help her solve this problem.

입력

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 a 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.

출력

Output two integers, separated by a space.

If there exists 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 two -1's separated by a space.

제한

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