Magic Board Transformation

Consider an n × m magic board divided into n rows and m columns. Each cell contains a light bulb which can be either on (1) or off (0). You are given two states of the board, represented as binary matrices A and B.

You can perform the following two operations any number of times:

• Row Flip: Choose any row and toggle every bulb in that row (turning 1 to 0 and 0 to 1).
• Column Swap: Choose any two columns and swap their positions.

The task is to determine whether it is possible to transform board A into board B by applying a sequence of these operations.

Mathematically, there must exist a permutation \(\pi\) on \(\{1,2,\ldots,m\}\) and a binary function \(f:\{1,2,\ldots,n\}\to\{0,1\}\) (where \(f(i)=1\) if row \(i\) is flipped and 0 otherwise) such that for every \(1 \le i \le n\) and \(1 \le j \le m\) the following holds:

\( \displaystyle B_{i,j} = A_{i,\pi(j)} \oplus f(i) \)

where \(\oplus\) denotes the XOR operation.

inputFormat

The first line contains two integers n and m (the number of rows and columns).

The next n lines each contain a binary string of length m representing the initial board state A. Each character is either 0 or 1.

This is followed by another n lines, each containing a binary string of length m representing the target board state B.

outputFormat

Output a single line containing YES if it is possible to transform board A into board B using the allowed operations; otherwise, output NO.

sample

2 2
01
10
01
10

YES