CF426B Sereja and Mirroring

Let's assume that we are given a matrix $ b $ of size $ x×y $ , let's determine the operation of mirroring matrix $ b $ . The mirroring of matrix $ b $ is a $ 2x×y $ matrix $ c $ which has the following properties: - the upper half of matrix $ c $ (rows with numbers from $ 1 $ to $ x $ ) exactly matches $ b $ ; - the lower half of matrix $ c $ (rows with numbers from $ x+1 $ to $ 2x $ ) is symmetric to the upper one; the symmetry line is the line that separates two halves (the line that goes in the middle, between rows $ x $ and $ x+1 $ ). Sereja has an $ n×m $ matrix $ a $ . He wants to find such matrix $ b $ , that it can be transformed into matrix $ a $ , if we'll perform on it several (possibly zero) mirrorings. What minimum number of rows can such matrix contain?

The first line contains two integers, $ n $ and $ m $ $ (1

In the single line, print the answer to the problem — the minimum number of rows of matrix $ b $ .

In the first test sample the answer is a $ 2×3 $ matrix $ b $ : `

001

110

`If we perform a mirroring operation with this matrix, we get the matrix $ a $ that is given in the input: `

001

110

110

001

`