AT_arc204_b [ARC204B] Sort Permutation

You are given positive integers $ N, K $ and a permutation $ P = (P_{1}, P_{2}, \dots, P_{NK}) $ of $ (1, 2, \dots, NK) $ . Alice repeatedly performs the following operation to sort $ P $ in ascending order. - Choose integers $ i $ and $ j $ $ (i\neq j) $ where $ 1 \leq i, j \leq NK $ , and swap $ P_{i} $ and $ P_{j} $ . If $ |i - j| $ is a multiple of $ N $ , Alice gets $ 1 $ point. Alice sorts $ P $ in ascending order with the minimum number of operations, and under that condition, she maximizes the sum of points she gets. Output the sum of points Alice gets.

The input is given from Standard Input in the following format: > $ N $ $ K $ $ P_{1} $ $ P_{2} $ $ \dots $ $ P_{NK} $

Output the answer.

### Sample Explanation 1 For example, $ P $ can be sorted in ascending order with four operations as follows. - Perform the operation with $ (i, j) = (2, 5) $ . After the operation, $ P = (1, 2, 5, 3, 6, 4) $ . - Perform the operation with $ (i, j) = (4, 6) $ . After the operation, $ P = (1, 2, 5, 4, 6, 3) $ . - Perform the operation with $ (i, j) = (3, 5) $ . After the operation, $ P = (1, 2, 6, 4, 5, 3) $ . - Perform the operation with $ (i, j) = (3, 6) $ . After the operation, $ P = (1, 2, 3, 4, 5, 6) $ . Among the above four operations, Alice gets $ 1 $ point from each of the $ 1 $ st and $ 4 $ th operations, so Alice gets a total of $ 2 $ points. This sequence of operations is one of the ways to sort $ P $ in ascending order with the minimum number of operations and maximize the sum of points under that condition, so output $ 2 $ . ### Constraints - $ 1\leq N\leq 500 $ - $ 1\leq K\leq 10 $ - $ (P_{1}, P_{2}, \dots , P_{NK}) $ is a permutation of $ (1, 2, \dots, NK) $ - All input values are integers.