CF1556A A Variety of Operations

William has two numbers $ a $ and $ b $ initially both equal to zero. William mastered performing three different operations with them quickly. Before performing each operation some positive integer $ k $ is picked, which is then used to perform one of the following operations: (note, that for each operation you can choose a new positive integer $ k $ ) 1. add number $ k $ to both $ a $ and $ b $ , or 2. add number $ k $ to $ a $ and subtract $ k $ from $ b $ , or 3. add number $ k $ to $ b $ and subtract $ k $ from $ a $ . Note that after performing operations, numbers $ a $ and $ b $ may become negative as well. William wants to find out the minimal number of operations he would have to perform to make $ a $ equal to his favorite number $ c $ and $ b $ equal to his second favorite number $ d $ .

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Let us demonstrate one of the suboptimal ways of getting a pair $ (3, 5) $ : - Using an operation of the first type with $ k=1 $ , the current pair would be equal to $ (1, 1) $ . - Using an operation of the third type with $ k=8 $ , the current pair would be equal to $ (-7, 9) $ . - Using an operation of the second type with $ k=7 $ , the current pair would be equal to $ (0, 2) $ . - Using an operation of the first type with $ k=3 $ , the current pair would be equal to $ (3, 5) $ .