CF479E Riding in a Lift

Imagine that you are in a building that has exactly $ n $ floors. You can move between the floors in a lift. Let's number the floors from bottom to top with integers from $ 1 $ to $ n $ . Now you're on the floor number $ a $ . You are very bored, so you want to take the lift. Floor number $ b $ has a secret lab, the entry is forbidden. However, you already are in the mood and decide to make $ k $ consecutive trips in the lift. Let us suppose that at the moment you are on the floor number $ x $ (initially, you were on floor $ a $ ). For another trip between floors you choose some floor with number $ y $ ( $ y≠x $ ) and the lift travels to this floor. As you cannot visit floor $ b $ with the secret lab, you decided that the distance from the current floor $ x $ to the chosen $ y $ must be strictly less than the distance from the current floor $ x $ to floor $ b $ with the secret lab. Formally, it means that the following inequation must fulfill: $ |x-y|

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Imagine that you are in a building that has exactly $ n $ floors. You can move between the floors in a lift. Let's number the floors from bottom to top with integers from $ 1 $ to $ n $ . Now you're on the floor number $ a $ . You are very bored, so you want to take the lift. Floor number $ b $ has a secret lab, the entry is forbidden. However, you already are in the mood and decide to make $ k $ consecutive trips in the lift. Let us suppose that at the moment you are on the floor number $ x $ (initially, you were on floor $ a $ ). For another trip between floors you choose some floor with number $ y $ ( $ y≠x $ ) and the lift travels to this floor. As you cannot visit floor $ b $ with the secret lab, you decided that the distance from the current floor $ x $ to the chosen $ y $ must be strictly less than the distance from the current floor $ x $ to floor $ b $ with the secret lab. Formally, it means that the following inequation must fulfill: $ |x-y|