And now the numerous qualifying tournaments for one of the most prestigious Russian contests Russian Codec Cup are over. All n participants who have made it to the finals found themselves in a huge m -floored 10 8 -star hotel. Of course the first thought to come in a place like this is "How about checking out the elevator?". The hotel's elevator moves between floors according to one never changing scheme. Initially (at the moment of time 0 ) the elevator is located on the 1 -st floor, then it moves to the 2 -nd floor, then — to the 3 -rd floor and so on until it reaches the m -th floor. After that the elevator moves to floor m - 1 , then to floor m - 2 , and so on until it reaches the first floor. This process is repeated infinitely. We know that the elevator has infinite capacity; we also know that on every floor people get on the elevator immediately. Moving between the floors takes a unit of time. For each of the n participant you are given s i , which represents the floor where the i -th participant starts, f i , which represents the floor the i -th participant wants to reach, and t i , which represents the time when the i -th participant starts on the floor s i . For each participant print the minimum time of his/her arrival to the floor f i . If the elevator stops on the floor s i at the time t i , then the i -th participant can enter the elevator immediately. If the participant starts on the floor s i and that's the floor he wanted to reach initially ( s i = f i ), then the time of arrival to the floor f i for this participant is considered equal to t i . The first line contains two space-separated integers n and m ( 1 ≤ n ≤ 10 5 , 2 ≤ m ≤ 10 8 ). Next n lines contain information about the participants in the form of three space-separated integers s i f i t i ( 1 ≤ s i , f i ≤ m , 0 ≤ t i ≤ 10 8 ), described in the problem statement. Print n lines each containing one integer — the time of the arrival for each participant to the required floor. Let's