B'In a simplified version of a "Mini Metro" game, there is only one subway line, and all the trains go in the same direction. There are n stations on the line, a_i people are waiting for the train at the i -th station at the beginning of the game. The game starts at the beginning of the 0 -th hour. At the end of each hour (couple minutes before the end of the hour), b_i people instantly arrive to the i -th station. If at some moment, the number of people at the i -th station is larger than c_i , you lose. A player has several trains which he can appoint to some hours. The capacity of each train is k passengers. In the middle of the appointed hour, the train goes from the 1 -st to the n -th station, taking as many people at each station as it can accommodate. A train can not take people from the i -th station if there are people at the i-1 -th station. If multiple trains are appointed to the same hour, their capacities are being added up and they are moving together. The player wants to stay in the game for t hours. Determine the minimum number of trains he will need for it. The first line contains three integers n , t , and k ( 1 <= q n, t <= q 200, 1 <= q k <= q 10^9 ) -- the number of stations on the line, hours we want to survive, and capacity of each train respectively. Each of the next n lines contains three integers a_i , b_i , and c_i ( 0 <= q a_i, b_i <= q c_i <= q 10^9 ) -- number of people at the i -th station in the beginning of the game, number of people arriving to i -th station in the end of each hour and maximum number of people at the i -th station allowed respectively. Output a single integer number -- the answer to the problem. Let 's look at the sample. There are three stations, on the first, there are initially 2 people, 3 people on the second, and 4 people on the third. Maximal capacities of the st'...