B"With a new body, our idol Aroma White (or should we call her Kaori Minamiya?) begins to uncover her lost past through the OS space. The space can be considered a 2D plane, with an infinite number of data nodes, indexed from 0 , with their coordinates defined as follows: Initially Aroma stands at the point (x_s, y_s) . She can stay in OS space for at most t seconds, because after this time she has to warp back to the real world. She doesn't need to return to the entry point (x_s, y_s) to warp home. While within the OS space, Aroma can do the following actions: Aroma wants to collect as many data as possible before warping back. Can you help her in calculating the maximum number of data nodes she could collect within t seconds? The first line contains integers x_0 , y_0 , a_x , a_y , b_x , b_y ( 1 <= q x_0, y_0 <= q 10^{16} , 2 <= q a_x, a_y <= q 100 , 0 <= q b_x, b_y <= q 10^{16} ), which define the coordinates of the data nodes. The second line contains integers x_s , y_s , t ( 1 <= q x_s, y_s, t <= q 10^{16} ) xe2 x80 x93 the initial Aroma's coordinates and the amount of time available. Print a single integer -- the maximum number of data nodes Aroma can collect within t seconds. In all three examples, the coordinates of the first 5 data nodes are (1, 1) , (3, 3) , (7, 9) , (15, 27) and (31, 81) (remember that nodes are numbered from 0 ). In the first example, the optimal route to collect 3 nodes is as follows: In the second example, the optimal route to collect 2 nodes is as follows: In the third example, Aroma can't collect any nodes. She should have taken proper rest instead of rushing into the OS space like that. "...