B'This is an interactive problem. To prevent the mischievous rabbits from freely roaming around the zoo, Zookeeper has set up a special lock for the rabbit enclosure. This lock is called the Rotary Laser Lock. The lock consists of n concentric rings numbered from 0 to n-1 . The innermost ring is ring 0 and the outermost ring is ring n-1 . All rings are split equally into nm sections each. Each of those rings contains a single metal arc that covers exactly m contiguous sections. At the center of the ring is a core and surrounding the entire lock are nm receivers aligned to the nm sections. The core has nm lasers that shine outward from the center, one for each section. The lasers can be blocked by any of the arcs. A display on the outside of the lock shows how many lasers hit the outer receivers. In the example above, there are n=3 rings, each covering m=4 sections. The arcs are colored in green (ring 0 ), purple (ring 1 ), and blue (ring 2 ) while the lasers beams are shown in red. There are nm=12 sections and 3 of the lasers are not blocked by any arc, thus the display will show 3 in this case. Wabbit is trying to open the lock to free the rabbits, but the lock is completely opaque, and he cannot see where any of the arcs are. Given the relative positions of the arcs, Wabbit can open the lock on his own. To be precise, Wabbit needs n-1 integers p_1,p_2, ldots,p_{n-1} satisfying 0 <= q p_i < nm such that for each i (1 <= q i < n) , Wabbit can rotate ring 0 clockwise exactly p_i times such that the sections that ring 0 covers perfectly aligns with the sections that ring i covers. In the example above, the relative positions are p_1 = 1 and p_2 = 7 . To operate the lock, he can pick any of the n rings and rotate them by 1 section either clockwise or anti-clockwise. You will s'...