Alice, Bob, and Carol visit a spring to collect water. Alice visits every (a) days (on days (a, 2a, 3a, \dots)), Bob visits every (b) days (on days (b, 2b, 3b, \dots)), and Carol visits every (c) days (on days (c, 2c, 3c, \dots)). When only one person visits, they collect (6) liters of water. If multiple people visit, the water is divided equally: two people take (3) liters each, and three people take (2) liters each. Your task is to calculate how much water Alice, Bob, and Carol collect over (m) days, starting from day (1). The first line contains a single integer (t) ((1 \le t \le 10^4)) — the number of test cases. The only line of each test case contains four integers (a), (b), (c), and (m) ((1 \le a, b, c \le 10^6); (1 \le m \le 10^{17})). For each test case, print three integers — the number of liters of water that Alice, Bob, and Carol collect over (m) days. Consider the first example: on day (1), only Bob visits the spring, and he collects (6) liters; on day (2), Alice and Bob visit the spring, and they each collect (3) liters; on day (3), Bob and Carol visit the spring, and they each collect (3) liters; on day (4), Alice and Bob visit the spring, and they each collect (3) liters; on day (5), only Bob visits the spring, and he collects (6) liters; on day (6), Alice, Bob, and Carol visit the spring, and they each collect (2) liters; on day (7), only Bob visits the spring, and he collects (6) liters; on day (8), Alice and Bob visit the spring, and they each collect (3) liters; on day (9), Bob and Carol visit the spring, and they each collect (3) liters; on day (10), Alice and Bob visit the spring, and they each collect (3) liters.