CF2204C Spring

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.