Codeforces Round 761 (Div. 2) |
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Finished |
Given a positive integer $$$n$$$. Find three distinct positive integers $$$a$$$, $$$b$$$, $$$c$$$ such that $$$a + b + c = n$$$ and $$$\operatorname{gcd}(a, b) = c$$$, where $$$\operatorname{gcd}(x, y)$$$ denotes the greatest common divisor (GCD) of integers $$$x$$$ and $$$y$$$.
The input consists of multiple test cases. The first line contains a single integer $$$t$$$ ($$$1 \le t \le 10^5$$$) — the number of test cases. Description of the test cases follows.
The first and only line of each test case contains a single integer $$$n$$$ ($$$10 \le n \le 10^9$$$).
For each test case, output three distinct positive integers $$$a$$$, $$$b$$$, $$$c$$$ satisfying the requirements. If there are multiple solutions, you can print any. We can show that an answer always exists.
6 18 63 73 91 438 122690412
6 9 3 21 39 3 29 43 1 49 35 7 146 219 73 28622 122661788 2
In the first test case, $$$6 + 9 + 3 = 18$$$ and $$$\operatorname{gcd}(6, 9) = 3$$$.
In the second test case, $$$21 + 39 + 3 = 63$$$ and $$$\operatorname{gcd}(21, 39) = 3$$$.
In the third test case, $$$29 + 43 + 1 = 73$$$ and $$$\operatorname{gcd}(29, 43) = 1$$$.
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