D. Plus Minus Permutationtime limit per test1 secondmemory limit per test256 megabytesinputstandard inputoutputstandard outputYou are given 3 integers — n, x, y. Let's call the score of a permutation^\dagger p_1, \ldots, p_n the following value:(p_{1 \cdot x} + p_{2 \cdot x} + \ldots + p_{\lfloor \frac{n}{x} \rfloor \cdot x}) - (p_{1 \cdot y} + p_{2 \cdot y} + \ldots + p_{\lfloor \frac{n}{y} \rfloor \cdot y})In other words, the score of a permutation is the sum of p_i for all indices i divisible by x, minus the sum of p_i for all indices i divisible by y.You need to find the maximum possible score among all permutations of length n.For example, if n = 7, x = 2, y = 3, the maximum score is achieved by the permutation [2,\color{red}{\underline{\color{black}{6}}},\color{blue}{\underline{\color{black}{1}}},\color{red}{\underline{\color{black}{7}}},5,\color{blue}{\underline{\color{red}{\underline{\color{black}{4}}}}},3] and is equal to (6 + 7 + 4) - (1 + 4) = 17 - 5 = 12.^\dagger A permutation of length n is an array consisting of n distinct integers from 1 to n in any order. For example, [2,3,1,5,4] is a permutation, but [1,2,2] is not a permutation (the number 2 appears twice in the array) and [1,3,4] is also not a permutation (n=3, but the array contains 4).InputThe first line of input contains an integer t (1 \le t \le 10^4) — the number of test cases.Then follows the description of each test case.The only line of each test case description contains 3 integers n, x, y (1 \le n \le 10^9, 1 \le x, y \le n).OutputFor each test case, output a single integer — the maximum score among all permutations of length n.ExampleInput
87 2 312 6 39 1 92 2 2100 20 5024 4 61000000000 5575 254504 4 1Output
12
-3
44
0
393
87
179179179436104
-6
NoteThe first test case is explained in the problem statement above.In the second test case, one of the optimal permutations will be [12,11,\color{blue}{\underline{\color{black}{2}}},4,8,\color{blue}{\underline{\color{red}{\underline{\color{black}{9}}}}},10,6,\color{blue}{\underline{\color{black}{1}}},5,3,\color{blue}{\underline{\color{red}{\underline{\color{black}{7}}}}}]. The score of this permutation is (9 + 7) - (2 + 9 + 1 + 7) = -3. It can be shown that a score greater than -3 can not be achieved. Note that the answer to the problem can be negative.In the third test case, the score of the permutation will be (p_1 + p_2 + \ldots + p_9) - p_9. One of the optimal permutations for this case is [9, 8, 7, 6, 5, 4, 3, 2, 1], and its score is 44. It can be shown that a score greater than 44 can not be achieved.In the fourth test case, x = y, so the score of any permutation will be 0.
87 2 312 6 39 1 92 2 2100 20 5024 4 61000000000 5575 254504 4 1
12 -3 44 0 393 87 179179179436104 -6 
['math', '*1200']