You 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 $$$4$$$).

Input

The 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 $$$n$$$, $$$x$$$, $$$y$$$ ($$$1 \le n \le 10^9$$$, $$$1 \le x, y \le n$$$).

Output

For each test case, output a single integer — the maximum score among all permutations of length $$$n$$$.

Note

The 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 $$$0$$$.

Plus Minus Permutation

Examples