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math

number theory

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E. Calendar Ambiguity

time limit per test

2 secondsmemory limit per test

256 megabytesinput

standard inputoutput

standard outputBerland year consists of $$$m$$$ months with $$$d$$$ days each. Months are numbered from $$$1$$$ to $$$m$$$. Berland week consists of $$$w$$$ days. The first day of the year is also the first day of the week. Note that the last week of the year might be shorter than $$$w$$$ days.

A pair $$$(x, y)$$$ such that $$$x < y$$$ is ambiguous if day $$$x$$$ of month $$$y$$$ is the same day of the week as day $$$y$$$ of month $$$x$$$.

Count the number of ambiguous pairs.

Input

The first line contains a single integer $$$t$$$ ($$$1 \le t \le 1000$$$) — the number of testcases.

Each of the next $$$t$$$ lines contains three integers $$$m$$$, $$$d$$$ and $$$w$$$ ($$$1 \le m, d, w \le 10^9$$$) — the number of months in a year, the number of days in a month and the number of days in a week.

Output

Print $$$t$$$ integers — for each testcase output the number of pairs $$$(x, y)$$$ such that $$$x < y$$$ and day $$$x$$$ of month $$$y$$$ is the same day of the week as day $$$y$$$ of month $$$x$$$.

Example

Input

5 6 7 4 10 7 12 12 30 7 1 1 1 3247834 10298779 625324

Output

6 9 5 0 116461800

Note

Here are the pairs for the first test case:

Codeforces (c) Copyright 2010-2024 Mike Mirzayanov

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