Berland 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 $x$.

见题面 Input 部分

见题面 Output 部分

Here are the pairs for the first test case: