E. Calendar Ambiguitytime limit per test2 secondsmemory limit per test256 megabytesinputstandard inputoutputstandard 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.InputThe 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.OutputPrint 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.ExampleInput
5
6 7 4
10 7 12
12 30 7
1 1 1
3247834 10298779 625324
Output
6
9
5
0
116461800
NoteHere are the pairs for the first test case:   
5
6 7 4
10 7 12
12 30 7
1 1 1
3247834 10298779 625324

6 9 5 0 116461800 
['math', 'number theory', '*2200']