Kickstart Round A 2017 Problem A. Square Counting 公式、數論逆元、除法取模
Problem
Mr. Panda has recently fallen in love with a new game called Square Off, in which players compete to find as many different squares as possible on an evenly spaced rectangular grid of dots. To find a square, a player must identify
four dots that form the vertices of a square. Each side of the square must have the same length, of course, but it does not matter what that length is, and the square does not necessarily need to be aligned with the axes of the grid. The player earns one point
for every different square found in this way. Two squares are different if and only if their sets of four dots are different.
Mr. Panda has just been given a grid with R
Input
The first line of the input gives the number of test cases, T. T lines follow. Each line has two integers R and C: the number of dots in each row and column of the
grid, respectively.
Output
For each test case, output one line containing Case #x: y, where x is the test
case number (starting from 1) and y is the number of different squares can be found in the grid.
Limits
1 ≤ T ≤ 100.
Small dataset
2 ≤ R ≤ 1000.
2 ≤ C ≤ 1000.
Large dataset
2 ≤ R ≤ 109.
2 ≤ C ≤ 109.
Sample
|
Input |
Output |
4 2 4 3 4 4 4 1000 500 |
Case #1: 3 Case #2: 10 Case #3: 20 Case #4: 624937395 |
The pictures below illustrate the grids from the three sample cases and a valid square in the third sample case.
