查找给定矩阵的元素

Question

You are given an infinite matrix whose upper-left square starts with 1. Here are the first five rows of the infinite matrix:

 1  2  9 10 25
 4  3  8 11 24
 5  6  7 12 23
16 15 14 13 22
17 18 19 20 21

Your task is to find out the number in presents at row x and column y after observing a certain kind of patter present in the matrix

Input Format The first input line contains an integer t: the number of test cases After this, there are t lines, each containing integer x and y

For each test, print the number present at xth row and yth column. sample input 3 2 3 1 1 4 2 sample output 8 1 15

Answer 1

Hint: the numbers at the right and bottom border of a left upper square are consecutive (going either down and left, or right and up). First determine in which border your position is, then find out which direction applies, and finally find the correct number at the position (which easy formula gives you the first number in the border?).