B. Long Legs
brute force; math
A robot is placed in a cell \((0, 0)\) of an infinite grid. This robot has adjustable length legs. Initially, its legs have length \(1\).Let the robot currently be in the cell \((x, y)\) and have legs of length \(m\). In one move, it can perform one of the following three actions: jump into the cell \((x + m, y)\); jump into the cell \((x, y + m)\); increase the length of the legs by \(1\), i. e. set it to \(m + 1\). What's the smallest number of moves robot has to make to reach a cell \((a, b)\)?
The first line contains a single integer \(t\) (\(1 \le t \le 100\)) — the number of test cases.The only line of each test case contains two integers \(a\) and \(b\) (\(1 \le a, b \le 10^9\)) — the ending cell.
For each test case, print a single integer — the smallest number of moves the robot is required to make to reach a cell \((a, b)\) from a cell \((0, 0)\).
In the first testcase, the robot can first jump to \((0, 1)\), then to \((1, 1)\). If it ever increases the length of its legs, it will only be able to jump past \((1, 1)\).In the second testcase, the robot can jump to \((1, 0)\), then increase the length of its length to \(2\) and jump three times to reach \((1, 6)\).In the third testcase, the robot can increase the length of its legs three times to make it \(4\). Then jump to \((0, 4)\). Then jump twice to reach \((8, 4)\).