题目描述

There are three points $A(a, 0)$, $B(0, b)$, $C(0, 0)$ in the plane rectangular coordinate system. Define the size of triangle $ABC$ as the number of squares that belong to it.

For integers $x,y$, one square is defined by four points $(x, y)$, $(x + 1, y)$, $(x, y + 1)$, $(x + 1, y + 1)$. We consider a square to belong to a triangle if half or more of it is inside the triangle.

For example, when $a = 8, b = 6$, the square of triangle $ABC$ will be $24$. The image below shows which squares are counted in the triangle.

输入格式

The first line contains one integer $t$ ($1 \le t \le 10000$) —— the number of testcases.

The follow $t$ lines, for each line contain two integers $a\ (1\le a\le 10^6)$ and $b\ (1\le b\le 10^6)$.

输出格式

Print an integer: the size of triangle $ABC$.

Sample Iutput 1

3
6 8
5 5
1 999999

Sample Iutput 1

24
15
500000