Ray Gun

2 seconds
64 MB
Medium Hard
LOJ-1144 Udebug Debug
English

Ray Gun

You are in on m x n grid. You are standing in position (0, 0) and in each of the other lattice points (points with integer co-ordinates) an enemy is waiting. Now you have a ray gun that can fire up to infinity and no obstacle can stop it. Your target is to kill all the enemies. You have to find the minimum number of times you have to fire to kill all of them. For a 4 x 4 grid you have to fire 13 times. See the picture for illustration.

Input

Input starts with an integer T (≤ 100), denoting the number of test cases.

Each case contains two integers m, n (0 ≤ m, n ≤ 109) and at least one of them will be less than or equal to 106.

Output

For each case, print the case number and the minimum number of times you have to fire to kill all the enemies.

Sample

Sample Input Sample Output

2 4 4 10 10

Case 1: 13 Case 2: 65