OMWG  One more weird game
Leha is playing a very interesting game. The game will be played on a rectangular grid consisting of N rows and M columns. Initially all the cells of the grid are uncolored.
Leha's initial score is zero. At each turn, he chooses some cell that is yet not colored, and colors that cell. The score obtained in this step will be number of neighboring colored cells of the cell that Leha colored in this step. Two cells are neighbors of each other if they share a side between them. The game will end when all the cells are colored. Finally, total score obtained at the end of the game will sum of score obtained in each turn.
Leha wants to know what maximum score he can get? Can you please help him in finding this out?
Input
The first line contains a single integer T denoting the number of test cases. T test cases follow. Each of the following T lines contains two spaceseparated integers N, M denoting the dimensions of the grid.
Output
For each test case, output a single line containing an integer corresponding to the maximal possible score Leha can obtain.
Constraints
1 ≤ T ≤ 100
1 ≤ N, M ≤ 1 000
Example
Input: 1 2 2 Output: 4 Explaination Leha can obtain total score 4 in the following way. 1. In the first step, he colors down left cell, all the neighboring cells of this cell are uncolored. So, it adds 0 to total score. 2. In second step, he can color upper right cell, it also adds total 0 to the score. 3. In third step, he can color top left cell. There are two neighboring cell of this cell, both of which are colored. So, this add 2 to the score. 4. In the last step, he can choose the remaining down right cell. There are two neighboring cell of this cell, both of which are colored. So, this also add 2 to the score. Leha can't obtain a score more than 4. Hence 4 is the answer.
hide comments
anirudnits:
20181009 18:48:46
the graph approach passes :) 

aniket000:
20180131 14:52:08
nice! , no idea how to solve using graphs, but solved it in O(1) xd 

shiv2111:
20171221 11:04:13
graph contains vertices and "EDGES" :). 

abhilc:
20170512 17:30:48
O(1) is giving me TLE. What kind of sorcery is this? :o 

iharsh234:
20160821 13:09:49
tukka got AC. haha 

akshayvenkat:
20160714 16:48:49
there are only two TLE's for this problem ever and both are mine :p 

avisheksanvas:
20160708 05:14:56
The #graph tag though!


TUSHAR SINGHAL:
20160703 10:36:20
200th green .. #happy_me :D 

pranav_arora:
20160703 03:58:49
@Bhuvnesh Jain: There's a O(1) solution per testcase without any precomputation. ;) 

Bhuvnesh Jain:
20160702 18:00:42
@author, can you give some hint on how to improve the execution time? 
Added by:  Beer hu !! 
Date:  20160701 
Time limit:  0.5s1s 
Source limit:  50000B 
Memory limit:  1536MB 
Cluster:  Cube (Intel G860) 
Languages:  All except: ASM64 GOSU JSMONKEY 
Resource:  Codechef 