Problem:
Score : 400 points

Problem Statement

There is a bar of chocolate with a height of H blocks and a width of W blocks.
Snuke is dividing this bar into exactly three pieces.
He can only cut the bar along borders of blocks, and the shape of each piece must be a rectangle.

Snuke is trying to divide the bar as evenly as possible.
More specifically, he is trying to minimize S_{max} - S_{min}, where S_{max} is the area (the number of blocks contained) of the largest piece, and S_{min} is the area of the smallest piece.
Find the minimum possible value of S_{max} - S_{min}.

Constraints

2 ≤ H, W ≤ 10^5

Input

Input is given from Standard Input in the following format:

H W

Output

Print the minimum possible value of S_{max} - S_{min}.

Sample Input 1

3 5

Sample Output 1

0

In the division below, S_{max} - S_{min} = 5 - 5 = 0.

Sample Input 2

4 5

Sample Output 2

2

In the division below, S_{max} - S_{min} = 8 - 6 = 2.

Sample Input 3

5 5

Sample Output 3

4

In the division below, S_{max} - S_{min} = 10 - 6 = 4.

Sample Input 4

100000 2

Sample Output 4

1

Sample Input 5

100000 100000

Sample Output 5

50000

Solution in Go (1.6) (judge verdict: Accepted)

package main
import (
  "fmt"
  "os"
)
func main() {
  var h,w int64
  fmt.Scan(&h,&w)
  if h%3 == 0 || w%3 == 0 {
    fmt.Println(0)
    os.Exit(0)
  }
  var d,dmin,s1,s2,s3,h1,w1 int64
  dmin = min(h,w)
  h1 = h/3
  w1 = (w+1)/2
  s1 = h1*w
  s2 = (h-h1)*w1
  s3 = (h-h1)*(w-w1)
  d = max(s1,s2,s3)-min(s1,s2,s3)
  dmin = min(dmin,d)
  h1 = (h+2)/3
  w1 = (w+1)/2
  s1 = h1*w
  s2 = (h-h1)*w1
  s3 = (h-h1)*(w-w1)
  d = max(s1,s2,s3)-min(s1,s2,s3)
  dmin = min(dmin,d)
  h1 = (h+1)/2
  w1 = w/3
  s1 = h*w1
  s2 = h1*(w-w1)
  s3 = (h-h1)*(w-w1)
  d = max(s1,s2,s3)-min(s1,s2,s3)
  dmin = min(dmin,d)
  h1 = (h+1)/2
  w1 = (w+2)/3
  s1 = h*w1
  s2 = h1*(w-w1)
  s3 = (h-h1)*(w-w1)
  d = max(s1,s2,s3)-min(s1,s2,s3)
  dmin = min(dmin,d)
  fmt.Println(dmin)
}
func max(n ...int64) int64 {
  var m int64 = n[0]
  for i:=0;i<len(n);i++ {
    if m < n[i] { m = n[i] }
  }
  return m
}
func min(n ...int64) int64 {
  var m int64 = n[0]
  for i:=0;i<len(n);i++ {
    if m > n[i] { m = n[i] }
  }
  return m
}