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 C (GCC 5.4.1) (judge verdict: Wrong Answer)

#include<stdio.h>
#include<stdlib.h>
#include<math.h>
#include<string.h>
#include<stdbool.h>
typedef long long ll;
typedef long double ld;
#define rep(i,l,r)for(ll i=(l);i<(r);i++)
#define repp(i,l,r,k)for(ll i=(l);i<(r);i+=(k))
#define rrep(i,l,r)for(ll i=(l);i>=(r);i--)
#define INF (1LL<<60)
#define MOD1 1000000007
#define MAX_N (1 << 17)
#define YES printf("Yes\n")
#define NO printf("No\n")


void swap(ll *a, ll *b){ll c;c=*b;*b=*a;*a=c;}
ll max2(ll a,ll b){return a>=b?a:b;}
ll min2(ll a,ll b){return a>=b?b:a;}
ll minn(ll n, ll a[n]){ll b=INF;rep(i,0,n) b=min2(b,a[i]);return b;}
ll maxn(ll n, ll a[n]){ll b=-INF;rep(i,0,n) b=max2(b,a[i]);return b;}
ll ABS(ll a){return a>=0?a:(-a);}
ll POW(ll a, ll b){ll c=1;rep(i,0,b) c*=a;return c;}
ll gcd(ll a,ll b){return b?gcd(b,a%b):a;}
ll lcm(ll a,ll b){return a/gcd(a,b)*b;}
ll mod(ll n){return n%=MOD1;}
int upll(const void*a, const void*b){return*(ll*)a<*(ll*)b?-1:*(ll*)a>*(ll*)b?1:0;}
int downll(const void*a, const void*b){return*(ll*)a<*(ll*)b?1:*(ll*)a>*(ll*)b?-1:0;}
void sortup(ll*a,int n){qsort(a,n,sizeof(ll),upll);}
void sortdown(ll*a,int n){qsort(a,n,sizeof(ll),downll);}

typedef struct{
    ll aa;
    ll bb;
}frequent;

int main(void){
    // char ;
    ll h,w,ans=INF;
    scanf("%lld%lld",&h,&w);
    if(h%3==0 || w%3==0){
        printf("0\n");
        return 0;
    }
    if(h%2){
        rep(i,1,w/3+2){
            ll s[3]={h*i,(h/2+1)*(w-i),h/2*(w-i)};
            sortup(s,3);
            if( ans < s[2]-s[0] ) break;
            ans= s[2]-s[0] ;
        }
    }else{
        rep(i,1,w/3+2){
            if( ans < ABS(h*i-h/2*(w-i)) ) break;
            ans= ABS(h*i-h/2*(w-i)) ;
        }
    }
    if(w%2){
        rep(i,1,w/3+2){
            ll s[3]={h*i,(h/2+1)*(w-i),h/2*(w-i)};
            sortup(s,3);
            ans= min2( ans , s[2]-s[0] );
        }
    }else{
        rep(i,1,h/3+2){
            ans= min2( ans , ABS(w*i-w/2*(h-i)) );
        }
    }
    printf("%lld\n",ans);
    return 0;
}