Problem:
Score : 400 points

Problem Statement

We have N points in a two-dimensional plane.

The coordinates of the i-th point (1 \leq i \leq N) are (x_i,y_i).

Let us consider a rectangle whose sides are parallel to the coordinate axes that contains K or more of the N points in its interior.

Here, points on the sides of the rectangle are considered to be in the interior.

Find the minimum possible area of such a rectangle.

Constraints

2 \leq K \leq N \leq 50

-10^9 \leq x_i,y_i \leq 10^9 (1 \leq i \leq N)

x_i≠x_j (1 \leq i<j \leq N)

y_i≠y_j (1 \leq i<j \leq N)

All input values are integers. (Added at 21:50 JST)

Input

Input is given from Standard Input in the following format:

N K
x_1 y_1
:
x_{N} y_{N}

Output

Print the minimum possible area of a rectangle that satisfies the condition.

Sample Input 1

4 4
1 4
3 3
6 2
8 1

Sample Output 1

21

One rectangle that satisfies the condition with the minimum possible area has the following vertices: (1,1), (8,1), (1,4) and (8,4).

Its area is (8-1) × (4-1) = 21.

Sample Input 2

4 2
0 0
1 1
2 2
3 3

Sample Output 2

1

Sample Input 3

4 3
-1000000000 -1000000000
1000000000 1000000000
-999999999 999999999
999999999 -999999999

Sample Output 3

3999999996000000001

Watch out for integer overflows.

Solution in C++14 (GCC 5.4.1) (judge verdict: Wrong Answer)

#include "bits/stdc++.h"

typedef long long ll;
#define int ll
#define fi first
#define se second
#define SORT(a) sort(a.begin(),a.end())
#define REP(i,n) for (int i = 0;i < (n) ; i++) 
#define MP(a,b) make_pair(a,b)
#define pb(a) push_back(a)

using namespace std;

signed main(){
    
    int n,K;
    cin >> n >> K;

    vector<pair<int,int>> p;

    REP(i,n){
        int a,b;
        cin >> a >> b;
        p.pb(MP(a,b));
    }
    //SORT(p);
    int ans = 4234567890123456789;

    REP(i,n) for(int j=i+1;j<n;j++){
        int x_min = min({p[i].fi,p[j].fi});
        int x_max = max({p[i].fi,p[j].fi});
        int y_min = min({p[i].se,p[j].se});
        int y_max = max({p[i].se,p[j].se});
        
        int cnt = 0;
        REP(c,n){//長方形内の点をカウント
            int x = p[c].fi;
            int y = p[c].se;
            if(x_min <= x && x <= x_max && y_min <= y && y <= y_max){
                cnt++;
            }
        }
        if(cnt >= K) ans = min(ans,(x_max - x_min)*(y_max - y_min));
    }
    
    REP(i,n) for(int j=i+1;j<n;j++) for(int k=j+1;k<n;k++){
        int x_min = min({p[i].fi,p[j].fi,p[k].fi});
        int x_max = max({p[i].fi,p[j].fi,p[k].fi});
        int y_min = min({p[i].se,p[j].se,p[k].se});
        int y_max = max({p[i].se,p[j].se,p[k].se});
        
        int cnt = 0;
        REP(c,n){//長方形内の点をカウント
            int x = p[c].fi;
            int y = p[c].se;
            if(x_min <= x && x <= x_max && y_min <= y && y <= y_max){
                cnt++;
            }
        }
        if(cnt >= K) ans = min(ans,(x_max - x_min)*(y_max - y_min));
    }

    cout << ans << endl;
    
    return 0;
}
//g++ -std=c++14 code1.cpp