Problem: 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.

Examples

Input

4 4
1 4
3 3
6 2
8 1


Output

21


Input

4 2
0 0
1 1
2 2
3 3


Output

1


Input

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


Output

3999999996000000001

Solution (in CPP):

Solution:
#include <bits/stdc++.h>
using namespace std;
#define rep(i,a,b) for(int i=int(a);i<int(b);i++)
typedef long long ll;


int main(){
    ll n,K;cin>>n>>K;
    ll x[55],y[55];
    rep(i,0,n)cin>>x[i]>>y[i];
    ll cn,an=8e18;
    rep(i,0,n){
        rep(j,0,n){
            rep(k,0,n){
                rep(m,0,n){
                    cn=0;
                    ll u=y[i],d=y[j],r=x[k],l=x[m];
                    if(d>u||l>r)continue;
                    rep(I,0,n){
                        if(d<=y[I]&&y[I]<=u&&l<=x[I]&&x[I]<=r)cn++;
                    }
                    if(cn==K){an=min(an,(u-d)*(r-l));}
                }
            }
        }
    }
    cout<<an<<endl;
}