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>
#define rep(i,n) for (int i=0; i<(n); ++i)
using namespace std;
using ll = long long;
using P = pair<int,int>;

int main(){
    int n,k;
    cin>>n>>k;
    vector<int>x(n),y(n);
    rep(i,n)cin>>x[i]>>y[i];
    ll ans=LONG_LONG_MAX;
    rep(a,n)rep(b,n)rep(c,n)rep(d,n){
        int L=x[a],R=x[b],D=y[c],U=y[d];
        if(R<L||U<D)continue;
        int cnt=0;
        rep(v,n){
            if(L<=x[v]&&x[v]<=R&&D<=y[v]&&y[v]<=U)cnt++;
        }
        if(cnt>=k)ans=min(ans,(ll)(R-L)*(U-D));
    }
    cout<<ans<<endl;
}