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;
typedef long long ll;

//read_kaisetsu
int main() {
    int n,k;cin>>n>>k;
    ll x[n],y[n],x1[n],y1[n];
    rep(i,n){
        cin>>x[i]>>y[i];
        x1[i]=x[i];
        y1[i]=y[i];
    }
    sort(x1,x1+n);
    sort(y1,y1+n);
    ll ans = (x1[n-1]-x1[0])*(y1[n-1]-y1[0]);
    rep(i,n)rep(j,n)rep(l,i)rep(m,j){
        int cc=0;
        ll x_s = min(x[i],x[l]);
        ll x_l = max(x[i],x[l]);
        ll y_s = min(y[j],y[m]);
        ll y_l = max(y[j],y[m]);
        rep(t,n)if(x[t]>=x_s && x[t]<=x_l && y[t]>=y_s && y[t]<=y_l)++cc;
        
        if(cc>=k)ans = min(ans, (x_l - x_s)*(y_l - y_s));
    }
    cout<<ans<<endl;
	return 0;
}