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 FOR(i,a,b) for(int i=(a);i<(b);++i)
#define rep(i,n)   FOR(i,0,n)
#define pb emplace_back
#define mp make_pair
typedef long long ll;
typedef pair<int,int> pint;

ll x[51],y[51],xc[51],yc[51];
int main(){
    int n,k;
    cin>>n>>k;
    rep(i,n) cin>>x[i]>>y[i];
    rep(i,n) xc[i]=x[i],yc[i]=y[i];
    sort(x,x+n);
    sort(y,y+n);
    ll ans=LLONG_MAX;
    rep(xi,n)FOR(xj,xi+1,n)rep(yi,n)FOR(yj,yi+1,n){
        int cnt=0;
        rep(i,n){
            if(x[xi]<=xc[i]&&x[xj]>=xc[i]&&y[yi]<=yc[i]&&y[yj]>=yc[i]) ++cnt;
        }
        if(cnt>=k) ans=min(ans,(x[xj]-x[xi])*(y[yj]-y[yi]));
    }
    cout<<ans<<endl;
    return 0;
}