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;
using ll = long long;
using P = pair<ll,ll>;
#define rep(i,n) for(int (i)=0;(i)<(n);(i)++)
#define rep2(i,m,n) for(int (i)=(m);(i)<(n);(i)++)
const ll INF = 1LL<<60;
const ll MOD = 1e9+7;


int main(){
    ios::sync_with_stdio(false);
    cin.tie(0);
    int n,K;cin>>n>>K;
    vector<ll> x(n),y(n);
    rep(i,n)cin>>x[i]>>y[i];
    ll ans = 4*INF;
    rep(i,n)rep(j,n)rep(k,n)rep(l,n){
        ll lx=x[i],rx=x[j],ly=y[k],ry=y[l];
        if(lx>rx||ly>ry)continue;
        int cnt = 0;
        for(int m=0; m<n&&cnt<K; m++){
            if(lx<=x[m]&&x[m]<=rx&&ly<=y[m]&&y[m]<=ry)cnt++;
        }
        if(cnt==K)ans=min(ans,(lx-rx)*(ly-ry));
    }
    cout<<ans<<endl;
    return 0;
}