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,n) for(int i=0;i<int(n);++i)
typedef long long ll;
#define x first
#define y second

int main(void){
    int N,K;
    cin>>N>>K;
    vector<pair<ll,ll>> p(N);
    rep(i,N) cin>>p[i].x>>p[i].y;
    ll res = LLONG_MAX;
    rep(a,N)rep(b,N)rep(c,N)rep(d,N){
        ll L = min({p[a].x, p[b].x, p[c].x, p[d].x});
        ll R = max({p[a].x, p[b].x, p[c].x, p[d].x});
        ll D = min({p[a].y, p[b].y, p[c].y, p[d].y});
        ll U = max({p[a].y, p[b].y, p[c].y, p[d].y});
        int cnt=0;
        rep(i,N) if(L<=p[i].x && p[i].x<=R && D<=p[i].y && p[i].y<=U)
            cnt++;
        if(cnt>=K) res = min(res,(R-L)*(U-D));
    }
    cout<<res<<endl;
}