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 ll long long
#define INF (1LL<<62)

ll x[50],y[50];
int N,K;

int check(ll lx,ll ly,ll rx,ll ry){
	int ans = 0;
	for(int i = 0;i < N;i++){
		ll nx = x[i];
		ll ny = y[i];
		if(!(lx <= nx && nx <= rx))continue;
		if(!(ly <= ny && ny <= ry))continue;
		ans++;
	}
	return ans;
}

ll saiki(int num,int at,ll lx,ll ly,ll rx,ll ry){

	ll ret = (rx-lx)*(ry-ly);
	if(check(lx,ly,rx,ry)!=K)ret = INF;
	if(num == 4)return ret;

	for(int i = at;i<N;i++){
		ll nx = x[i];
		ll ny = y[i];
		ll v = saiki(num+1,i+1,min(lx,nx),min(ly,ny),max(rx,nx),max(ry,ny));
		ret = min(ret,v);
	}
	return ret;
}

int main(){
	cin>>N>>K;
	for(int i = 0;i < N;i++){
		cin >> x[i] >> y[i];
	}

	cout << saiki(0,0,INF,INF,-INF,-INF) << endl;
}