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 F first
#define S second
using namespace std;

typedef pair < int, int > P;
vector < P > vec;

int main(){
	
	int n, k;
	cin >> n >> k;
	
	for(int i=0;i<n;i++){
		int a, b;
		cin >> a >> b;
		vec.push_back( P(a, b) );
	}

	long long int ans = 1LL<<62;
	
	for(int l=0;l<n;l++){
		for(int r=0;r<n;r++){
			for(int u=0;u<n;u++){
				for(int d=0;d<n;d++){
					
					int cnt = 0;
					int ll = vec[l].F, rr = vec[r].F, uu = vec[u].S, dd = vec[d].S;
					
					for(int i=0;i<n;i++){
						int x = vec[i].F, y = vec[i].S;
						if(ll <= x && rr >= x && uu >= y && dd <= y) cnt++;
					}
					
					if(cnt >= k) ans = min(ans, 1LL * (rr-ll)*(uu-dd));
					}
				}
			}
		}
	
	
	cout << ans << endl;
}