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 lint = long long;
typedef pair<lint, lint> P;

signed main(){
	lint N, K; cin >> N >> K;
	vector<lint> x(N), y(N), xa, ya;
	for(int i = 0; i < N; i++) cin >> x[i] >> y[i], xa.push_back(x[i]), ya.push_back(y[i]);
	sort(xa.begin(), xa.end());
	sort(ya.begin(), ya.end());
	lint ans = 5e18;
	for(int i = 0; i < N; i++){
		for(int j = i + 1; j < N; j++){
			for(int k = 0; k < N; k++){
				for(int l = k + 1; l < N; l++){
					lint x1 = xa[i], x2 = xa[j], y1 = ya[k], y2 = ya[l];
					int c = 0;
					for(int m = 0; m < N; m++){
						if(x1 <= x[m] && x[m] <= x2 && y1 <= y[m] && y[m] <= y2) c++;
					}
					if(c >= K) ans = min(ans, (x2 - x1) * (y2 - y1));
				}
			}
		}
	}
	cout << ans << endl;
}