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;
int main() {
	int N, K; cin >> N >> K;
	long long X[N], Y[N];
	for (int i = 0; i < N; i++) cin >> X[i] >> Y[i];	
	long long xl[N], xr[N], yu[N], yb[N];
	for (int i = 0; i < N; i++) {
		xl[i] = X[i];
		xr[i] = X[i];
		yu[i] = Y[i];
		yb[i] = Y[i];
	}
	sort(xl, xl + N);
	sort(xr, xr + N);
	sort(yu, yu + N);
	sort(yb, yb + N);
	long long ans = 1LL * (xl[N - 1] - xl[0])*(yu[N- 1] - yb[0]);
	for (int l = 0; l < N - 1; l++) {
		for (int r = l + 1; r < N; r++) {
			for (int b = 0; b < N-1; b++) {
				for (int u = b + 1; u < N; u++) {
					int cnt = 0;
					for (int i = 0; i < N; i++) {
						if (xl[l] <= X[i] && xr[r] >= X[i] && yb[b] <= Y[i] && Y[i] <= yu[u]) cnt++;
					}
					if (cnt >= K) ans = min(ans, 1LL * (xr[r] - xl[l])*(yu[u] - yb[b]));
				}
			}
		}
	}
	cout << ans << endl;
}