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 <iostream>
#include <string>
#include <algorithm>
#include <vector>
#include <cmath>
#include <queue>
#include <map>
#include <unordered_map>
#include <set>
#include <functional>
using namespace std;

typedef long long ll;

int n, k;
ll x[52], y[52];
ll ans = 8e18;

int main() {
	cin >> n >> k;
	for (int i = 0; i < n; ++i) cin >> x[i] >> y[i];
	for (int p = 0; p < n; ++p) {
		for (int q = p; q < n; ++q) {
			for (int r = 0; r < n; ++r) {
				for (int s = r; s < n; ++s) {
					int c = 0;
					for (int i = 0; i < n; ++i) {
						if (min(x[p], x[q]) <= x[i] && x[i] <= max(x[p], x[q])) {
							if (min(y[r], y[s]) <= y[i] && y[i] <= max(y[r], y[s])) ++c;
						}
					}
					if (c >= k) ans = min(ans, abs(x[q] - x[p])*abs(y[s] - y[r]));
				}
			}
		}
	}
	cout << ans << endl;
	return 0;
}