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 <string>
#include <string.h>
#include <cmath>
#include <cstdio>
#include <vector>
#include <algorithm>
#include <iostream>
#include <queue>
#include <tuple>
#include <functional>
#include <set>

using namespace std;
int n;
int k;
int x[50];
int y[50];

int main()
{
	cin >> n >> k;
	for (int i = 0; i < n; ++i) {
		cin >> x[i] >> y[i];
	}
	//50^5=
	long long ans = 6e18;
	for (int x1 : x) {
		for (int x2 : x) {
			if (x1 >= x2)continue;
			for (int y1 : y) {
				for (int y2 : y) {
					if (y1 >= y2)continue;
					int cnt = 0;
					for (int i = 0; i < n; ++i) {
						if (x1 <= x[i] && x[i] <= x2&&y1 <= y[i] && y[i] <= y2) {
							++cnt;
						}
					}
					if (cnt >= k) {
						ans = min(ans, (long long)(x2 - x1)*(y2 - y1));
					}

				}
			}
		}
	}
	cout << ans << endl;
	return 0;
}