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 <cstdio>
#define N 55
using namespace std;

typedef long long ll;
ll n,s, t1,t2, t3, t4, sz, mn = -1, x[N], y[N];
int main()
{
	ll i,j, k, w, r;
	cin >> n >>sz;
	for (i = 0; i < n; i++) {
		scanf ("%lld %lld", &x[i], &y[i]);
	}
	for (i = 0; i < n; i++) {
		for (j = i; j < n; j++) {
			t1 = min(x[i], x[j]);
			t2 = min(y[i], y[j]);
			for (k = 0; k < n; k++) {
				for (w = k; w < n; w++) {
					t3 = max(x[k], x[w]);
					t4 = max(y[k], y[w]);
					s = 0;
					for (r = 0; r < n; r++) {
						if (t1 <= x[r] && x[r] <= t3 && t2 <= y[r] && y[r] <= t4) s++;
					}
					if (s >= sz) {
						ll num = (t3 - t1) * (t4 - t2);
						if (mn == -1 || num < mn) mn = num;
					}
				}
			}
		}
	}
	cout << mn;
	return 0;
}