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;

typedef long long ll;

const int N = 51;

pair<ll,ll> pts[N];
ll x[N], y[N];

int main () {
	int n, k; cin >> n >> k;
	for (int i = 0; i < n; i++) {
		cin >> x[i] >> y[i];
		pts[i] = {x[i], y[i]};
	}
	sort(x, x+n); sort(y, y+n);
	ll ans = (x[n-1]-x[0])*(y[n-1]-y[0]);
	for (int x0 = 0; x0 < n; x0++) {
		for (int y0 = 0; y0 < n; y0++) {
			for (int x1 = x0+1; x1 < n; x1++) {
				for (int y1 = y0+1; y1 < n; y1++) {
					ll temp = (x[x1]-x[x0])*(y[y1]-y[y0]);
					if (temp < ans) {
						int cnt = 0;
						for (int i = 0; i < n; i++)
							if (x[x0] <= pts[i].first and pts[i].first <= x[x1] and y[y0] <= pts[i].second and pts[i].second <= y[y1])
								cnt++;
						if (cnt >= k)
							ans = temp;
					}
				}
			}
		}
	}
	cout << ans << endl;
	return 0;
}