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<vector>
#include<algorithm>
using namespace std;
typedef long long int ll;
#define rep(i,n) for(int i=0;i<n;i++)
int main(){
	ll n, k; cin >> n >> k;
	vector<ll> x(n), y(n), xx, yy;
	rep(i, n) cin >> x[i] >> y[i];
	xx = x; yy = y;
	sort(x.begin(), x.end());
	sort(y.begin(), y.end());
	ll ans = 1LL * (x[n - 1] - x[0])*(y[n - 1] - y[0]);
	rep(a, n) {
		for (int b = a + 1; b < n; b++) {
			rep(c, n) {
				for (int d = c + 1; d < n; d++) {
					int cnt = 0;
					rep(i, n) {
						if (x[a] <= xx[i] && xx[i] <= x[b] && y[c] <= yy[i] && yy[i] <= y[d])
							cnt++;
					}if (cnt >= k)ans = min(ans, 1LL * (x[b] - x[a])*(y[d] - y[c]));
				}
			}
		}
	}cout << ans << endl;
}