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;
#define ll long long

int main() {
	ll n,k; cin>>n>>k;
	vector<ll> x(n),y(n);
	for (ll i=0; i<n; i++)
		cin>>x[i]>>y[i];

	ll ans=~(1LL<<63);
	for (ll a=0; a<n; a++) {
		for (ll b=a; b<n; b++) {
			for (ll c=b; c<n; c++) {
				for (ll d=c; d<n; d++) {
					ll right = max({x[a],x[b],x[c],x[d]});
					ll left = min({x[a],x[b],x[c],x[d]});
					ll top = max({y[a],y[b],y[c],y[d]});
					ll bot = min({y[a],y[b],y[c],y[d]});
					ll area = abs((top-bot) * (right-left));
					ll contains=0;
					for (ll m=0; m<n; m++)
						if (x[m]>=left and x[m]<=right and y[m]>=bot and y[m]<=top)
							contains++;
					if (contains>=k and area<ans)
						ans=area;
				}
			}
		}
	}
	cout << ans << endl;
	return 0;
}