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 <algorithm>
#include <string>
#include <vector>
#include <map>
using namespace std;
typedef long long  ll;
#define rep(i,s,n)for(ll i=s;i<n;i++)
#define repe(i,s,n)for(ll i=s;i<=n;i++)

int main() {
	ll n, k; cin >> n >> k;
	ll y[50] = {};
	ll x[50] = {};
	rep(i, 0, n) {
		cin >> x[i] >> y[i];
	}

	ll rect = 1e20;
	rep(y1, 0, n) {
		rep(y2, 0, n) {
			rep(x1, 0, n) {
				rep(x2, 0, n) {
					ll cnt_k = 0;
					rep(k, 0, n) {
						if (x[x1] <= x[k] && x[k] <= x[x2] && y[y1] <= y[k] && y[k] <= y[y2]) {
							cnt_k++;
						}
					}
					if (cnt_k >= k) {
						rect = min(rect, abs(x[x1] - x[x2])* abs(y[y1] - y[y2]));
					}
				}
			}
		}
	}
	cout << rect << endl;

	return 0;
}