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>

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 x[50] = {};
	ll y[50] = {};
	ll s = (ll)1 << 62;

	ll n, K; cin >> n >> K;
	rep(i, 0, n)cin >> x[i] >> y[i];
	rep(i, 0, n) {
		rep(j, 0, n) {
			rep(k, 0, n) {
				rep(l, 0, n) {
					ll cnt = 0;
					rep(g, 0, n) {
						if (x[i] <= x[g] && x[g] <= x[j] && y[k] <= y[g] && y[g] <= y[l]) {
							cnt++;
						}
					}
					if (cnt >= K) {
						s = min(s, abs(x[i] - x[j]) * abs(y[k] - y[l]));
					}
				}
			}
		}
	}

	cout << s << endl;

	return 0;
}