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;
using ll = long long;
using ld = long double;
#define rep(i,n) for(int i=0;i<(int)(n);i++)
#define reps(i,s,n) for(int i=(int)(s);i<(int)(n);i++)
const ll mod = 1e9 + 7;
const ll INF = 1e20;
int main() {
	cin.sync_with_stdio(false);
	int N, K;
	cin >> N >> K;
	vector<ll>x(N), y(N);
	rep(i, N) {
		cin >> x[i] >> y[i];
	}
	ll minx, maxx, miny, maxy,ans=INF;
	rep(i, N) {
		minx = x[i];
		rep(j, N) {
			maxx = x[j];
			if (minx >= maxx)continue;
			rep(k, N) {
				miny = y[k];
				rep(l, N) {
					maxy = y[l];
					if (miny >= maxy)continue;
					int cnt = 0;
					rep(s, N) {
						if (x[s] >= minx&&x[s] <= maxx&&y[s] >= miny&&y[s] <= maxy)cnt++;
					}
					if (cnt >= K)ans = min(ans, (maxx - minx)*(maxy - miny));
				}
			}
		}
	}
	cout << ans << endl;
	return 0;
}