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<limits>
#include<algorithm>
using namespace std;
typedef long long ll;
const int maxn = 105;
int N, K;

int main()
{
	cin >> N >> K;
	ll x[maxn], y[maxn], a[maxn], b[maxn];
	for (int i = 0; i<N; i++) {
		cin >> a[i] >> b[i];
		x[i] = a[i], y[i] = b[i];
	}
	sort(x, x + N);
	sort(y, y + N);
	ll ans = 1ll << 62;
	for (int i = 0; i < N; i++) {
		for(int j=i+1;j<N;j++)
			for (int k = 0; k < N; k++) {
				for (int l = k + 1; l < N; l++) {
					ll sx = x[i];
					ll gx = x[j];
					ll sy = y[k];
					ll gy = y[l];
					int cnt = 0;
					for (int m = 0; m < N; m++) {
						if (a[m] >= sx&&a[m] <= gx&&b[m] >= sy&&b[m] <= gy)
							cnt++;
					}
					if (cnt >= K)
						ans = min(ans, (gx - sx)*(gy - sy));
				}
			}
	}
	cout << ans << endl;
	return 0;
}