Problem:
Score : 400 points

Problem Statement

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.

Sample Input 1

4 4
1 4
3 3
6 2
8 1

Sample Output 1

21

One rectangle that satisfies the condition with the minimum possible area has the following vertices: (1,1), (8,1), (1,4) and (8,4).

Its area is (8-1) × (4-1) = 21.

Sample Input 2

4 2
0 0
1 1
2 2
3 3

Sample Output 2

1

Sample Input 3

4 3
-1000000000 -1000000000
1000000000 1000000000
-999999999 999999999
999999999 -999999999

Sample Output 3

3999999996000000001

Watch out for integer overflows.

Solution in C++14 (GCC 5.4.1) (judge verdict: Wrong Answer)

#include <bits/stdc++.h>
using namespace std;
#define rep(i,n) for(int i=0;i<(n);i++)
#define rep1(i,n) for(int i=1;i<=(n);i++)
#define all(x) (x).begin(),(x).end()
#define V vector
typedef V<int> vi;
typedef V<vi> vvi;
typedef long long ll;
typedef pair<int, int> P;
typedef tuple<int, int, int> T;
constexpr auto INF = INT_MAX >> 1;
constexpr auto LINF = 5000000000000000;
constexpr auto MOD = 1000000007;

int n, k;

ll mnlec(V<P> xy) {

	ll re = LLONG_MAX;
	rep(i, n - k + 1) {
		int mxy = -INF, mny = INF;
		ll x = xy[i + k - 1].first - xy[i].first;
		rep(j, k) {
			mxy = max(mxy, xy[i + j].second);
			mny = min(mny, xy[i + j].second);
		}
		re = min(re, x * ((ll)mxy - mny));
	}

	return re;
}

int main() {

	cin >> n >> k;
	V<P> xy(n);

	rep(i, n) {
		int x, y;
		cin >> x >> y;
		xy[i] = P(x, y);
	}

	ll ans = LLONG_MAX;

	sort(all(xy));
	ans = min(ans, mnlec(xy));

	rep(i, n)swap(xy[i].first, xy[i].second);

	sort(all(xy));
	ans = min(ans, mnlec(xy));

	cout << ans << endl;

}