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;

#define rep(i, a, b) for (int i = (a); i < (b); ++i)
#define sz(s) (int)s.size()

int main() {
    int n, k;
    cin >> n >> k;
    vector<int> x(n), y(n);
    vector<int> xs(n), ys(n);
    rep(i, 0, n) {
        cin >> x[i] >> y[i];
        xs[i] = x[i]; ys[i] = y[i];
    }
    sort(xs.begin(), xs.end());
    sort(ys.begin(), ys.end());
    long long area = 1LL * (xs.back() - xs[0]) * (ys.back() - ys[0]);
    rep(lx, 0, n) rep(rx, lx, n) rep(ly, 0, n) rep(ry, ly, n) {
        int ps = 0;
        rep(i, 0, n) if (xs[lx] <= x[i] && x[i] <= xs[rx] && ys[ly] <= y[i] && y[i] <= ys[ry])
            ++ps;
        if (ps >= k) area = min(area, 1LL * (xs[rx] - xs[lx]) * (ys[ry] - ys[ly]));
    }
    cout << area << '\n';
}