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;
typedef long long ll;
#define rep(i, n) for (int i = 0; i < (n); i++)

int main() {
    int n, k;
    cin >> n >> k;
    vector<ll> x(n), y(n);
    rep(i, n) cin >> x[i] >> y[i];

    ll ans = LLONG_MAX;
    rep(i, n) rep(j, n) rep(s, n) rep(t, n) {
        ll xl = x[i];
        ll xr = x[j];
        ll yl = y[s];
        ll yr = y[t];
        if (xl >= xr || yl >= yr) continue;
        int cnt = 0;
        rep(k, n) {
            if(xl <= x[k] && x[k] <= xr && yl <= y[k] && y[k] <= yr){
                cnt++;
            }
        }
        if(cnt >= k){
            ans = min(ans, (xr - xl) * (yr - yl));
        }
    }
    cout << ans << endl;
}