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<climits>
using namespace std;

#define rep(i,n) for(int (i)=0;(i)<(n);(i)++)
#define POINT_MAX 50
#define ll long long

int main(void) {
    int n, k;
    ll x[POINT_MAX], y[POINT_MAX];
    ll ans=LONG_LONG_MAX;
    cin >> n >> k;
    rep(i, n) cin >> x[i] >> y[i];
    rep(l, n) {
        rep(r, n) {
            if (x[l] >= x[r]) continue;
            rep(b, n) {
                rep(t, n) {
                    if (y[b] >= y[t]) continue;
                    int cnt = 0;
                    rep(i, n) {
                        if (x[i]>=x[l] and x[i]<=x[r] and y[i]>=y[b] and y[i]<=y[t]) cnt++;
                    }
                    if (cnt>=k) ans=min(ans, (x[r]-x[l])*(y[t]-y[b]));
                }
            }
        }
    }
    cout << ans << endl;
    return 0; 
}