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>
#define rep(i,N) for(ll (i)=0;(i)<(N);(i)++)
#define chmax(x,y) x=max(x,y)
#define chmin(x,y) x=min(x,y)
using namespace std;
typedef long long ll;
typedef pair<int,int> P;
const int mod = 1000000007;

int main() {
  int n, need;
  cin >> n >> need;
  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(k, n) {
        rep(s, n) {
          ll l = x[i];
          ll r = x[j];
          ll u = y[k];
          ll d = y[s];
          int cnt = 0;
          rep(kk, n) {
            if(l <= x[kk] && x[kk] <= r && d <= y[kk] && y[kk] <= u) cnt++;
          }
          if(cnt >= need) ans = min(ans, abs(r - l) * abs(u - d));
        }
      }
    }
  }
  cout << ans << endl;

}