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 (ll i = (a); i < (b); i++)
typedef uint64_t ull;
typedef int64_t ll;
typedef std::pair<ll, ll> PLL;

signed main() {
    ll N,K;
    cin>>N>>K;
    vector<ll> x(N),y(N);
    rep(i,0,N){
        cin>>x[i]>>y[i];
    }

    ll ans = 1ll << 62;
    rep(i,0,N)
    rep(j,0,N)
    rep(k,0,N)
    rep(l,0,N) {
        ll lx = x[i];
        ll ux = x[j];
        ll ly = y[k];
        ll uy = y[l];
        ll n = 0;
        rep(i,0,N){
            if (lx<=x[i] && x[i]<=ux && ly<=y[i] && y[i]<=uy){
                n++;
            }
        }
        if (n >= K){
            ans = min(ans, (ux-lx)*(uy-ly));
        }
    }
    cout<<ans<<endl;
    return 0;
}