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,a,b) for(int i=int(a);i<int(b);++i)
using namespace std;
typedef long long ll;
ll INF = (1LL << 62) - 1;
int MOD = 1e9+7;
int main(){
    int N,K;
    cin >> N >> K;
    vector<ll> X(N),Y(N);
    rep(i,0,N)cin >> X[i] >> Y[i];

    ll mini = INF;
    rep(i,0,N)rep(j,0,N)rep(k,0,N)rep(l,0,N){
        ll miniX = min({X[i], X[j], X[k], X[l]});
        ll maxiX = max({X[i], X[j], X[k], X[l]});
        ll miniY = min({Y[i], Y[j], Y[k], Y[l]});
        ll maxiY = max({Y[i], Y[j], Y[k], Y[l]});
        int cnt = 0;
        rep(m,0,N){
            if(X[m] >= miniX && X[m] <= maxiX && Y[m] >= miniY && Y[m] <= maxiY)cnt++;
        }
        if(cnt >= K){
            mini = min(mini, (maxiX - miniX) * (maxiY - miniY));
        }
    }
    cout << mini << endl;
}