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,n) for(int i = 0; i < n; ++i)
typedef long long ll;
const ll MOD = 1e9+7;



int main(){
    int n, k; cin >> n >> k;
    vector<ll> x(n),y(n); rep(i,n) cin >> x[i] >> y[i];
    ll ans = 4000000000000000002;
    for(int x1 = 0; x1 < n; ++x1){ // 左端
        for(int x2 = 0; x2 < n; ++x2){ // 右端
            for(int y1 = 0; y1 < n; ++y1){ // 下端
                for(int y2 = 0; y2 < n; ++y2){ // 上端
                    int cnt = 0;
                    for(int i = 0; i < n; ++i){
                        if(x[i] >= x[x1] && x[i] <= x[x2] && y[i] >= y[y1] && y[i] <= y[y2]) cnt++;
                    }
                    if(cnt >= k) ans = min(ans, (y[y2]-y[y1])*(x[x2]-x[x1]));
                }
            }
        }
    }    
    cout << ans << endl;
}