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 ull unsigned long long
#define ll long long
#define ii pair<ll, ll>
#define x first
#define y second

ll n, k, a ,b;
vector<ii> v;

int main(){
    cin >> n >> k;
    for (int i = 1; i <= n; i++){
        cin >> a >> b;
        v.push_back(ii(a, b));
    }
    ull ans = 1e19;
    sort(v.begin(), v.end());
    for (int i = 0; i + k - 1 < n; i++){
        for (int j = i + k - 1; j < n; j++){
            vector<ll> q;
            for (int t = i; t <= j; t++) q.push_back(v[t].y);
            sort(q.begin(), q.end());
            for (int t = 0; t <= j - i - k + 1; t++)
            ans = min(ans, (ull)(q[t + k - 1] - q[t])*abs(v[i].x-v[j].x));
        }
    }
    cout << ans;
}