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((i)=0;(i)<(int)(n);(i)++)
typedef long long ll;
typedef pair<ll, ll> P;
const int MOD = 1000000007;
const int Maxn = 60;

ll x[Maxn], y[Maxn];

int main(){
    int i, j, k, l, n, m, p;
    cin >> n >> m;

    for (int i = 0; i < n; i++){
        cin >> x[i] >> y[i];
    }
    
    ll ans = LONG_LONG_MAX;
    REP(i, n)REP(j, n)REP(k, n)REP(l, n){
        ll cnt = 0;
        REP(p, n) if (x[i] <= x[p] && x[p] <= x[j] && y[k] <= y[p] && y[p] <= y[l]) cnt++;
        if (cnt >= m) ans = min(ans, (x[j] - x[i]) * (y[l] - y[k]));
    }

    cout << ans << endl;
    
    return 0;
}