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>
#include <algorithm>
#include <queue>
using namespace std;
int main(){
	int N, K; 
	cin >> N >> K; 
	long long int X[55] = {}; 
	long long int Y[55] = {}; 
	for(int i = 0; i < N; i++){
		cin >> X[i] >> Y[i];
	}
	long long int ans = 4e18; 
	for(int l = 0; l < N; l++){
		for(int r = l+1; r < N; r++){
			for(int d = 0; d < N; d++){
				for(int u = d+1; u < N; u++){
					int count = 0; 
					for(int i = 0; i < N; i++){
						if(X[i] <= max(X[l], X[r]) && X[i] >= min(X[l],X[r]) && Y[i] <= max(Y[d],Y[u]) && Y[i] >= min(Y[d],Y[u])){
							count ++; 
						}
					if(count >= K){
						long long int area = abs(X[l] - X[r]) * abs(Y[d] - Y[u]); 
						ans = min(ans, area); 
					}
					}
				}
			}
		}
	}
	cout << ans << endl; 
}