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 PYTHON3):

Solution:
# coding: utf-8
# Your code here!

import sys
sys.setrecursionlimit(10**6)
readline = sys.stdin.readline

#n = int(input())
#n,a = [int(i) for i in readline().split()]
n,k = [int(i) for i in readline().split()]
xy = [[int(i) for i in readline().split()] for i in range(n)]

xy.sort()
#print(xy)
ans = 4*10**18+10
for i in range(n):
    for j in range(i+k-1,n):
        dx = xy[j][0] - xy[i][0]
        y = sorted(xy[k][1] for k in range(i,j+1))
#        print(y,i,j)
        L = len(y)-k+1
        for i in range(L):
            dy = y[i+k-1]-y[i]
            ans = min(ans,dy*dx)
        


print(ans)