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:
from itertools import product,combinations
N,K=map(int,input().split())
L=[tuple(map(int,input().split())) for i in range(N)]
ans=10**37
def f(i,j,k,l):
    n=0
    s=min(L[j][0],L[i][0])
    t=max(L[j][0],L[i][0])
    u=min(L[k][1],L[l][1])
    w=max(L[k][1],L[l][1])
    for e in L:
        if s<=e[0]<=t and u<=e[1]<=w:
            n+=1
    if n>=K:
        return (t-s)*(w-u)
    return 10**37
for i,j in combinations(range(N),2):
    for k,l in combinations(range(N),2):
        #print(i,j,k,l)
        ans=min(ans,f(i,j,k,l))
print(ans)