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:
import sys
def LI(): return [int(x) for x in sys.stdin.readline().split()]

N,K = LI()
p = []
for i in range(N):
    a,b = LI()
    p.append((a,b,i))
sx = sorted(p)
ans = 10**50
for x,y,i in sx:
    for x2,y2,i2 in sx:
        if x2 <= x:
            continue
        points = sx.index((x2,y2,i2)) - sx.index((x,y,i)) + 1
        if points < K:
            continue
        sy = sorted(sx[sx.index((x,y,i)):sx.index((x2,y2,i2))+1],key=lambda sx: sx[1])
        for j in range(len(sy)-K+1):
            if sy[j][1] <= y and y2 <= sy[j+K-1][1]:
                ans = min(ans, (x2 - x) * (sy[j+K-1][1]-sy[j][1])) 
print(ans)