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 input(): return sys.stdin.readline().strip()
def mapint(): return map(int, input().split())
sys.setrecursionlimit(10**9)

N, K = mapint()
XY = [list(mapint()) for _ in range(N)]

from itertools import combinations_with_replacement as cwr

ans = 10**20
for p1, p2, p3, p4 in cwr(XY, 4):
    x1, y1 = p1
    x2, y2 = p2
    x3, y3 = p3
    x4, y4 = p4
    lx, rx = min(x1, x2, x3, x4), max(x1, x2, x3, x4)
    ly, ry = min(y1, y2, y3, y4), max(y1, y2, y3, y4)
    cnt = 0
    for x, y in XY:
        if lx<=x<=rx and ly<=y<=ry:
            cnt += 1
    if cnt>=K:
        ans = min(ans, (rx-lx)*(ry-ly))

print(ans)