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 PYTHON):

Solution:
N,K = map(int, raw_input().split(" "))

points = []
pointsx = []
pointsy = []

smin = 0

for i in range(N):
    x,y = map(int, raw_input().split(" "))
    pointsx.append(x)
    pointsy.append(y)

spx = sorted(pointsx)

for i in range(N-K+1):
    for h in range(N-K-i+1):
        yneed = []
        for k in range(N):
            if pointsx[k]>=spx[i] and pointsx[k]<=spx[i+K+h-1]:
                yneed.append(pointsy[k])
        spy = sorted(yneed)
        ylength = 0
        xlength = spx[i+K+h-1]-spx[i]
        for k in range(len(spy) - K + 1):
            if ylength == 0: ylength = spy[k+K-1]-spy[k]
            elif ylength > spy[k+K-1]-spy[k]: ylength = spy[k+K-1]-spy[k]
        if smin == 0: smin = ylength * xlength
        elif smin > ylength * xlength:
            smin = ylength * xlength


print smin