Problem:
Score : 400 points

Problem Statement

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.

Sample Input 1

4 4
1 4
3 3
6 2
8 1

Sample Output 1

21

One rectangle that satisfies the condition with the minimum possible area has the following vertices: (1,1), (8,1), (1,4) and (8,4).

Its area is (8-1) × (4-1) = 21.

Sample Input 2

4 2
0 0
1 1
2 2
3 3

Sample Output 2

1

Sample Input 3

4 3
-1000000000 -1000000000
1000000000 1000000000
-999999999 999999999
999999999 -999999999

Sample Output 3

3999999996000000001

Watch out for integer overflows.

Solution in Python (3.4.3) (judge verdict: Wrong Answer)

n, k = map(int, input().split())

x = [0 for _ in range(n)]
y = [0 for _ in range(n)]
for i in range(n):
    x[i], y[i] = map(int, input().split())

min_x = min(x)
min_y = min(y)
for i in range(n):
    x[i] -= min_x
    y[i] -= min_y

sx = sorted(x)
sy = sorted(y)

if n == k:
    print(sx[n - 1] * sy[n - 1])
    exit()

d = [[0 for _ in range(n + 1)] for _ in range(n + 1)]
for i in range(n):
    d[sx.index(x[i]) + 1][sy.index(y[i]) + 1] = 1

#for p in d: print(p)

for i in range(n + 1):
    for j in range(1, n + 1):
        d[i][j] += d[i][j - 1]

for i in range(n + 1):
    for j in range(1, n + 1):
        d[j][i] += d[j - 1][i]

sx = [0] + sx
sy = [0] + sy

a = 0
b = 1
ans = sx[n] * sy[n]
temp = 0
for p in range(n):
    for q in range(p + 1, n + 1):
        for a in range(n):
            for b in range(a + 1, n + 1):
                temp = d[q][b] - d[q][a] - d[p][b] + d[p][a]
                if temp >= k:
                    break
            if temp >= k:
                ans = min(ans, max(1, (sx[b] - sx[a + 1])) * max(1, (sy[q] - sy[p + 1])))

print(ans)