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: Accepted)

n,k_num = map(int,input().split())
info =[list(map(int,input().split())) for i in range(n)]
li_x = []
li_y = []

for i in range(n):
 # if info[i][0] not in li_x:
    li_x.append(info[i][0])
 # if info[i][1] not in li_y:
    li_y.append(info[i][1])

li_x = sorted(li_x)
li_y = sorted(li_y)

bunpu = [[0]*n for i in range(n)]
for i in range(n):
  for j in range(n):
    if info[i][0]==li_x[j]:
      zahyo_x=j
      break
  for k in range(n):
    if info[i][1]==li_y[k]:
      zahyo_y=k
      break
  bunpu[zahyo_x][zahyo_y]=1

ruiseki = [[0]*n for i in range(n)]


for i in range(0,n):
  for j in range(0,n):
    ruiseki[i][j] = bunpu[i][j]
#横方向(j)の累積
for i in range(n):
  for j in range(1,n):
    ruiseki[i][j] = ruiseki[i][j-1] + ruiseki[i][j]
#縦方向(i)の累積
for j in range(n):
  for i in range(1,n):
    ruiseki[i][j] = ruiseki[i-1][j] + ruiseki[i][j]

#print(bunpu)
#print(ruiseki)

ans = float("inf")

for i in range(len(li_x)):
  for j in range(i,len(li_x)):
    for k in range(len(li_y)):
      for l in range(k,len(li_y)):
        count = ruiseki[j][l]
        if 0<=k-1:
          count -= ruiseki[j][k-1]
        if 0<=i-1:
          count -= ruiseki[i-1][l]
        if 0<=k-1 and 0<=i-1:
          count += ruiseki[i-1][k-1]      
        if count ==k_num:
          ans = min(ans,(li_x[j]-li_x[i])*(li_y[l]-li_y[k]))
print(ans)