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:
n,K=list(map(int,input().split()))
xy=sorted([list(map(int,input().split())) for _ in range(n)],key=lambda x:x[0])

dp=[[[] for _ in range(n)] for _ in range(n)]
for i in range(n):
    for j in range(i+1,n):
        for k in range(i,j+1):
            dp[i][j].append(xy[k][1])
        
        dp[i][j].sort()

ans=10**19

for x in range(K,n+1):
    for i in range(n-x+1):
        left=xy[i][0]
        right=xy[i+x-1][0]

        for j in range(len(dp[i][i+x-1])-K+1):
            down=dp[i][i+x-1][j]
            up=dp[i][i+x-1][j+K-1]

            ans=min(ans,(right-left)*(up-down))

print(ans)