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 = map(int, input().split())
P = [tuple(map(int, input().split())) for _ in range(N)]
X = sorted([p[0] for p in P])
Y = sorted([p[1] for p in P])

ans = 10**20
for i in range(N-1):
    for j in range(i+1, N):
        x0 = X[i]
        x1 = X[j]

        for k in range(N-1):
            for l in range(k+1, N):
                y0 = Y[k]
                y1 = Y[l]

                c = 0
                for m in range(N):
                    if x0 <= P[m][0] <= x1 and y0 <= P[m][1] <= y1:
                        c += 1

                if c >= K:
                    ans = min(ans, (x1-x0)*(y1-y0))

print(ans)