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())
X = []
Y = []
for _ in range(N):
    x, y = map(int, input().split())
    X.append(x)
    Y.append(y)
Xs = sorted(X)
Ys = sorted(Y)
ans = float('inf')
for left in range(N - 1):
    for right in range(left + 1, N):
        for down in range(N - 1):
            for up in range(down + 1, N):
                count = 0
                for i in range(N):
                    if Xs[left] <= X[i] <= Xs[right] and Ys[down] <= Y[i] <= Ys[up]:
                            count += 1
                if count >= K:
                    ans = min(ans, (Xs[right] - Xs[left]) * (Ys[up] - Ys[down]))
print(ans)