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())
graph = []
Y = []
X = []
for _ in range(n):
    x, y = map(int, input().split())
    graph.append([x, y])
    Y.append(y)
    X.append(x)

Y.sort()
X.sort()
ans = []
for sx in range(n):
    for ex in range(n-1, sx, -1):
        for sy in range(n):
            for ey in range(n-1, sy, -1):
                x1, x2, y1, y2 = X[sx], X[ex], Y[sy], Y[ey]
                count = len([True for x, y in graph if x1 <= x <= x2 and y1 <= y <= y2])
                if count >= k:
                    ans.append((x2-x1)*(y2-y1))
                else:
                    break

print(min(ans))