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())
ps = [tuple(map(int,input().split())) for i in range(n)]

sx = sorted(ps,key = lambda x: x[0]) # x座標でソート
nx = list(enumerate(sx)) # 頂点番号を付加
ans = 5e18

for f, (x1,y1) in nx[:n-k+1]: # 左辺の頂点
    for e, (x2,y2) in nx[f+k-1:]: # 右辺の頂点
        dx = x2 - x1 # 横
        sy = sorted(y for x,y in sx[f:e+1]) # 含まれる頂点をy座標でソート
        for y3,y4 in zip(sy,sy[k-1:]): # y3=下辺の頂点，y4=上辺の頂点
            if y3 <= y1 and y4 >= y2: # 左右辺の頂点を含むこと
                ans = min(ans, dx * (y4 - y3))

print(ans)