Problem:
Score : 400 points

Problem Statement

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.

Sample Input 1

4 4
1 4
3 3
6 2
8 1

Sample Output 1

21

One rectangle that satisfies the condition with the minimum possible area has the following vertices: (1,1), (8,1), (1,4) and (8,4).

Its area is (8-1) × (4-1) = 21.

Sample Input 2

4 2
0 0
1 1
2 2
3 3

Sample Output 2

1

Sample Input 3

4 3
-1000000000 -1000000000
1000000000 1000000000
-999999999 999999999
999999999 -999999999

Sample Output 3

3999999996000000001

Watch out for integer overflows.

Solution in Python (3.4.3) (judge verdict: Time Limit Exceeded)




N,K = map(int, input().split())
XY = [tuple(map(int, input().split())) for _ in range(N)]

"""
辺の上に点が乗っていても四角形の中に含まれると見なされるので、辺はいずれかの点の上を通るように引くと面積を小さくできる
各点のx,yをsetで持っておいて、全探索できるか？
→ N <= 50なので4つの辺の選び方が50**4、この範囲にK個以上入っているかでさらに *50なので間に合うか微妙？
小さい値で ^5 なので、間に合うかも
"""

LR = [] # left,right
TB = [] # top, bottom
for x,y in XY:
    LR.append(x)
    TB.append(y)


LR = list(set(LR))
LR.sort()
TB = list(set(TB))
TB.sort()


def more_than_K(l,r,t,b):
    cnt = 0
    for x,y in XY:
        if l <= x <= r and b <= y <= t:
            cnt += 1
    return cnt >= K

ans = float("inf")
for p in range(len(LR)):
    for q in range(p+1, len(LR)):
        for r in range(len(TB)):
            for s in range(r+1, len(TB)):

                if more_than_K(LR[p], LR[q], TB[s], TB[r]):
                    ans = min(ans, (LR[q] - LR[p]) * (TB[s] - TB[r]))


print(ans)