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())
s = []
for i in range(n):#h:高さ
    s.append([int(m) for m in input().split()])

count = 0
recli = []
if k == 2:
    for i in range(n):
        for j in range(i + 1, n):
            larx = max(s[i][0], s[j][0])
            smax = min(s[i][0], s[j][0])
            lary = max(s[i][1], s[j][1])
            smay = min(s[i][1], s[j][1])
            rec = (larx - smax) * (lary - smay)
            for l in range(n):
                if smax <= s[l][0] <= larx and smay <= s[l][1] <= lary:
                    count += 1
            if count >= k:
                recli.append(rec)
            count = 0

elif k == 3:
    for i in range(n):
        for j in range(i + 1, n):
            for p in range(j + 1, n):
                larx = max(s[i][0], s[j][0], s[p][0])
                smax = min(s[i][0], s[j][0], s[p][0])
                lary = max(s[i][1], s[j][1], s[p][1])
                smay = min(s[i][1], s[j][1], s[p][1])
                rec = (larx - smax) * (lary - smay)
                for l in range(n):
                    if smax <= s[l][0] <= larx and smay <= s[l][1] <= lary:
                        count += 1
                if count >= k:
                    recli.append(rec)
                count = 0
else:
    for i in range(n):
        for j in range(i + 1, n):
            for p in range(j + 1, n):
                for q in range(p + 1, n):
                    larx = max(s[i][0], s[j][0], s[p][0], s[q][0])
                    smax = min(s[i][0], s[j][0], s[p][0], s[q][0])
                    lary = max(s[i][1], s[j][1], s[p][1], s[q][1])
                    smay = min(s[i][1], s[j][1], s[p][1], s[q][1])
                    rec = (larx - smax) * (lary - smay)
                    for l in range(n):
                        if smax <= s[l][0] <= larx and smay <= s[l][1] <= lary:
                            count += 1
                    if count >= k:
                        recli.append(rec)
                    count = 0

print(min(recli))