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 PYTHON):

Solution:
from collections import defaultdict, Counter
from itertools import combinations
INF = float("inf")


memo1 = {}
memo2 = {}

def ok(y1, y2, x1, x2, yd, yd2, xd, xd2, K):
    if (y1, y2) in memo1:
        y = memo1[(y1, y2)]
    else:
        a = yd2[y1]
        b = yd[y2]
        y = b.difference(a)
        memo1[(y1, y2)] = y

    if (x1, x2) in memo2:
        x = memo2[(x1, x2)]
    else:
        c = xd2[x1]
        d = xd[x2]
        x = d.difference(c)
        memo2[(x1, x2)] = x

    # print(a, b, c, d)
    # print(y, x)

    n = len(y & x)

    return n >= K


def main():
    import time
    N, K = map(int, raw_input().split())
    ys, xs = [], []
    for i in range(N):
        x, y = map(int, raw_input().split())
        ys.append((y, i))
        xs.append((x, i))

    ys.sort()
    yd = defaultdict(set)
    yd2 = defaultdict(set)
    old = set()
    for y, i in ys:
        yd2[y] = old.copy()
        old.add(i)
        yd[y] = old.copy()

    xs.sort()
    xd = defaultdict(set)
    xd2 = defaultdict(set)
    old = set()
    for x, i in xs:
        xd2[x] = old.copy()
        old.add(i)
        xd[x] = old.copy()

    ans = INF

    # print(yd)
    # print(xd)
    #
    # print(ok(1, 4, 1, 8, yd, yd2, xd, xd2, K))
    for i, j in combinations(range(N), 2):
        for k, l in combinations(range(N), 2):
            a, b, c, d = ys[i], ys[j], xs[k], xs[l]
            y1 = min(a[0], b[0])
            y2 = max(a[0], b[0])

            x1 = min(c[0], d[0])
            x2 = max(c[0], d[0])

            kkk = abs(x1 - x2) * abs(y1 - y2)
            if kkk < ans:
                # print(i, j)
                # print(x1, x2, abs(x1 - x2))
                # print(y1, y2, abs(y1 - y2))
                # print(ok(y1, y2, x1, x2, yd, yd2, xd, xd2, K))
                if ok(y1, y2, x1, x2, yd, yd2, xd, xd2, K):
                    ans = kkk

    print(ans)

if __name__ == '__main__':
    main()