Buggy python submission (verdict: Time Limit Exceeded):
from collections import defaultdict, Counter
from itertools import combinations
INF = float("inf")


def main():
    N, K = map(int, input().split())
    points = []
    for i in range(N):
        x, y = map(int, input().split())
        points.append((y, x))

    ans = INF
    for i in range(N):
        for j in range(N):
            for k in range(N):
                for l in range(N):
                    y1, y2, x1, x2 = points[i][0], points[j][0], points[k][1], points[l][1]

                    n = 0
                    for p in points:
                        n += y1 <= p[0] <= y2 and x1 <= p[1] <= x2
                    if n >= K:
                        ans = min(ans, abs(y1 - y2) * abs(x1 - x2))
    print(ans)


if __name__ == '__main__':
    main()


Fixed submission:
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()

Buggy python submission (verdict: Time Limit Exceeded):
from collections import defaultdict, Counter
from itertools import product, groupby, count, permutations, combinations
from math import pi, sqrt
from collections import deque
from bisect import bisect, bisect_left, bisect_right
INF = float("inf")


memo1 = {}
memo2 = {}

def ok(y1, y2, x1, x2, yd, yd2, xd, xd2, K):
    global memo1, memo2
    if (y1, y2) in memo1:
        a, b = memo1[(y1, y2)]
    else:
        a = yd2[y1]
        b = yd[y2]
        memo1[(y1, y2)] = (a, b)
    y = b.difference(a)

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

    x = d.difference(c)
    # print(a, b, c, d)
    # print(y, x)

    n = len(y & x)

    return n >= K


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


Fixed submission:
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()

Buggy python submission (verdict: Time Limit Exceeded):
from collections import defaultdict, Counter
from itertools import product, groupby, count, permutations, combinations
from math import pi, sqrt
from collections import deque
from bisect import bisect, bisect_left, bisect_right
INF = float("inf")



def ok(y1, y2, x1, x2, yd, yd2, xd, xd2, K):

    a = yd2[y1]
    b = yd[y2]
    y = b.difference(a)
    c = xd2[x1]
    d = xd[x2]
    x = d.difference(c)
    # print(a, b, c, d)
    # print(y, x)

    n = len(y & x)

    return n >= K


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

            # 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 = min(ans, abs(x1 - x2) * abs(y1 - y2))

    print(ans)


if __name__ == '__main__':
    main()


Fixed submission:
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()

Buggy python submission (verdict: Time Limit Exceeded):
from collections import defaultdict, Counter
from itertools import product, groupby, count, permutations, combinations
from math import pi, sqrt
from collections import deque
from bisect import bisect, bisect_left, bisect_right
INF = float("inf")



def ok(y1, y2, x1, x2, yd, yd2, xd, xd2, K):

    a = yd2[y1]
    b = yd[y2]
    y = b.difference(a)
    c = xd2[x1]
    d = xd[x2]
    x = d.difference(c)
    # print(a, b, c, d)
    # print(y, x)

    n = len(y & x)

    return n >= K


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

            # 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 = min(ans, abs(x1 - x2) * abs(y1 - y2))

    print(ans)


if __name__ == '__main__':
    main()


Fixed submission:
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()