Buggy python submission (verdict: Time Limit Exceeded):
def solve(N, K, XYs):
    ans = 10 ** 19 + 1
    Ys = [y for x, y in XYs]
    Xs = [x for x, y in XYs]
    for y1 in Ys:
        for y2 in Ys:
            if y1 >= y2:
                continue
            for x1 in Xs:
                for x2 in Xs:
                    if x1 >= x2:
                        continue
                    y1, y2 = min(y1, y2), max(y1, y2)
                    x1, x2 = min(x1, x2), max(x1, x2)
                    if len([(x, y) for x, y in XYs if x1 <= x <= x2 and y1 <= y <= y2]) >= K:
                        ans = min(ans, abs(y2 - y1) * abs(x2 - x1))
    return ans

if __name__ == "__main__":
    N, K = tuple(map(int, input().split(" ")))
    XYs = [tuple(map(int, input().split(" "))) for _ in range(N)]
    print(solve(N, K, XYs))


Fixed submission:

def solve(N, K, XYs):
    ans = 10 ** 19 + 1

    XYs.sort(key=lambda x: x[0])
    for i in range(N):
        for j in range(i+K-1, N):
            narrowedXY = XYs[i:j+1]
            narrowedXY.sort(key=lambda x: x[1])
            for y1 in range(len(narrowedXY)):
                for y2 in range(y1+K, len(narrowedXY)+1):
                    min_x = XYs[i][0]
                    max_x = XYs[j][0]
                    ys = [xy[1] for xy in narrowedXY[y1:y2]]
                    max_y = max(ys)
                    min_y = min(ys)
                    ans = min(ans, abs(max_x - min_x) * abs(max_y - min_y))

    return ans

if __name__ == "__main__":
    N, K = tuple(map(int, input().split(" ")))
    XYs = [tuple(map(int, input().split(" "))) for _ in range(N)]
    print(solve(N, K, XYs))

Buggy python submission (verdict: Time Limit Exceeded):
from itertools import combinations

def solve(N, K, XYs):
    ans = 10 ** 19 + 1
    Ys = [y for x, y in XYs]
    Xs = [x for x, y in XYs]
    for y1, y2 in combinations(Ys, r=2):
        for x1, x2 in combinations(Xs, r=2):
            y1, y2 = min(y1, y2), max(y1, y2)
            x1, x2 = min(x1, x2), max(x1, x2)
            if len([(x, y) for x, y in XYs if x1 <= x <= x2 and y1 <= y <= y2]) >= K:
                ans = min(ans, abs(y2 - y1) * abs(x2 - x1))
    return ans


if __name__ == "__main__":
    N, K = tuple(map(int, input().split(" ")))
    XYs = [tuple(map(int, input().split(" "))) for _ in range(N)]
    print(solve(N, K, XYs))


Fixed submission:

def solve(N, K, XYs):
    ans = 10 ** 19 + 1

    XYs.sort(key=lambda x: x[0])
    for i in range(N):
        for j in range(i+K-1, N):
            narrowedXY = XYs[i:j+1]
            narrowedXY.sort(key=lambda x: x[1])
            for y1 in range(len(narrowedXY)):
                for y2 in range(y1+K, len(narrowedXY)+1):
                    min_x = XYs[i][0]
                    max_x = XYs[j][0]
                    ys = [xy[1] for xy in narrowedXY[y1:y2]]
                    max_y = max(ys)
                    min_y = min(ys)
                    ans = min(ans, abs(max_x - min_x) * abs(max_y - min_y))

    return ans

if __name__ == "__main__":
    N, K = tuple(map(int, input().split(" ")))
    XYs = [tuple(map(int, input().split(" "))) for _ in range(N)]
    print(solve(N, K, XYs))

Buggy python submission (verdict: Time Limit Exceeded):
from itertools import combinations


def solve(N, K, XYs):
    ans = 10 ** 19 + 1
    for candidate in combinations(XYs, r=K):
        candidate = list(candidate)
        xs = sorted([x for x, y in candidate])
        max_x = xs[-1]
        min_x = xs[0]
        ys = sorted([y for x, y in candidate])
        max_y = ys[-1]
        min_y = ys[0]

        ans = min(ans, abs(max_x - min_x) * abs(max_y - min_y))
    return ans


if __name__ == "__main__":
    N, K = tuple(map(int, input().split(" ")))
    XYs = [tuple(map(int, input().split(" "))) for _ in range(N)]
    print(solve(N, K, XYs))


Fixed submission:

def solve(N, K, XYs):
    ans = 10 ** 19 + 1

    XYs.sort(key=lambda x: x[0])
    for i in range(N):
        for j in range(i+K-1, N):
            narrowedXY = XYs[i:j+1]
            narrowedXY.sort(key=lambda x: x[1])
            for y1 in range(len(narrowedXY)):
                for y2 in range(y1+K, len(narrowedXY)+1):
                    min_x = XYs[i][0]
                    max_x = XYs[j][0]
                    ys = [xy[1] for xy in narrowedXY[y1:y2]]
                    max_y = max(ys)
                    min_y = min(ys)
                    ans = min(ans, abs(max_x - min_x) * abs(max_y - min_y))

    return ans

if __name__ == "__main__":
    N, K = tuple(map(int, input().split(" ")))
    XYs = [tuple(map(int, input().split(" "))) for _ in range(N)]
    print(solve(N, K, XYs))