Buggy python submission (verdict: Time Limit Exceeded):
from itertools import combinations, product
from functools import reduce
import bisect as bs
from collections import namedtuple

Area = namedtuple('Area', ['xinf', 'xsup', 'yinf', 'ysup'])

def tuple_int(iterable):
    return tuple(map(int, iterable.split()))

def insert_xy(line):
    x, y = map(int, line.split())
    X.insert(bs.bisect_left(X,x), x)
    Y.insert(bs.bisect_left(Y,y), y)
    return X, Y

def S_with_K_plots(X, Y, K):
    result = []
    for x, y in product(combinations(X,2), combinations(Y,2)):
        area = Area(xinf=min(x),xsup=max(x),yinf=min(y),ysup=max(y))
        S = (area.xsup-area.xinf)*(area.ysup-area.yinf)
        if count_plots(area) == K:
            result.append(S)
    return result

def count_plots(area):
    is_in_the_area = lambda x: is_in_area(x, area)
    return sum(map(is_in_the_area, plots))

def is_in_area(plot, area):
    between = lambda a, b, c:True if b <= a <= c else False
    x, y = plot
    x1, x2, y1, y2 = area
    if between(x, x1, x2) and between(y, y1, y2):
        return 1
    else:
        return 0

if __name__ == '__main__':
    with open(0) as f:
        N, K = map(int, f.readline().split())
        data = f.readlines()
    plots = list(map(tuple_int, data))
    X, Y = [], []
    for x, y in plots:
        X.append(x); Y.append(y)
    print(min(S_with_K_plots(X, Y, K)))

Fixed submission:
N, K = (int(x) for x in input().split())
Plot = [tuple(int(x) for x in input().split()) for _ in range(N)]
X = [p[0] for p in Plot]
Y = [p[1] for p in Plot]
X.sort()
Y.sort()
#全2点間で長方形の辺を作り、その内内部点がK個のものだけ面積を比較する。
ans = 10e20
from itertools import combinations
for x1, x2 in combinations(X, 2):
    for y1 in Y:
        y2 = [y for x,y in Plot if x1 <= x <= x2 and y1 <= y]
        if len(y2) < K:
            break
        y2.sort()
        S = (x2-x1)*(y2[K-1]-y1)
        ans = min(ans, S)
print(ans)

Buggy python submission (verdict: Time Limit Exceeded):
N, K = (int(x) for x in input().split())
Plot = [tuple(int(x) for x in input().split()) for _ in range(N)]
X = [p[0] for p in Plot]
Y = [p[1] for p in Plot]
X.sort()
Y.sort()
#全2点間で長方形の辺を作り、その内内部点がK個のものだけ面積を比較する。
ans = 10e20
from itertools import combinations
for x1, x2 in combinations(X, 2):
    for y1, y2 in combinations(Y, 2):
        cnt = sum(x1 <= x <= x2 and y1 <= y <= y2 for x,y in Plot)
        if cnt == K:
            S = (x2-x1)*(y2-y1)
            ans = min(ans, S)
print(ans)


Fixed submission:
N, K = (int(x) for x in input().split())
Plot = [tuple(int(x) for x in input().split()) for _ in range(N)]
X = [p[0] for p in Plot]
Y = [p[1] for p in Plot]
X.sort()
Y.sort()
#全2点間で長方形の辺を作り、その内内部点がK個のものだけ面積を比較する。
ans = 10e20
from itertools import combinations
for x1, x2 in combinations(X, 2):
    for y1 in Y:
        y2 = [y for x,y in Plot if x1 <= x <= x2 and y1 <= y]
        if len(y2) < K:
            break
        y2.sort()
        S = (x2-x1)*(y2[K-1]-y1)
        ans = min(ans, S)
print(ans)

Buggy python submission (verdict: Time Limit Exceeded):
N, K = (int(x) for x in input().split())
Plot = [tuple(int(x) for x in input().split()) for _ in range(N)]
X = [p[0] for p in Plot]
Y = [p[1] for p in Plot]
X.sort()
Y.sort()
#全2点間で長方形の辺を作り、その内内部点がK個のものだけ面積を比較する。
ans = 10e20
from itertools import combinations
for x1, x2 in combinations(X, 2):
    for y1, y2 in combinations(Y, 2):
        S = (x2-x1)*(y2-y1)
        cnt = sum(x1 <= p[0] <= x2 and y1 <= p[1] <= y2 for p in Plot)
        if cnt == K and S != 0:
            ans = min(ans, S)
print(ans)


Fixed submission:
N, K = (int(x) for x in input().split())
Plot = [tuple(int(x) for x in input().split()) for _ in range(N)]
X = [p[0] for p in Plot]
Y = [p[1] for p in Plot]
X.sort()
Y.sort()
#全2点間で長方形の辺を作り、その内内部点がK個のものだけ面積を比較する。
ans = 10e20
from itertools import combinations
for x1, x2 in combinations(X, 2):
    for y1 in Y:
        y2 = [y for x,y in Plot if x1 <= x <= x2 and y1 <= y]
        if len(y2) < K:
            break
        y2.sort()
        S = (x2-x1)*(y2[K-1]-y1)
        ans = min(ans, S)
print(ans)

Buggy python submission (verdict: Time Limit Exceeded):
N, K = (int(x) for x in input().split())
Plot = [tuple(int(x) for x in input().split()) for _ in range(N)]
X = [p[0] for p in Plot]
Y = [p[1] for p in Plot]
X.sort()
Y.sort()
#全2点間で長方形の辺を作り、その内内部点がK個のものだけ面積を比較する。
ans = 10e20
from itertools import combinations
for x1, x2 in combinations(X, 2):
    for y1, y2 in combinations(Y, 2):
        S = (x2-x1)*(y2-y1)
        cnt = 0
        for p in Plot:
            if x1 <= p[0] <= x2 and y1 <= p[1] <= y2:
                cnt += 1
        if cnt == K and S != 0:
            ans = min(ans, S)
print(ans)


Fixed submission:
N, K = (int(x) for x in input().split())
Plot = [tuple(int(x) for x in input().split()) for _ in range(N)]
X = [p[0] for p in Plot]
Y = [p[1] for p in Plot]
X.sort()
Y.sort()
#全2点間で長方形の辺を作り、その内内部点がK個のものだけ面積を比較する。
ans = 10e20
from itertools import combinations
for x1, x2 in combinations(X, 2):
    for y1 in Y:
        y2 = [y for x,y in Plot if x1 <= x <= x2 and y1 <= y]
        if len(y2) < K:
            break
        y2.sort()
        S = (x2-x1)*(y2[K-1]-y1)
        ans = min(ans, S)
print(ans)

Buggy python submission (verdict: Time Limit Exceeded):
N, K = (int(x) for x in input().split())
Plot = [tuple(int(x) for x in input().split()) for _ in range(N)]
X = [p[0] for p in Plot]
Y = [p[1] for p in Plot]
X.sort()
Y.sort()
#全2点間で長方形の辺を作り、その内内部点がK個のものだけ面積を比較する。
#2点p,qが頂点にある長方形は確かに最小の長方形を成す
#2点が頂点でない場合、内部点の個数が変わらないように適当な2点p,qを取って頂点とすることでより小さい長方形を形成できる
ans = 10e20
while len(X) != 0:
    x1 = X[0]
    X.pop(0)
    for x2 in X:
        Ycopy = Y.copy()
        while len(Ycopy) != 0:
            y1 = Ycopy[0]
            Ycopy.pop(0)
            for y2 in Ycopy:
                    S = (x2-x1)*(y2-y1)
                    cnt = 0
                    for p in Plot:
                        if x1 <= p[0] <= x2 and y1 <= p[1] <= y2:
                            cnt += 1
                    if cnt == K and S != 0:
                        ans = min(ans, S)
print(ans)

Fixed submission:
N, K = (int(x) for x in input().split())
Plot = [tuple(int(x) for x in input().split()) for _ in range(N)]
X = [p[0] for p in Plot]
Y = [p[1] for p in Plot]
X.sort()
Y.sort()
#全2点間で長方形の辺を作り、その内内部点がK個のものだけ面積を比較する。
ans = 10e20
from itertools import combinations
for x1, x2 in combinations(X, 2):
    for y1 in Y:
        y2 = [y for x,y in Plot if x1 <= x <= x2 and y1 <= y]
        if len(y2) < K:
            break
        y2.sort()
        S = (x2-x1)*(y2[K-1]-y1)
        ans = min(ans, S)
print(ans)

Buggy python submission (verdict: Time Limit Exceeded):
N, K = (int(x) for x in input().split())
Plot = [tuple(int(x) for x in input().split()) for _ in range(N)]
X = [p[0] for p in Plot]
Y = [p[1] for p in Plot]
#全2点間で長方形の辺を作り、その内内部点がK個のものだけ面積を比較する。
#2点p,qが頂点にある長方形は確かに最小の長方形を成す
#2点が頂点でない場合、内部点の個数が変わらないように適当な2点p,qを取って頂点とすることでより小さい長方形を形成できる
ans = 10e20
for x1 in X:
    for x2 in X:
        if x1 < x2:
            minx, maxx = x1, x2
        else:
            minx, maxx = x2, x1
        for y1 in Y:
            for y2 in Y:
                if y1 < y2:
                    miny, maxy = y1, y2
                else:
                    miny, maxy = y2, y1
                S = (maxx-minx)*(maxy-miny)
                cnt = 0
                for r in Plot:
                    if minx <= r[0] <= maxx and miny <= r[1] <= maxy:
                        cnt += 1
                if cnt == K and S != 0:
                    ans = min(ans, S)
print(ans)

Fixed submission:
N, K = (int(x) for x in input().split())
Plot = [tuple(int(x) for x in input().split()) for _ in range(N)]
X = [p[0] for p in Plot]
Y = [p[1] for p in Plot]
X.sort()
Y.sort()
#全2点間で長方形の辺を作り、その内内部点がK個のものだけ面積を比較する。
ans = 10e20
from itertools import combinations
for x1, x2 in combinations(X, 2):
    for y1 in Y:
        y2 = [y for x,y in Plot if x1 <= x <= x2 and y1 <= y]
        if len(y2) < K:
            break
        y2.sort()
        S = (x2-x1)*(y2[K-1]-y1)
        ans = min(ans, S)
print(ans)