Harryxun/testdata huggingface dataset:
Buggy python submission (verdict: Time Limit Exceeded):
from collections import defaultdict
import sys,heapq,bisect,math,itertools,string
sys.setrecursionlimit(10**8)
INF = float('inf')
mod = 10**9+7
AtoZ = [chr(i) for i in range(65,65+26)]
atoz = [chr(i) for i in range(97,97+26)]

N,W = map(int,(input().split()))
ww = []
vv = []

for i in range(N):
	w,v = map(int,(input().split()))
	ww.append(w)
	vv.append(v)

dp =  [[0 for i in range(W+1)] for j in range(N+1)]

for i in range(1,N+1):
	weight = ww[i-1]
	value = vv[i-1]
	for j in range(W+1):
		if j >= weight:
			dp[i][j] = max(dp[i-1][j],dp[i-1][j-weight]+value)
		else:
			dp[i][j] = dp[i-1][j]

print(dp[N][W])

Fixed submission:
from collections import defaultdict
import sys,heapq,bisect,math,itertools,string
sys.setrecursionlimit(10**8)
INF = float('inf')
mod = 10**9+7
AtoZ = [chr(i) for i in range(65,65+26)]
atoz = [chr(i) for i in range(97,97+26)]

N,W = map(int,(input().split()))
wv = [[] for i in range(4)]


w,v = map(int,(input().split()))
min_w = w
wv[0].append(v)

for i in range(N-1):
	w,v = map(int,(input().split()))
	wv[w-min_w].append(v)

wv[0].sort(reverse=True)
wv[1].sort(reverse=True)
wv[2].sort(reverse=True)
wv[3].sort(reverse=True)
L1 = len(wv[0])
L2 = len(wv[1])
L3 = len(wv[2])
L4 = len(wv[3])

SUM = 0
sum_wv1 = [0]
for i in range(L1):
	SUM += wv[0][i]
	sum_wv1.append(SUM)

SUM = 0
sum_wv2 = [0]
for i in range(L2):
	SUM += wv[1][i]
	sum_wv2.append(SUM)

SUM = 0
sum_wv3 = [0]
for i in range(L3):
	SUM += wv[2][i]
	sum_wv3.append(SUM)

SUM = 0
sum_wv4 = [0]
for i in range(L4):
	SUM += wv[3][i]
	sum_wv4.append(SUM)

ans = 0

for n1 in range(L1+1):
	for n2 in range(L2+1):
		for n3 in range(L3+1):
			for n4 in range(L4+1):
				weight = min_w*(n1+n2+n3+n4) + n2 + 2*n3 + 3*n4
				if weight <= W:
					ans = max(ans,sum_wv1[n1]+sum_wv2[n2]+sum_wv3[n3]+sum_wv4[n4])

print(ans)
Buggy python submission (verdict: Runtime Error):
if a=='H':
	print(b)
else:
	if b=='H':
		print('D')
	else:
		print('H')

Fixed submission:
a, b = input().split()

if a=='H':
	print(b)
else:
	if b=='H':
		print('D')
	else:
		print('H')
Buggy python submission (verdict: Runtime Error):
X = int(input())
N = int(math.sqrt(2*X))-1

while True:
	if N*(N+1)//2 >= X:
		print(N)
		break
	N += 1

Fixed submission:
from collections import defaultdict
import sys,heapq,bisect,math,itertools,string
sys.setrecursionlimit(10**8)
INF = float('inf')
mod = 10**9+7

X = int(input())
N = int(math.sqrt(2*X))-1

while True:
	if N*(N+1)//2 >= X:
		print(N)
		break
	N += 1
Buggy python submission (verdict: Runtime Error):
N,A,B = map(int,list(input()))
S = input()
tmp = 0
tmpf = 0
for i in range(1,N+1):
  s = S[i]
  if s == "a":
    if tmp <= A+B:
      print("Yes")
      tmp +=1
    else:
      print("No")
  elif s == "b":
    if tmp <= A+B and tmpf <=B:
      print("Yes")
      tmp +=1
      tmpf += 1
    else:
      print("No")
  else:
    print("No")
  
  
  

Fixed submission:
from collections import defaultdict,deque
import sys,heapq,bisect,math,itertools,string,queue,datetime
sys.setrecursionlimit(10**8)
INF = float('inf')
mod = 10**9+7
eps = 10**-7
def inp(): return int(input())
def inpl(): return list(map(int, input().split()))
def inpls(): return list(input().split())

N,A,B = inpl()
S = input()
tmp = 1
tmpf = 1

for s in S:
	if s == 'a':
		if tmp <= A+B:
			print('Yes')
			tmp += 1
		else:
			print('No')
	elif s == 'b':
		if tmp <= A+B and tmpf <= B:
			print('Yes')
			tmpf += 1
			tmp += 1
		else:
			print('No')
	else:
		print('No')
Buggy python submission (verdict: Time Limit Exceeded):
X = input()

while 'ST' in X:
	X = X.replace('ST','')

print(len(X))

Fixed submission:
from collections import defaultdict,deque
import sys,heapq,bisect,math,itertools,string,queue,datetime
sys.setrecursionlimit(10**8)
INF = float('inf')
mod = 10**9+7
eps = 10**-7
def inpl(): return list(map(int, input().split()))
def inpl_s(): return list(input().split())

S = input()
ans = 0
tmp = 0
for s in S:
	if s == 'S':
		tmp += 1
	elif s == 'T':
		tmp -= 1
		if tmp < 0:
			tmp = 0
			ans += 1

print(ans+tmp)
Buggy python submission (verdict: Runtime Error):
from collections import defaultdict,deque
import sys,heapq,bisect,math,itertools,string,queue,datetime
sys.setrecursionlimit(10**8)
INF = float('inf')
mod = 10**9+7
def inpl(): return list(map(int, input().split()))
def inpls(): return list(input().split())

N = int(input())
xx = inpl()
L = int(input())

K = N.bit_length()
db_r = [[0]*K for i in range(N)]
for i,x in enumerate(xx):
    ind = bisect.bisect_right(xx,x+L)
    db_r[i][0] = ind-1

for k in range(1,K):
    for i in range(N):
        db_r[i][k] = db_r[db_r[i][k-1]][k-1]

def check(a,b,d):
    L = d.bit_length()
    for k in range(L):
        if d & (1<<k):
            a = db_r[a][k]
    return a >= b

Q = int(input())
for i in range(Q):
    a,b = inpl()
    a -= 1
    b -= 1
    a,b = min(a,b),max(a,b)
    OK = N
    NG = 0
    while OK-NG>1:
        mid = (OK+NG)//2
        if check(a,b,mid): OK = mid
        else: NG = mid
    print(OK)


Fixed submission:
from collections import defaultdict,deque
import sys,heapq,bisect,math,itertools,string,queue,copy,time
sys.setrecursionlimit(10**8)
INF = float('inf')
mod = 10**9+7
eps = 10**-7
def inp(): return int(sys.stdin.readline())
def inpl(): return list(map(int, sys.stdin.readline().split()))
def inpl_str(): return list(sys.stdin.readline().split())

N,A = inpl()
aa = inpl()

dp = [[[0]*(50*N+5) for j in range(N+1)] for i in range(N)]
# dp[i][j][k] : i 枚目まで見て，j枚選んで，合計がk の通り

for i in range(N):
    dp[i][0][0] = 1


for i in range(N):
    a = aa[i]
    for j in range(1,i+2):
        for k in range(50*j+5):
            dp[i][j][k] = dp[i-1][j][k]
            if k >= a:
                dp[i][j][k] += dp[i-1][j-1][k-a]

ans = 0
for j in range(N+1):
    ans += dp[-1][j][j*A]

print(ans-1)
Buggy python submission (verdict: Time Limit Exceeded):
from collections import defaultdict,deque
import sys,heapq,bisect,math,itertools,string,queue,datetime
sys.setrecursionlimit(10**8)
INF = float('inf')
mod = 10**9+7
eps = 10**-7
def inpl(): return list(map(int, input().split()))
def inpl_s(): return list(input().split())

H,W,A,B=inpl()
ans = 0

def Comb(n,k):#nCk
	gyakugen = [1]*(n+1)
	fac = [1]*(n+1)

	for i in range(1,n+1):
		fac[i] = (fac[i-1]*i)%mod
	gyakugen[n] = pow(fac[n],mod-2,mod)

	for i in range(n,0,-1):
		gyakugen[i-1] = (gyakugen[i]*i)%mod
	com = [1]*(n+1)

	for i in range(1,n+1):
		com[i] = (fac[n]*gyakugen[i]*gyakugen[n-i])%mod

	return com[k]%mod

for x1 in range(B+1,W+1):
	y1 = H-A
	x2 = A
	y2 = W-x1+1
	ans += (Comb(x1+y1-2,y1-1)*Comb(x2+y2-2,y2-1))%mod
	ans %= mod

print(ans)


Fixed submission:
from collections import defaultdict,deque
import sys,heapq,bisect,math,itertools,string,queue,datetime
sys.setrecursionlimit(10**8)
INF = float('inf')
mod = 10**9+7
eps = 10**-7
def inpl(): return list(map(int, input().split()))
def inpl_s(): return list(input().split())

H,W,A,B=inpl()
ans = 0

MAX = H+W
fac = [1]*(MAX+1)
for i in range(1,MAX+1):
	fac[i] = (fac[i-1]*i)%mod

gyakugen = [1]*(MAX+1)
gyakugen[MAX] = pow(fac[MAX],mod-2,mod)
for i in range(MAX,0,-1):
	gyakugen[i-1] = (gyakugen[i]*i)%mod

def Comb(n,k):#nCk
	return (fac[n]*gyakugen[k]*gyakugen[n-k])%mod

for x1 in range(B+1,W+1):
	y1 = H-A
	x2 = A
	y2 = W-x1+1
	ans += (Comb(x1+y1-2,y1-1)*Comb(x2+y2-2,y2-1))%mod
	ans %= mod

print(ans)
Buggy python submission (verdict: Time Limit Exceeded):
from bisect import bisect_left, bisect_right
n = int(input())
ls = sorted(list(map(int, input().split())))
total = 0
for i in range(n):
    for j in range(i+1, n):
        b, c = ls[i], ls[j]
        lower = abs(b-c) + 0.5
        upper = b+c - 0.5
        ii = bisect_left(ls, lower)
        jj = bisect_left(ls, upper)
        cnt = jj - ii
        if i in range(ii, jj):
            cnt -= 1
        if j in range(ii, jj):
            cnt -= 1
        total += cnt
total //= 3

print(total)


Fixed submission:
from bisect import bisect_left, bisect_right
n = int(input())
ls = sorted(list(map(int, input().split())))
total = 0
for i in range(n):
    for j in range(i+1, n):
        b, c = ls[i], ls[j]
        lower = abs(b-c) + 0.5
        upper = b+c - 0.5
        ii = bisect_left(ls, lower)
        jj = bisect_left(ls, upper)
        cnt = jj - ii
        if ii <= i < jj:
            cnt -= 1
        if ii <= j < jj:
            cnt -= 1
        total += cnt
total //= 3

print(total)
Buggy python submission (verdict: Time Limit Exceeded):
def divisors(n):
    ds = []
    for i in range(1, int(n**0.5)+1):
        if n % i == 0:
            ds.append(i)
            if i != n // i:# and i != 1:
                ds.append(n//i)
    # divisors.sort()
    return ds

n = int(input())
aa = list(map(int, input().split()))
counts = {}
balls = {}


for i in range(len(aa)):
    if aa[i] == 1:
        counts[i + 1] = 1
    else:
        counts[i + 1] = 0

for i in range(n, 0, -1):
    #print(f'i = {i}, counts={counts}')
    if counts[i] % 2 == 0:
        continue
    # put ball in i
    balls[i] = True
    ds = divisors(i)
    for d in ds:
        counts[d] += 1
balls = list(balls.keys())
print(len(balls))
if len(balls) > 0:
    print(' '.join(map(str, balls)))





Fixed submission:
def divisors(n):
    ds = []
    for i in range(1, int(n**0.5)+1):
        if n % i == 0:
            ds.append(i)
            if i != n // i:# and i != 1:
                ds.append(n//i)
    # divisors.sort()
    return ds

n = int(input())
aa = list(map(int, input().split()))
counts = {}
balls = {}


for i in range(len(aa)):
    if aa[i] == 1:
        counts[i + 1] = 1
    else:
        counts[i + 1] = 0

for i in range(n, 0, -1):
    #print(f'i = {i}, counts={counts}')
    if counts[i] % 2 == 0:
        continue
    # put ball in i
    balls[i] = True
    ds = divisors(i)
    for d in ds:
        counts[d] += 1
balls = list(balls.keys())
print(len(balls))
if len(balls) > 0:
    print(' '.join(map(str, balls)))
Buggy python submission (verdict: Time Limit Exceeded):
mod = int(1e9+7)

n, m = map(int, input().split())
s = list(map(int, input().split()))
t = list(map(int, input().split()))

dp = []
for i in range(len(s)+1):
  dp.append([0] * (len(t)+1))

for i in range(1, len(s)+1):
  for j in range(1, len(t)+1):
    if s[i-1] == t[j-1]:
      dp[i][j] = (1 + dp[i-1][j] + dp[i][j-1]) % mod
    else:
      dp[i][j] = (dp[i-1][j] + dp[i][j-1] - dp[i-1][j-1]) % mod
ans = dp[-1][-1] + 1 % mod
print(ans)


Fixed submission:
mod = int(1e9+7)

n, m = map(int, input().split())
s = list(map(int, input().split()))
t = list(map(int, input().split()))

dp = []
for i in range(len(s)+1):
  dp.append([0] * (len(t)+1))

for i in range(1, len(s)+1):
  for j in range(1, len(t)+1):
    if s[i-1] == t[j-1]:
      dp[i][j] = (1 + dp[i-1][j] + dp[i][j-1]) % mod
    else:
      dp[i][j] = (dp[i-1][j] + dp[i][j-1] - dp[i-1][j-1]) % mod
ans = dp[-1][-1] + 1 % mod
print(ans)
Buggy python submission (verdict: Runtime Error):
n = int(input())
xys = {}
xy = []
for _ in range(n):
  x, y = map(int, input().split())
  xys[(x,y)] = True
  xy.append((x,y))

scores = []

for i in range(n):
  for j in range(n):
    if i == j:
      continue
    xi, yi = xy[i]
    xj, yj = xy[j]
    p = xj-xi
    q = yj-yi
    score = n
    for k in range(n):
      xk, yk = xy[k]
      if (xk+p, yk+q) in xys:
        score -= 1
    scores.append(score)

print(min(scores))


Fixed submission:
n = int(input())
xys = {}
xy = []
for _ in range(n):
  x, y = map(int, input().split())
  xys[(x,y)] = True
  xy.append((x,y))

scores = []

if n == 1:
  print(1)
  exit(0)
for i in range(n):
  for j in range(n):
    if i == j:
      continue
    xi, yi = xy[i]
    xj, yj = xy[j]
    p = xj-xi
    q = yj-yi
    score = n
    for k in range(n):
      xk, yk = xy[k]
      if (xk+p, yk+q) in xys:
        score -= 1
    scores.append(score)

print(min(scores))
Buggy python submission (verdict: Runtime Error):
n, k = map(int, input().split())
vs = list(map(int, input().split()))

values = []

for num_enqueue in range(k // 2):
  for num_dequeue in range(k-num_enqueue+1):
    for num_dequeue_left in range(num_dequeue+1):
      num_dequeue_right = num_dequeue - num_dequeue_left
      if num_dequeue >= n:
        dequeued = vs[:]
      else:
        dequeued = vs[:num_dequeue_left] + ([] if num_dequeue_right == 0 else vs[-num_dequeue_right:])
      dequeued_pos = [v for v in dequeued if v >= 0]
      dequeued_neg = sorted([v for v in dequeued if v < 0], reverse=True)

      for _ in range(num_enqueue):
        if dequeued_neg:
          dequeued_neg.pop()
      value = sum(dequeued_pos) + sum(dequeued_neg)
      #print(f'value={value}, enq={num_enqueue}, left={num_dequeue_left}, right={num_dequeue_right}, dequeued={dequeued}')
      values.append(value)

#print(values)
print(max(values))




Fixed submission:
n, k = map(int, input().split())
vs = list(map(int, input().split()))

values = []

if k > 1:
  for num_enqueue in range(k // 2):
    for num_dequeue in range(k-num_enqueue+1):
      for num_dequeue_left in range(num_dequeue+1):
        num_dequeue_right = num_dequeue - num_dequeue_left
        if num_dequeue >= n:
          dequeued = vs[:]
        else:
          dequeued = vs[:num_dequeue_left] + ([] if num_dequeue_right == 0 else vs[-num_dequeue_right:])
        dequeued_pos = [v for v in dequeued if v >= 0]
        dequeued_neg = sorted([v for v in dequeued if v < 0], reverse=True)

        for _ in range(num_enqueue):
          if dequeued_neg:
            dequeued_neg.pop()
        value = sum(dequeued_pos) + sum(dequeued_neg)
        #print(f'value={value}, enq={num_enqueue}, left={num_dequeue_left}, right={num_dequeue_right}, dequeued={dequeued}')
        values.append(value)
  print(max(values))
else:
  print(max(vs[0], vs[-1], 0))
Buggy python submission (verdict: Runtime Error):
from collections import defaultdict
dic = defaultdict(int)

n, m = map(int, input().split())
ar_a = map(int, input().split())
for i in range(m):
  b, c = map(int, input().split())
  dic[c] += b

ar = []
for c in sorted(dic.keys(), reverse=True):
  cnt = dic[c]
  ar += [c] * cnt
  if len(ar) >= n:
    break

if len(ar) < n:
  ar += [0] * (n-len(ar))

sum = 0
for x, y in zip(ar, sorted(ar_a)):
  sum += max([x,y])
print(sum)


Fixed submission:
dic = {}

n, m = map(int, input().split())
ar_a = map(int, input().split())
for i in range(m):
  b, c = map(int, input().split())
  if c not in dic:
    dic[c] = 0
  dic[c] += b

ar = []
for c in sorted(dic.keys(), reverse=True):
  cnt = dic[c]
  if cnt > n:
    cnt = n
  ar += [c] * cnt
  if len(ar) >= n:
    break

if len(ar) < n:
  ar += [0] * (n-len(ar))

sum = 0
for x, y in zip(ar, sorted(ar_a)):
  sum += max([x,y])
print(sum)
Buggy python submission (verdict: Time Limit Exceeded):
import math
n, m, k = map(int, input().split())

mod = 10**9 + 7


def choose(n,k):
  return (math.factorial(n) // (math.factorial(n - k) * math.factorial(k))) % mod

sum = 0
for i in range(1, n+1):
  for j in range(1, m+1):
    score = i-1 + j-1
    cnt = (n-i+1) * (m-j+1)
    sum += (score * cnt) % mod
    #print((i,j), score, cnt)

for i in range(2, n+1):
  for j in range(1, m):
    score = i-1 + m-j
    cnt = (n-i+1) * j
    sum += (score * cnt) % mod
    #print((i,j), score, cnt)

sum = sum * choose(m*n-2,k-2)
sum = sum % mod
print(sum)



Fixed submission:
import math
n, m, k = map(int, input().split())

mod = 10**9 + 7

def mpow(x, n):
  ans = 1
  while n != 0:
    if n&1:
      ans = ans * x % mod
    x = x * x % mod
    n = n // 2
  return ans

fac = [0] * (n*m+2)
finv = [0] * (n*m+2)
inv = [0] * (n*m+2)
fac[0] = 1
fac[1] = 1
finv[0] = 1
finv[1] = 1
inv[1] = 1

for i in range(2, n*m+1):
  fac[i] = fac[i-1] * i % mod
  inv[i] = mod - inv[mod%i] * (mod // i) % mod
  finv[i] = finv[i-1] * inv[i] % mod

def choose(n,k):
  if n == 0 and k == 0:
    return 1
  if n < 0:
    return 0
  if n < k:
    return 0
  return fac[n] * (finv[k] * finv[n-k] % mod) % mod


sum = 0
for i in range(1, n+1):
  for j in range(1, m+1):
    score = i-1 + j-1
    cnt = (n-i+1) * (m-j+1)
    sum += (score * cnt) % mod
    #print((i,j), score, cnt)

for i in range(2, n+1):
  for j in range(1, m):
    score = i-1 + m-j
    cnt = (n-i+1) * j
    sum += (score * cnt) % mod
    #print((i,j), score, cnt)

sum = sum * choose(m*n-2,k-2)
sum = sum % mod
print(sum)
Buggy python submission (verdict: Time Limit Exceeded):
r,g,b,n = map(int, input().split())


#def cnt2(sum, a, b):

cnt = 0
for rr in range(n // r + 1):
  sum = r * rr
  rest = n - sum
  #cnt += cnt2(rest, g, b)
  for gg in range(rest // g + 1):
    sum = r * rr + g * gg
    rest = n - sum
    if rest < 0:
      break
    if rest % b == 0:
      bb = (n-sum) // b
      cnt += 1

print(cnt)


Fixed submission:
r,g,b,n = map(int, input().split())

cnt = 0
for rr in range(n // r + 1):
  for gg in range((n - r * rr) // g + 1):
    rest = n - r * rr - g * gg
    cnt += (rest % b == 0)

print(cnt)

Buggy python submission (verdict: Time Limit Exceeded):
r,g,b,n = map(int, input().split())

cnt = 0
for rr in range(n // r + 1):
  for gg in range(n // g + 1):
    sum = r * rr + g * gg
    rest = n - sum
    if rest < 0:
      continue
    if rest % b == 0:
      bb = (n-sum) // b
      cnt += 1

print(cnt)


Fixed submission:
r,g,b,n = map(int, input().split())

cnt = 0
for rr in range(n // r + 1):
  for gg in range((n - r * rr) // g + 1):
    rest = n - r * rr - g * gg
    cnt += (rest % b == 0)

print(cnt)
Buggy python submission (verdict: Runtime Error):
import itertools
n = int(input())
ns = list(range(1,n+1))
cs = list(itertools.combinations(ns, 2))
top = n if n % 2 == 0 else n-1

for nn in range(n):
  tpl = (nn+1, top-nn)
  if tpl[0] >= tpl[1]:
    break
  #print(f'removing {tpl}')
  cs.remove(tpl)

print(len(cs))
for a, b in cs:
  print(f'{a} {b}')



Fixed submission:
import itertools
n = int(input())
ns = list(range(1,n+1))
cs = list(itertools.combinations(ns, 2))
top = n if n % 2 == 0 else n-1

for nn in range(n):
  tpl = (nn+1, top-nn)
  if tpl[0] >= tpl[1]:
    break
  #print(f'removing {tpl}')
  cs.remove(tpl)

print(len(cs))
for a, b in cs:
  print('{0} {1}'.format(a, b))
Buggy python submission (verdict: Time Limit Exceeded):
n, p = map(int, input().split())
gcd = 1
f = 2

while True:
  fcnt = 0
  while p%f == 0:
    p /= f
    fcnt += 1
    if fcnt == n:
      gcd *= f
      fcnt = 0
  if f == 2:
    f = 3
  else:
    f += 2
  if f > p or n > p:
    break

print(gcd)


Fixed submission:
import math
n, p = map(int, input().split())
gcd = 1
f = 2
upper = math.floor(math.pow(p, 1/n))

if n == 1:
  gcd = p
else:
  while True:
    if f > upper:
      break
    fn = f**n
    while p%fn == 0:
      gcd *= f
      p /= fn
    if f == 2:
      f = 3
    else:
      f += 2

print(gcd)
Buggy python submission (verdict: Runtime Error):
n, m = map(int, input().split())
ipy = []
for i in range(m):
  p, y = map(int, input().split())
  ipy.append([i, p, y])

dict_p = {}
dict_c = {}

for i, p, y in sorted(ipy, key=lambda x: x[2]):
  if not p in dict_p:
    dict_p[p] = 0
  dict_p[p] += 1
  dict_c[p,i] = dict_p[p]

for i, p, y in ipy:
  print(f'{p:06}{dict_c[p,i]:06}')


Fixed submission:
n, m = map(int, input().split())
ipy = []
for i in range(m):
  p, y = map(int, input().split())
  ipy.append([i, p, y])

dict_p = {}
dict_c = {}

for i, p, y in sorted(ipy, key=lambda x: x[2]):
  if not p in dict_p:
    dict_p[p] = 0
  dict_p[p] += 1
  dict_c[p,i] = dict_p[p]

for i, p, y in ipy:
  print('{0:06}{1:06}'.format(p, dict_c[p,i]))
Buggy python submission (verdict: Time Limit Exceeded):
n, k = map(int, input().split())

xys = {}
xs = []
ys = []
for i in range(n):
  x, y = map(int, input().split())
  xys[i] = (x, y)
  xs.append(x)
  ys.append(y)
xs = sorted(xs)
ys = sorted(ys)
min_area = float('inf')

for li in range(n):
  for ri in range(li+1, n):
    left = xs[li]
    right = xs[ri]
    for bi in range(n):
      for ti in range(bi+1, n):
        bottom = ys[bi]
        top = ys[ti]
        area = (top - bottom) * (right - left)
        cnt = 0
        for i in range(n):
          xi, yi = xys[i]
          if (left <= xi <= right) and (bottom <= yi <= top):
            cnt += 1
            if cnt >= k:
              break
        if cnt >= k:
          min_area = min([min_area, area])

print(min_area)


Fixed submission:
n, k = map(int, input().split())

xys = {}
xs = []
ys = []
for i in range(n):
  x, y = map(int, input().split())
  xys[i] = (x, y)
  xs.append(x)
  ys.append(y)
xs = sorted(xs)
ys = sorted(ys)
min_area = float('inf')

for li in range(n):
  for ri in range(li+1, n):
    left = xs[li]
    right = xs[ri]
    for bi in range(n):
      for ti in range(bi+1, n):
        bottom = ys[bi]
        top = ys[ti]
        area = (top - bottom) * (right - left)
        cnt = 0
        for i in range(n):
          xi, yi = xys[i]
          if (left <= xi <= right) and (bottom <= yi <= top):
            cnt += 1
            if cnt >= k:
              break
        if cnt >= k:
          min_area = min([min_area, area])

print(min_area)
Buggy python submission (verdict: Runtime Error):
n,a,b = (int(x) for x input().split())
ans = 0

def k(N):
    sum = 0
    while N>0:
        sum += N%10
        N = N//10
    return sum

for i in range(1,n+1):
    if a<=k(i)<=b:
        ans +=i
print(ans)


Fixed submission:
n,a,b = map(int,input().split())
ans = 0

def k(N):
    sum = 0
    while N>0:
        sum += N%10
        N = N//10
    return sum

for i in range(1,n+1):
    if a<=k(i)<=b:
        ans +=i
print(ans)
Buggy python submission (verdict: Time Limit Exceeded):
DP = {}

def solve(n, a, b, c, d):
    if n <= 0: 
        return 0
    if n == 1:
        return d
    if n in DP:
        return DP[n]
    ans = float('inf')
    for i in range(-4, 5):
        num = n + i
        trash = abs(i)*d
        if num < 0:
            continue
        if num%5 == 0 and num // 5 < n:
            ans = min(ans, solve(num//5, a, b, c, d) + min(c, d*(num-(num//5))) + trash)
        if num%3 == 0 and num // 3 < n:
            ans = min(ans, solve(num//3, a, b, c, d) + min(b, d*(num-(num//3))) + trash)
        if num%2 == 0 and num // 2 < n:
            ans = min(ans, solve(num//2, a, b, c, d) + min(a, d*(num-(num//2))) + trash)
        # print(str(n) + ' ' + str(ans) + ' ' + str(num) + ' ' + str(i))
    DP[n] = int(ans)

    return int(ans)

def solve2():
    DP.clear()
    ans = float('inf')
    n, a, b, c, d = map(int, input().split())
    # for i in range(0, 65):
    #     for j in range(0, 30):
    #             for k in range(0, 10):
    #                 val = pow(2, i)*pow(3, j)*pow(5, k)
    #                 ans = min(ans, a*i + b*j + c*k + abs(n - val)*(d))
    # print(ans)
                    
    print(solve(n, a, b, c,d))
    
t = int(input())
for _ in range(t):
    solve2()


Fixed submission:
DP = {}

def solve(n, a, b, c, d):
    if n <= 0: 
        return 0
    if n == 1:
        return d
    if n in DP:
        return DP[n]
    ans = float('inf')
    for i in range(-3, 4):
        num = n + i
        trash = abs(i)*d
        if num < 0:
            continue
        if num%5 == 0 and num // 5 < n:
            ans = min(ans, solve(num//5, a, b, c, d) + min(c, d*(num-(num//5))) + trash)
        if num%3 == 0 and num // 3 < n:
            ans = min(ans, solve(num//3, a, b, c, d) + min(b, d*(num-(num//3))) + trash)
        if num%2 == 0 and num // 2 < n:
            ans = min(ans, solve(num//2, a, b, c, d) + min(a, d*(num-(num//2))) + trash)
        # print(str(n) + ' ' + str(ans) + ' ' + str(num) + ' ' + str(i))
    DP[n] = int(ans)

    return int(ans)

def solve2():
    DP.clear()
    ans = float('inf')
    n, a, b, c, d = map(int, input().split())
    # for i in range(0, 65):
    #     for j in range(0, 30):
    #             for k in range(0, 10):
    #                 val = pow(2, i)*pow(3, j)*pow(5, k)
    #                 ans = min(ans, a*i + b*j + c*k + abs(n - val)*(d))
    # print(ans)
                    
    print(solve(n, a, b, c,d))
    
t = int(input())
for _ in range(t):
    solve2()
Buggy python submission (verdict: Runtime Error):
s = input()

print(x * len(s))

Fixed submission:
s = input()
 
print('x' * len(s))