Harryxun/testdata huggingface dataset:
Buggy python submission (verdict: Runtime Error):
from collections import deque
N,K = map(int,input().split())
P = list(map(int,input().split()))

upper = [1 for i in range(N)]
for i in range(1, N):
	x = N-i-1
	if P[x] < P[x+1]:
		upper[x] = upper[x+1] + 1

skip = [-1,-1]
flg = False
for i in range(N):
	if upper[N-i-1] >= K:
		skip.append(N-i-1)

skip.pop()
deq_min = deque([P[0]])
deq_max = deque([P[0]])
minlen = 1
maxlen = 1
for i in range(1, K):
	while minlen > 0 and deq_min[-1] > P[i]:
		deq_min.pop()
		minlen -= 1
	deq_min.append(P[i])
	minlen += 1
	while maxlen > 0 and deq_max[-1] < P[i]:
		deq_max.pop()
		maxlen -= 1
	deq_max.append(P[i])
	maxlen += 1

ans = 1
next_skip = skip.pop()
for i in range(1, N-K+1):
	new_i = i+K-1
	min_rem = (deq_min[0] == P[i-1])
	max_add = (deq_max[0] < P[new_i])
	if not (min_rem and max_add):
		if i != next_skip:
			ans += 1
	if i == next_skip:
		next_skip = skip.pop()
	if min_rem:
		deq_min.popleft()
	while minlen > 0 and deq_min[-1] > P[new_i]:
		deq_min.pop()
		minlen -= 1
	deq_min.append(P[new_i])
	minlen += 1
	while maxlen > 0 and deq_max[-1] < P[new_i]:
		deq_max.pop()
		maxlen -= 1
	deq_max.append(P[new_i])
	maxlen += 1
print(ans)

Fixed submission:
from collections import deque
N,K = map(int,input().split())
P = list(map(int,input().split()))

upper = [1 for i in range(N)]
for i in range(1, N):
	x = N-i-1
	if P[x] < P[x+1]:
		upper[x] = upper[x+1] + 1

skip = [-1,-1]
flg = False
for i in range(N):
	if upper[N-i-1] >= K:
		skip.append(N-i-1)

skip.pop()
deq_min = deque([P[0]])
deq_max = deque([P[0]])
minlen = 1
maxlen = 1
for i in range(1, K):
	while minlen > 0 and deq_min[-1] > P[i]:
		deq_min.pop()
		minlen -= 1
	deq_min.append(P[i])
	minlen += 1
	while maxlen > 0 and deq_max[-1] < P[i]:
		deq_max.pop()
		maxlen -= 1
	deq_max.append(P[i])
	maxlen += 1

ans = 1
next_skip = skip.pop()
for i in range(1, N-K+1):
	new_i = i+K-1
	min_rem = (deq_min[0] == P[i-1])
	max_add = (deq_max[0] < P[new_i])
	if not (min_rem and max_add):
		if i != next_skip:
			ans += 1
	if i == next_skip:
		next_skip = skip.pop()
	if min_rem:
		deq_min.popleft()
		minlen -= 1
	if deq_max[0] == P[i-1]:
		deq_max.popleft()
		maxlen -= 1
	while minlen > 0 and deq_min[-1] > P[new_i]:
		deq_min.pop()
		minlen -= 1
	deq_min.append(P[new_i])
	minlen += 1
	while maxlen > 0 and deq_max[-1] < P[new_i]:
		deq_max.pop()
		maxlen -= 1
	deq_max.append(P[new_i])
	maxlen += 1
print(ans)
Buggy python submission (verdict: Time Limit Exceeded):
N = int(input())
A = list(map(int,input().split()))
cur = [0 for i in range(N)]
ball = []
ball_num = 0
for x in range(N):
	i = N-1 - x
	n = i + 1
	if A[i] != cur[i]:
		ball.append(n)
		ball_num += 1
		for j in range(n // 2 + 1):
			m = j + 1
			if m * m > n:
				break
			if n % m == 0:
				cur[j] = 1 - cur[j]
				if n//m != m:
					cur[n//m - 1] = 1 - cur[n//m - 1]  
print(ball_num)
print(" ".join(list(map(str, ball))))

Fixed submission:
N = int(input())
A = list(map(int,input().split()))
cur = [0 for i in range(N)]
ball = []
ball_num = 0
for x in range(N):
	i = N-1 - x
	n = i + 1
	if A[i] != cur[i]:
		ball.append(n)
		ball_num += 1
		for j in range(n // 2 + 1):
			m = j + 1
			if m * m > n:
				break
			if n % m == 0:
				cur[j] = 1 - cur[j]
				if n//m != m:
					cur[n//m - 1] = 1 - cur[n//m - 1]  
print(ball_num)
print(" ".join(list(map(str, ball))))

Buggy python submission (verdict: Time Limit Exceeded):
N = int(input())
A = list(map(int,input().split()))
cur = [0 for i in range(N)]
ball = []
ball_num = 0
for x in range(N):
	i = N-1 - x
	n = i + 1
	if A[i] != cur[i]:
		ball.append(n)
		ball_num += 1
		for j in range(n // 2):
			if n % (j+1) == 0:
				cur[j] = 1 - cur[j]
print(ball_num)
print(" ".join(list(map(str, ball))))

Fixed submission:
N = int(input())
A = list(map(int,input().split()))
cur = [0 for i in range(N)]
ball = []
ball_num = 0
for x in range(N):
	i = N-1 - x
	n = i + 1
	if A[i] != cur[i]:
		ball.append(n)
		ball_num += 1
		for j in range(n // 2 + 1):
			m = j + 1
			if m * m > n:
				break
			if n % m == 0:
				cur[j] = 1 - cur[j]
				if n//m != m:
					cur[n//m - 1] = 1 - cur[n//m - 1]  
print(ball_num)
print(" ".join(list(map(str, ball))))
Buggy python submission (verdict: Runtime Error):
N = int(input())
A = list(map(int,input().split()))
setA = list(set(A))
if len(setA) == and setA[0] == 0:
	print("Yes")
	exit()
if N % 3 != 0:
	print("No")
	exit()
if len(setA) == 1 or len(setA) > 3:
	print("No")
	exit()
if len(setA) == 2:
	if 0 in setA:
		setA.sort()
		if A.count(0) == N // 3 and A.count(setA[1]) == (N // 3) * 2:
			print("Yes")
			exit()
	print("No")
	exit()

if setA[0] ^ setA[1] != setA[2]:
	print("No")
	exit()
for a in setA:
	if A.count(a) != N // 3:
		print("No")
		exit()
print("Yes")
exit()

Fixed submission:
N = int(input())
A = list(map(int,input().split()))
setA = list(set(A))
if len(setA) == 1 and setA[0] == 0:
	print("Yes")
	exit()
if N % 3 != 0:
	print("No")
	exit()
if len(setA) == 1 or len(setA) > 3:
	print("No")
	exit()
if len(setA) == 2:
	if 0 in setA:
		setA.sort()
		if A.count(0) == N // 3 and A.count(setA[1]) == (N // 3) * 2:
			print("Yes")
			exit()
	print("No")
	exit()

if setA[0] ^ setA[1] != setA[2]:
	print("No")
	exit()
for a in setA:
	if A.count(a) != N // 3:
		print("No")
		exit()
print("Yes")
exit()
Buggy python submission (verdict: Time Limit Exceeded):
# coding: utf-8
# Your code here!
N,M = map(int,input().split())
S = list(map(int,input().split()))
T = list(map(int,input().split()))
LAST = 10**6
MOD = 10**9 + 7
S.append(LAST)
T.append(LAST)
total = [[0 for j in range(M+2)] for i in range(N+2)]
for i in range(N+1):
    for j in range(M+1):
        I,J = i+1,j+1
        if S[i] != T[j]:
            total[I][J] = (total[I][J-1] + total[I-1][J] - total[I-1][J-1]) % MOD
        else:
            total[I][J] = (total[I][J-1] + total[I-1][J] + 1) % MOD
        
print((total[N][M] + 1) % MOD)

Fixed submission:
# coding: utf-8
# Your code here!
N,M = map(int,input().split())
S = list(map(int,input().split()))
T = list(map(int,input().split()))
LAST = 10**6
MOD = 10**9 + 7
S.append(LAST)
T.append(LAST)
dp = [[0 for j in range(M+2)] for i in range(N+2)]
total = [[0 for j in range(M+2)] for i in range(N+2)]
for i in range(N+1):
    for j in range(M+1):
        I,J = i+1,j+1
        total[I][J] = (total[I][J-1] + total[I-1][J] - total[I-1][J-1]) % MOD
        if S[i] != T[j]:
            continue
        
        dp[I][J] = total[I-1][J-1] + 1
        total[I][J] = (total[I][J] +  dp[I][J]) % MOD
print(dp[N+1][M+1])

Buggy python submission (verdict: Time Limit Exceeded):
# coding: utf-8
# Your code here!
N,M = map(int,input().split())
S = list(map(int,input().split()))
T = list(map(int,input().split()))
LAST = 10**6
MOD = 10**9 + 7
S.append(LAST)
T.append(LAST)
dp = [[0 for j in range(M+2)] for i in range(N+2)]
total = [[0 for j in range(M+2)] for i in range(N+2)]
for i in range(N+1):
    for j in range(M+1):
        I,J = i+1,j+1
        total[I][J] = (total[I][J-1] + total[I-1][J] - total[I-1][J-1]) % MOD
        if S[i] != T[j]:
            continue
        
        dp[I][J] = total[I-1][J-1] + 1
        total[I][J] = (total[I][J] +  dp[I][J]) % MOD
print(dp[N+1][M+1])

Fixed submission:
# coding: utf-8
# Your code here!
N,M = map(int,input().split())
S = list(map(int,input().split()))
T = list(map(int,input().split()))
LAST = 10**6
MOD = 10**9 + 7
S.append(LAST)
T.append(LAST)
dp = [[0 for j in range(M+2)] for i in range(N+2)]
total = [[0 for j in range(M+2)] for i in range(N+2)]
for i in range(N+1):
    for j in range(M+1):
        I,J = i+1,j+1
        total[I][J] = (total[I][J-1] + total[I-1][J] - total[I-1][J-1]) % MOD
        if S[i] != T[j]:
            continue
        
        dp[I][J] = total[I-1][J-1] + 1
        total[I][J] = (total[I][J] +  dp[I][J]) % MOD
print(dp[N+1][M+1])
Buggy python submission (verdict: Runtime Error):
A,P = map(int,input().split())
p = A*3 + p
print(p//2)

Fixed submission:
A,P = map(int,input().split())
p = A*3 + P
print(p//2)
Buggy python submission (verdict: Runtime Error):
A,B = map(input().split())
if A < 7:
  print(0)
elif A < 13:
  print(B//2)
else:
  print(B)

Fixed submission:
A,B = map(int, input().split())
if A < 6:
  print(0)
elif A < 13:
  print(B//2)
else:
  print(B)
Buggy python submission (verdict: Runtime Error):
# coding: utf-8
# Your code here!
N,M = map(int,input().split())
lst = [i for i in range(N)]

def root(n):
    if n == lst[n]:
        return n
    lst[n] = func(lst[n])
    return lst[n]

def union(x,y):
    rootX, rootY = root(x), root(y)
    if rootX != rootY:
        lst[max(x,y)] = min(x,y)

for i in range(M):
    X,Y,Z = map(int,input().split())
    X -= 1
    Y -= 1
    union(X, Y)

for i in range(N):
    func(i)

ans = len([i for i in range(N) if lst[i] == i])
print(ans)



Fixed submission:
# coding: utf-8
# Your code here!
N,M = map(int,input().split())
lst = [i for i in range(N)]

def root(n):
    if n == lst[n]:
        return n
    lst[n] = root(lst[n])
    return lst[n]

def union(x,y):
    rootX, rootY = root(x), root(y)
    if rootX != rootY:
        if rootX > rootY:
            lst[rootX] = rootY
        if rootY > rootX:
            lst[rootY] = rootX

for i in range(M):
    X,Y,Z = map(int,input().split())
    X -= 1
    Y -= 1
    union(X, Y)

ans = len([i for i in range(N) if root(i) == i])
print(ans)

Buggy python submission (verdict: Runtime Error):
# coding: utf-8
# Your code here!
N,M = map(int,input().split())
lst = [i for i in range(N)]

def root(n):
    if n == lst[n]:
        return n
    lst[n] = func(lst[n])
    return lst[n]

def union(x,y)
    rootX, rootY = root(x), root(y)
    if rootX != rootY:
        lst[max(x,y)] = min(x,y)

for i in range(M):
    X,Y,Z = map(int,input().split())
    X -= 1
    Y -= 1
    union(X, Y)

for i in range(N):
    func(i)

ans = len([i for i in range(N) if lst[i] == i])
print(ans)



Fixed submission:
# coding: utf-8
# Your code here!
N,M = map(int,input().split())
lst = [i for i in range(N)]

def root(n):
    if n == lst[n]:
        return n
    lst[n] = root(lst[n])
    return lst[n]

def union(x,y):
    rootX, rootY = root(x), root(y)
    if rootX != rootY:
        if rootX > rootY:
            lst[rootX] = rootY
        if rootY > rootX:
            lst[rootY] = rootX

for i in range(M):
    X,Y,Z = map(int,input().split())
    X -= 1
    Y -= 1
    union(X, Y)

ans = len([i for i in range(N) if root(i) == i])
print(ans)
Buggy python submission (verdict: Time Limit Exceeded):
MOD = 10**9 + 7

N,X = map(int,input().split())
S = list(map(int,input().split()))
S.sort()
S = [None] + S
dp = [[0 for i in range(X+1)] for j in range(N+1)]
dp[1] = [i % S[1] for i in range(X+1)]
for n in range(2, N+1):
	for x in range(X+1):
		dp[n][x] = (dp[n-1][x] * (n-1) + dp[n-1][x%S[n]]) % MOD
print(dp[N][X])

Fixed submission:
MOD = 10**9 + 7

N,X = map(int,input().split())
S = list(map(int,input().split()))
S.sort()
S = [None] + S
dp = [[0 for i in range(X+1)] for j in range(N+1)]
dp[1] = [i % S[1] for i in range(X+1)]
for n in range(2, N+1):
	for x in range(X+1):
		dp[n][x] = (dp[n-1][x] * (n-1) + dp[n-1][x%S[n]]) % MOD
print(dp[N][X])
Buggy python submission (verdict: Runtime Error):
n = int(input())
v = list(map(int,input().split()))

v_e_cnt = [0 for i in range(10**6)]
v_o_cnt = [0 for i in range(10**6)]
for x in range(n):
	if x % 2 == 0:
		v_e_cnt[v[x]] += 1
	else:
		v_o_cnt[v[x]] += 1

max_e = [(0,0),(0,0)]
max_o = [(0,0),(0,0)]
for i in range(10**5+1):
	if max_e[1][0] < v_e_cnt[i]:
		if max_e[0][0] < v_e_cnt[i]:
			max_e[1] = max_e[0]
			max_e[0] = (v_e_cnt[i], i)
		else:
			max_e[1] = (v_e_cnt[i], i)
	if max_o[1][0] < v_o_cnt[i]:
		if max_o[0][0] > v_o_cnt[i]:
			max_o[1] = max_o[0]
			max_o[0] = (v_o_cnt[i], i)
		else:
			max_o[0] = (v_o_cnt[i], i)

ans = n - e[0][0] - o[0][0]
if e[0][1] == o[0][1]:
	ans = n - max(e[0][0] + o[1][0], e[1][0] + o[0][0])

print(ans)


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

v_e_cnt = [0 for i in range(10**6)]
v_o_cnt = [0 for i in range(10**6)]
for x in range(n):
	if x % 2 == 0:
		v_e_cnt[v[x]] += 1
	else:
		v_o_cnt[v[x]] += 1

max_e = [(0,0),(0,0)]
max_o = [(0,0),(0,0)]
for i in range(10**5+1):
	if max_e[1][0] < v_e_cnt[i]:
		if max_e[0][0] < v_e_cnt[i]:
			max_e[1] = max_e[0]
			max_e[0] = (v_e_cnt[i], i)
		else:
			max_e[1] = (v_e_cnt[i], i)
	if max_o[1][0] < v_o_cnt[i]:
		if max_o[0][0] < v_o_cnt[i]:
			max_o[1] = max_o[0]
			max_o[0] = (v_o_cnt[i], i)
		else:
			max_o[1] = (v_o_cnt[i], i)

ans = n - max_e[0][0] - max_o[0][0]
if max_e[0][1] == max_o[0][1]:
	ans = n - max(max_e[0][0] + max_o[1][0], max_e[1][0] + max_o[0][0])

print(ans)
Buggy python submission (verdict: Runtime Error):
Q = int(input())
for i in range(Q):
	A,B = map(int,input().split())
	if A == 1 and B == 1:
		print(0)
		continue
	score = A * B
	root = int((score-1) ** 0.5)
	ans = 2 * root
	if root >= A:
		ans -= 1
	if root >= B:
		ans -= 1
	if (score - 1) // root == root:
		ans -= 1
	print(ans)

Fixed submission:
l = sorted(list(map(int,input().split())))
C,B,A = l[0],l[1],l[2]
cnt = 0
while A != B or B != C or C != A:
	if A == B:
		if C < A:
			C += 2
			cnt += 1
		elif C > A:
			A += 1
			B += 1
			cnt += 1
	else:
		B += 1
		C += 1
		cnt += 1
print(cnt)
Buggy python submission (verdict: Runtime Error):
X,Y = map(int,input().split())
if x%y > 0 or y%x > 0:
	print(-1)
	exit()
if 2*x % y == 0:
	print(2*x)
	exit()
else:
	print(-1)


Fixed submission:
x,y = map(int,input().split())
if x % y == 0:
	print(-1)
	exit()
ans = 0
for i in range(y):
	ans += x
	if ans % y > 0:
		break
if ans == x*y:
	print(-1)
	exit()
print(ans)
Buggy python submission (verdict: Time Limit Exceeded):
m = 'Male'
f = 'Female'
v = 'Vacant'

N = int(input())
x = 0
y = N - 1
cnt = 2
print(x)
h_bef = input()
if h_bef == v:
	print(0)
	exit()
while cnt < 20:
	p = (x+y+1)//2
	print(p)
	h = input()
	if h == v:
		break
	mod = 0 if h_bef == h else 1
	if (p-x) % 2 == mod:
		x = p
	else:
		y = p - 1
	h_bef = h
	cnt += 1
exit()

Fixed submission:
m = 'Male'
f = 'Female'
v = 'Vacant'

N = int(input())
x = 0
y = N
cnt = 1
print(0)
p_bef = 0
h_bef = input()
if h_bef == v:
	exit()
while cnt < 50:
	p = (x+y+1)//2
	print(p)
	h = input()
	if h == v:
		break
	mod = 0 if h_bef == h else 1
	if (p-x) % 2 == mod:
		x = p
		h_bef = h
	else:
		y = p
	cnt += 1
exit()

Buggy python submission (verdict: Time Limit Exceeded):
m = 'Male'
f = 'Female'
v = 'Vacant'

N = int(input())
x = 0
y = N - 1
cnt = 2
print(x)
h_bef = input()
if h_bef == v:
	print(0)
	exit()
while cnt < 20:
	p = (x+y+1)//2
	print(p, cnt)
	h = input()
	if h == v:
		break
	mod = 0 if h_bef == h else 1
	if (p-x) % 2 == mod:
		x = p
	else:
		y = p - 1
	h_bef = h
	cnt += 1
exit()

Fixed submission:
m = 'Male'
f = 'Female'
v = 'Vacant'

N = int(input())
x = 0
y = N
cnt = 1
print(0)
p_bef = 0
h_bef = input()
if h_bef == v:
	exit()
while cnt < 50:
	p = (x+y+1)//2
	print(p)
	h = input()
	if h == v:
		break
	mod = 0 if h_bef == h else 1
	if (p-x) % 2 == mod:
		x = p
		h_bef = h
	else:
		y = p
	cnt += 1
exit()
Buggy python submission (verdict: Runtime Error):
x,y = input().split()
if x < y:
	print('<')
elif x == y:
	print('=')
else
	print('>')


Fixed submission:
x,y = input().split()
if x < y:
	print('<')
elif x == y:
	print('=')
else:
	print('>')
Buggy python submission (verdict: Runtime Error):
N,Z,W = map(int,input().split())
a = list(map(int,input().split()))

std = abs(Z-W)
last = a[0]

absList = [abs(last-i) for i in a]

ans = ans(last-W)
for i in range(N-1):
	testList = absList[i+1:]
	if min(absList) > ans:
		ans = max(absList)
print(ans)

Fixed submission:
N,Z,W = map(int,input().split())
a = list(map(int,input().split()))

std = abs(Z-W)
last = a[N-1]

absList = [abs(last-i) for i in a]
absList.pop(N-1)
ans = max(abs(last-W), abs(last-a[N-2]))
for i in range(N-1):
	testList = absList[i+1:]
	if min(absList) > ans:
		ans = max(absList)
print(ans)
Buggy python submission (verdict: Runtime Error):
N = int(input())
K = int(input())
ans = 1
for i in range(N)
	if ans < K:
		ans *= 2
	else:
		ans += K
print(ans)

Fixed submission:
N = int(input())
K = int(input())
ans = 1
for i in range(N):
	if ans < K:
		ans *= 2
	else:
		ans += K
print(ans)
Buggy python submission (verdict: Runtime Error):
S = input()
T = input()

start = len(S) - len(T)
end = len(S)

ans = ''
while start >= 0:
	test = S[start:end]
	solve = True
	for i in range(len(T)):
		c1,c2 = test[i],T[i]
		if c1 != c2 and c1 != '?':
			solve = False
			break
	if solve:
		ans = S[:start] + T + S[end:]
		break
	start -= 1
	end -= 1
if len(ans > 0):
	print(ans.replace('?', 'a'))
else:
	print('UNRESTORABLE')

Fixed submission:
S = input()
T = input()

start = len(S) - len(T)
end = len(S)

ans = ''
while start >= 0:
	test = S[start:end]
	solve = True
	for i in range(len(T)):
		c1,c2 = test[i],T[i]
		if c1 != c2 and c1 != '?':
			solve = False
			break
	if solve:
		ans = S[:start] + T + S[end:]
		break
	start -= 1
	end -= 1
if len(ans) > 0:
	print(ans.replace('?', 'a'))
else:
	print('UNRESTORABLE')
Buggy python submission (verdict: Runtime Error):
A,B,C = map(int,input.split())
if A == B:
	print(C)
elif B == C:
	print(A)
else:
	print(B)

Fixed submission:
A,B,C = map(int,input().split())
if A == B:
	print(C)
elif B == C:
	print(A)
else:
	print(B)
Buggy python submission (verdict: Time Limit Exceeded):
N,K = map(int,input().split())
points1 = []
points2 = []
for i in range(N):
	x,y = tuple((map(int,input().split())))
	points1.append((x,y))
	points2.append(y)
points1.sort()
points2.sort()

xDict = {}
index = 0
for x,y in points1:
	if index in xDict:
		if xDict[index] != x:
			index += 1
			xDict[index] = x
	else:
		xDict[index] = x

yDict = {}
index = 0
for y in points2:
	if index in yDict:
		if yDict[index] != y:
			index += 1 
			yDict[index] = y
	else:
		yDict[index] = y

nPoints = [[0 for j in range(len(yDict))] for i in range(len(xDict))]

for kx,vx in xDict.items():
	for ky,vy in yDict.items():
		exists = 1 if (vx,vy) in points1 else 0
		if kx == 0 and ky == 0:
			nPoints[kx][ky] += exists
		elif kx == 0 and ky > 0:
			nPoints[kx][ky] += nPoints[kx][ky-1] + exists
		elif kx > 0 and ky == 0:
			nPoints[kx][ky] += nPoints[kx-1][ky] + exists
		else:
			nPoints[kx][ky] += nPoints[kx-1][ky] + nPoints[kx][ky-1] - nPoints[kx-1][ky-1] + exists

ans = -1
for x1 in range(len(xDict)):
	for x2 in range(x1+1):
		for y1 in range(len(yDict)):
			for y2 in range(y1+1):
				point = nPoints[x1][y1]
				if x2 > 0:
					point -= nPoints[x2-1][y1]
				if y2 > 0:
					point -= nPoints[x1][y2-1]
				if x2 > 0 and y2 > 0:
					point += nPoints[x2-1][y2-1]
				if point >= K:
					area = (xDict[x1]-xDict[x2]) * (yDict[y1]-yDict[y2])
					if ans < 0:
						ans = area
					else:
						ans = min(ans, area)
print(ans)

Fixed submission:
N,K = map(int,input().split())
points1 = []
points2 = []
for i in range(N):
	x,y = tuple((map(int,input().split())))
	points1.append((x,y))
	points2.append(y)
points1.sort()
points2.sort()

xDict = {}
index = 0
for x,y in points1:
	if index in xDict:
		if xDict[index] != x:
			index += 1
			xDict[index] = x
	else:
		xDict[index] = x

yDict = {}
index = 0
for y in points2:
	if index in yDict:
		if yDict[index] != y:
			index += 1 
			yDict[index] = y
	else:
		yDict[index] = y

nPoints = [[0 for j in range(len(yDict))] for i in range(len(xDict))]

for kx,vx in xDict.items():
	for ky,vy in yDict.items():
		exists = 1 if (vx,vy) in points1 else 0
		if kx == 0 and ky == 0:
			nPoints[kx][ky] += exists
		elif kx == 0 and ky > 0:
			nPoints[kx][ky] += nPoints[kx][ky-1] + exists
		elif kx > 0 and ky == 0:
			nPoints[kx][ky] += nPoints[kx-1][ky] + exists
		else:
			nPoints[kx][ky] += nPoints[kx-1][ky] + nPoints[kx][ky-1] - nPoints[kx-1][ky-1] + exists

ans = -1
for x1 in range(len(xDict)):
	for x2 in range(x1+1,-1,-1):
		for y1 in range(len(yDict)):
			for y2 in range(y1+1,-1,-1):
				point = nPoints[x1][y1]
				if x2 > 0:
					point -= nPoints[x2-1][y1]
				if y2 > 0:
					point -= nPoints[x1][y2-1]
				if x2 > 0 and y2 > 0:
					point += nPoints[x2-1][y2-1]
				if point >= K:
					area = (xDict[x1]-xDict[x2]) * (yDict[y1]-yDict[y2])
					if ans < 0:
						ans = area
					else:
						ans = min(ans, area)
					break
print(ans)
Buggy python submission (verdict: Runtime Error):
a,b,c = map(raw_input().split(), int)
if a+c == 2*b:
    print('YES')
else:
    print('NO')


Fixed submission:
a,b,c = map(int,input().split())
if a+c == 2*b:
	print('YES')
else:
	print('NO')

Buggy python submission (verdict: Runtime Error):
a,b,c = map(raw_input().split(), int)
if a+c == 2*b:
    print('YES')
else:
    print('NO')


Fixed submission:
a,b,c = map(int,input().split())
if a+c == 2*b:
	print('YES')
else:
	print('NO')

Buggy python submission (verdict: Runtime Error):
a,b,c = map(raw_input().split(), int)
2.if a+c == 2*b:
3.    print('YES')
4.else:
5.    print('NO')


Fixed submission:
a,b,c = map(int,input().split())
if a+c == 2*b:
	print('YES')
else:
	print('NO')

Buggy python submission (verdict: Runtime Error):
a,b,c = map(input().split(), int)
2.if a+c == 2*b:
3.    print('YES')
4.else:
5.    print('NO')


Fixed submission:
a,b,c = map(int,input().split())
if a+c == 2*b:
	print('YES')
else:
	print('NO')

Buggy python submission (verdict: Runtime Error):
a,b,c = map(input().split(), int)
if a+c == 2*b:
    print('YES')
else:
    print('NO')

Fixed submission:
a,b,c = map(int,input().split())
if a+c == 2*b:
	print('YES')
else:
	print('NO')
Buggy python submission (verdict: Time Limit Exceeded):
S = input()
T = input()
q = int(input())
for i in range(q):
	a,b,c,d = map(int, input().split())
	s = S[a-1:b]
	t = T[c-1:d]
	x = (s.count("A") + 2 * s.count("B")) % 3
	y = (t.count("A") + 2 * t.count("B")) % 3
	if x == y:
		print("YES")
	else:
		print("NO")

Fixed submission:
S = input()
T = input()
q = int(input())

s = [0]
t = [0]
v = 0
for c in S:
	v = (v + (ord(c) - ord("A") + 1)) % 3
	s.append(v)
v = 0
for c in T:
	v = (v + (ord(c) - ord("A") + 1)) % 3
	t.append(v)
for i in range(q):
	a,b,c,d = map(int, input().split())
	x = (3 + s[b] - s[a-1]) % 3
	y = (3 + t[d] - t[c-1]) % 3
	if x == y:
		print("YES")
	else:
		print("NO")
Buggy python submission (verdict: Runtime Error):
S = input()
s = ""
i = 0
for c in S:
  if c == '0' or c == '1':
    s[i] = c
    i += 1
  else:
    if i > 0:
      s[i] = ''
      i -= 1

Fixed submission:
S = input()
s = ['' for c in S]
i = 0
for c in S:
  if c == '0' or c == '1':
    s[i] = c
    i += 1
  else:
    if i > 0:
      i -= 1
      s[i]=''
print(''.join(s))
Buggy python submission (verdict: Runtime Error):
n,m = list(map(int,input().split()));
a = list(map(int,input().split()));
 
a.sort(reverse = True);
 
i = 0;
while 4*m*a[i] >= sum(a) and i < n:
    i += 1;
 
if i >= m :
    print('Yes');
else :
    print('No');

Fixed submission:
n,m = list(map(int,input().split()));
a = list(map(int,input().split()));
 
a.sort(reverse = True);
 
i = 0;
while i<n and a[i] >= sum(a)/(4*m):
    i += 1;
 
if i >= m :
    print('Yes');
else :
    print('No');

Buggy python submission (verdict: Runtime Error):
n,m = list(map(int,input().split()));
a = list(map(int,input().split()));
 
a.sort(reverse = True);
 
i = 0;
while a[i] >= sum(a)//(4*m) and i < n:
    i += 1;
 
if i >= m :
    print('Yes');
else :
    print('No');

Fixed submission:
n,m = list(map(int,input().split()));
a = list(map(int,input().split()));
 
a.sort(reverse = True);
 
i = 0;
while i<n and a[i] >= sum(a)/(4*m):
    i += 1;
 
if i >= m :
    print('Yes');
else :
    print('No');