Harryxun/testdata huggingface dataset:
Buggy python submission (verdict: Runtime Error):
N,M=map(int,input().split())
A = list(map(int,input().split()))
import numpy as np
import math
A = np.array(A)
A = np.unique(A)
x=0
while np.all(A%2==0):
  A //= 2
  x+=1
  
if np.any(A%2==0):
  print(0)
  exit()
m = max(A)
l = np.array([0]*(m+1))
l[1]=1
for a in A:
  for i in range(3,a+1,2):
    n=0
    while a%i==0:
      a//=i
      n+=1
      
    l[i]=max(l[i],n*i)
  

k = np.cumprod(l[l>=1])[-1]*5*pow(2,x)//10
  
ans = math.ceil(M/k/2)
print(ans)

Fixed submission:
N,M=map(int,input().split())
A = list(map(int,input().split()))
import numpy as np
import math
import fractions
import functools
A = np.array(A)
A = np.unique(A)
B = A.copy()
x=0
while np.all(B%2==0):
  B//=2
  x+=1
if np.any(B%2==0):
  print(0)
  exit()
  
A /= 2
n = A[0]
for a in A[1::]:
  n = n*a//fractions.gcd(n,a)
ans = math.ceil(M//n/2)
print(ans)

Buggy python submission (verdict: Runtime Error):
N,M=map(int,input().split())
A = list(map(int,input().split()))
import numpy as np
import math
A = np.array(A)
A = np.unique(A)
x=0
while np.all(A%2==0):
  A //= 2
  x+=1
  
if np.any(A%2==0):
  print(0)
  exit()
m = max(A)
l = np.array([0]*(m+1))
l[1]=1
for a in A:
  for i in range(3,a+1,2):
    n=0
    while a%i==0:
      a//=i
      n+=1
      
    l[i]=max(l[i],n*i)
  

k = np.cumprod(l[l>=1])[-1]*pow(2,x)
if 1 in A:
  k/=2
  
ans = math.ceil(M/k/2)
print(ans)

Fixed submission:
N,M=map(int,input().split())
A = list(map(int,input().split()))
import numpy as np
import math
import fractions
import functools
A = np.array(A)
A = np.unique(A)
B = A.copy()
x=0
while np.all(B%2==0):
  B//=2
  x+=1
if np.any(B%2==0):
  print(0)
  exit()
  
A /= 2
n = A[0]
for a in A[1::]:
  n = n*a//fractions.gcd(n,a)
ans = math.ceil(M//n/2)
print(ans)
Buggy python submission (verdict: Runtime Error):
N,M,V,P = map(int,input().split())
import numpy as np
A = list(map(int,input().split()))
A = np.array(sorted(A,reverse=True))
ans = P
x = A[P-1]
y = N-1
for i in range(P,N):
  a = A[i]
  if x==a:
    ans+=1
  else:
    y=i
    break

if y==N-1:
  print(N)
z = sum(A[P-1:y])
for i in range(y,N):
  a = A[i]
  d = a+M
  if x<=d:
    b = N-i+P-1
    c = M*(V-b)
    e = z+c
    f = d*(i-P+1)
    if f>=e:
      ans+=1
      
  z+=a
print(ans)


Fixed submission:
N,A,B = map(int,input().split())
x = B-A
if x%2==0:
  print(x//2)
  
else:
  x = min(max(A-1,B-1),max(N-A,N-B))
  y = N-B+1+(B-A-1)//2
  z = A+(B-A-1)//2
  print(min(x,y,z))
Buggy python submission (verdict: Runtime Error):
N,M,V,P = map(int,input().split())
import numpy as np
A = list(map(int,input().split()))
A = np.array(sorted(A,reverse=True))
ans = P
x = A[P-1]
for i in range(P,N):
  a = A[i]
  if x==a:
    ans+=1
  else:
    y=i
    break
    
z = sum(A[P-1:y])
for i in range(y,N):
  a = A[i]
  d = a+M
  if x<=d:
    b = N-i+P-1
    c = M*(V-b)
    e = z+c
    f = d*(i-P+1)
    if f>=e:
      ans+=1
      
  z+=a
        
print(ans)

Fixed submission:
N,M,V,P = map(int,input().split())
import numpy as np
A = list(map(int,input().split()))
A = np.array(sorted(A,reverse=True))
ans = P
x = A[P-1]
y=P
z = sum(A[P-1:y])
for i in range(y,N):
  a = A[i]
  d = a+M
  if x<=d:
    b = N-i+P-1
    c = M*(V-b)
    e = z+c
    f = d*(i-P+1)
    if f>=e:
      ans+=1
      
  z+=a
print(ans)

Buggy python submission (verdict: Runtime Error):
N,M,V,P = map(int,input().split())
import numpy as np
A = list(map(int,input().split()))
A = np.array(sorted(A,reverse=True))
ans = P
x = A[P-1]
for i in range(P,N):
  a = A[i]
  if x==a:
    ans+=1
  else:
    y=i
    break
    
for i in range(y,N):
  d = A[i]+M
  if x<=d:
    b = N-i+P-1
    c = M*(V-b)
    for j in range(i-1,P-2,-1):
      e = d-A[j]
      c-=(max(0,e))
      if c <=0:
        ans+=1
        break
      elif e<=0:
        break
        
print(ans)

Fixed submission:
N,M,V,P = map(int,input().split())
import numpy as np
A = list(map(int,input().split()))
A = np.array(sorted(A,reverse=True))
ans = P
x = A[P-1]
y=P
z = sum(A[P-1:y])
for i in range(y,N):
  a = A[i]
  d = a+M
  if x<=d:
    b = N-i+P-1
    c = M*(V-b)
    e = z+c
    f = d*(i-P+1)
    if f>=e:
      ans+=1
      
  z+=a
print(ans)

Buggy python submission (verdict: Runtime Error):
N,M,V,P = map(int,input().split())
import numpy as np
A = list(map(int,input().split()))
A = np.array(sorted(A,reverse=True))
ans = P
if N//2<=V:
  V = N-V
  A += M
  x = A[P-1]
  for i in range(P,N):
    a = A[i]
    if a==x:
      ans += 1
    else:
      y = i
      break
  
  for i in range(y,y+M):
    z = i
    a = A[i]
    if x-V<=a:
      ans+=1
    else:
      break

  for j in range(z+1,N):
    if a==A[j]:
      ans+=1
      
    else:
      break
  print(ans)
  
else:
  x = A[P-1]
  for i in range(P,N):
    a = A[i]
    if a==x:
      ans += 1
    else:
      y = i
      break
  for i in range(y,y+M):
    a = A[i]

Fixed submission:
N,M,V,P = map(int,input().split())
import numpy as np
A = list(map(int,input().split()))
A = np.array(sorted(A,reverse=True))
ans = P
x = A[P-1]
y=P
z = sum(A[P-1:y])
for i in range(y,N):
  a = A[i]
  d = a+M
  if x<=d:
    b = N-i+P-1
    c = M*(V-b)
    e = z+c
    f = d*(i-P+1)
    if f>=e:
      ans+=1
      
  z+=a
print(ans)
Buggy python submission (verdict: Runtime Error):
N,u,v = map(int,input().split())
AB = [list(map(int,input().split())) for _ in range(N-1)]
    
x = [[] for _ in range(N)]
for ab in AB:
  a = ab[0]
  b = ab[1]
  x[a-1].append(b-1)
  x[b-1].append(a-1)
  
flag1 = [False]*N
flag2 = [False]*N
length1 = [0]*N
length2 = [0]*N
go = [v-1]
while go!=[]:
  a = go.pop()
  if flag1[a]:
    continue
  else:
    flag1[a]=True
    for i in x[a]:
      if flag1[i]:
        continue
      else:
        length1[i]=length1[a]+1
        go.append(i)

go = [u-1]
while go!=[]:
  a = go.pop()
  if flag2[a]:
    continue
  else:
    flag2[a]=True
    for i in x[a]:
      if flag2[i]:
        continue
      else:
        length2[i]=length2[a]+1
        go.append(i)
        
print(max(length1))

Fixed submission:
A = int(input())
B = int(input())
l = [1,2,3]
l.remove(A)
l.remove(B)
print(l[0])
Buggy python submission (verdict: Runtime Error):
N=int(input())
A = list(map(int,input().split()))
lis = [0]*200000
ans=1
num_zero=0
mod = 1000000007
for i in A:
  lis[i]+=1
  if i!=0:
    ans*=lis[i-1]
    lis[i-1]-=1
    ans%=mod
    if lis[i-1]<0:
      ans=0
      break
    
  else:
    num_zero+=1

if num_zero>=2:
  mul = 6
  
elif num_zero = 0:
  mul = 0

else:
  mul = 3
  
print((ans*mul)%mod)

Fixed submission:
N=int(input())
A = list(map(int,input().split()))
lis = [0]*200000
ans=1
num_zero=0
mod = 1000000007
for i in A:
  lis[i]+=1
  if i!=0:
    ans*=lis[i-1]
    lis[i-1]-=1
    ans%=mod
    if lis[i-1]<0:
      ans=0
      break
    
  else:
    num_zero+=1

if (num_zero==2)or(num_zero==3):
  mul = 6
  
elif num_zero==1:
  mul = 3

else:
  mul = 0
  
print((ans*mul)%mod)
Buggy python submission (verdict: Runtime Error):
import numpy as np
import math
X,Y = map(int,input().split())
 
 
c1 = (2*Y-X)
if c1%3!=0:
  print(0)
 
else:
  def cmb(n, r, mod):
    if ( r<0 or r>n ):
        return 0
    r = min(r, n-r)
    return g1[n] * g2[r] * g2[n-r] % mod
  
  c1 = c1//3
  c2 = Y-2*c1
  c3 = c1+c2+1
  mod = 10**9+7
  c4 = min(c1,c2)
  x = 1
  y = 1
  for i in range(1,c4+1):
    x = (x * (c3-i)) % mod
    y = (y * i) % mod
    
  result = (x * pow(y,mod-2,mod)) % mod
 
  print(result)

Fixed submission:
r = int(input())

print(r**2)
Buggy python submission (verdict: Time Limit Exceeded):
import numpy as np
import math
X,Y = map(int,input().split())
 
 
c1 = (2*Y-X)
if c1%3!=0:
  print(0)
 
else:
  def cmb(n, r, mod):
    if ( r<0 or r>n ):
        return 0
    r = min(r, n-r)
    return g1[n] * g2[r] * g2[n-r] % mod
  
  c1 = c1//3
  c2 = Y-2*c1
  c3 = c1+c2+1
  mod = 10**9+7
  c4 = min(c1,c2)
  x = 1
  y = 1
  for i in range(1,c4+1):
    x = (x * (c3-i)) % mod
    y = (y * i) % mod
    
  result = 1
  for _ in range(mod-2):
    result = (result * y) % mod
    
  result = (result * x) % mod
 
  print(result)

Fixed submission:
import numpy as np
import math
X,Y = map(int,input().split())


c1 = (2*Y-X)
if c1%3!=0:
  print(0)

else:
  def cmb(n, r, mod):
    if ( r<0 or r>n ):
        return 0
    r = min(r, n-r)
    return g1[n] * g2[r] * g2[n-r] % mod
  
  c1 = c1//3
  c2 = Y-2*c1
  c3 = c1+c2
  mod = 10**9+7
  g1 = [1, 1]
  g2 = [1, 1]
  inverse = [0, 1]
  for i in range( 2,c3+1):
    g1.append( ( g1[-1] * i ) % mod )
    inverse.append( ( -inverse[mod % i] * (mod//i) ) % mod )
    g2.append( (g2[-1] * inverse[-1]) % mod )

  a = cmb(c3,c1,mod)

  print(a)
Buggy python submission (verdict: Runtime Error):
N = int(input())
D = list(map(int,input().split()))
from collections import Counter
print(0)


Fixed submission:
N = int(input())
import math
print(math.ceil(N/2)-1)
Buggy python submission (verdict: Runtime Error):
a,b,x = map(int,input().split())
import math

if x==1 and a==1 and b==1:
  print(0)
if x//a<=(a*b/2):
  print(90-math.degrees(math.atan((2*x)/(a*(b**2)))))
    
else:
  print(90-math.degrees(math.atan(a/(2*(b-(x/a**2))))))

Fixed submission:
a,b,x = map(int,input().split())
import math

if x==a**2*b:
  print(0)
elif x//a<=(a*b/2):
  print(90-math.degrees(math.atan((2*x)/(a*(b**2)))))
    
else:
  print(90-math.degrees(math.atan(a/(2*(b-(x/a**2))))))

Buggy python submission (verdict: Runtime Error):
a,b,x = map(int,input().split())
import math

if x//a<=(a*b/2):
  print(90-math.degrees(math.atan((2*x)/(a*(b**2)))))
    
else:
  print(90-math.degrees(math.atan(a/(2*(b-(x/a**2))))))

Fixed submission:
a,b,x = map(int,input().split())
import math

if x==a**2*b:
  print(0)
elif x//a<=(a*b/2):
  print(90-math.degrees(math.atan((2*x)/(a*(b**2)))))
    
else:
  print(90-math.degrees(math.atan(a/(2*(b-(x/a**2))))))

Buggy python submission (verdict: Runtime Error):
a,b,x = map(int,input().split())
import math

if x//a<=(a*b/2):
	print(90-math.degrees(math.atan((2*x)/(a*(b**2)))))
    
else:
  print(90-math.degrees(math.atan(a/(2*(b-(x/a**2))))))

Fixed submission:
a,b,x = map(int,input().split())
import math

if x==a**2*b:
  print(0)
elif x//a<=(a*b/2):
  print(90-math.degrees(math.atan((2*x)/(a*(b**2)))))
    
else:
  print(90-math.degrees(math.atan(a/(2*(b-(x/a**2))))))

Buggy python submission (verdict: Runtime Error):
a,b,x = map(int,input().split())
import math

if x//a<=(a*b/2):
	print(90-math.degrees(math.atan((2*x)/(a*(b**2)))))
    
else:
  print(90-math.degrees(math.atan(a/(2*(b-(x/a**2))))))

Fixed submission:
a,b,x = map(int,input().split())
import math

if x==a**2*b:
  print(0)
elif x//a<=(a*b/2):
  print(90-math.degrees(math.atan((2*x)/(a*(b**2)))))
    
else:
  print(90-math.degrees(math.atan(a/(2*(b-(x/a**2))))))
Buggy python submission (verdict: Time Limit Exceeded):
N = int(input())
L = list(map(int,input().split()))

ans = 0

for i in range(N-2):
  for j in range(i+1,N-1):
    for k in range(j+1,N):
      li = L[i]
      lj = L[j]
      lk = L[k]
      if ((li+lj)>lk)&((lj+lk)>li)&((li+lk)>lj):
        ans += 1
      else:
        continue
        
print(ans)

Fixed submission:
N = int(input())
L = list(map(int,input().split()))
import bisect
 
L.sort()
ans = 0
 
for i in range(N-2):
  for j in range(i+1,N-1):
    ans += bisect.bisect_left(L,L[i]+L[j])-(j+1)
    
print(ans)
Buggy python submission (verdict: Runtime Error):
S = input()
K = int(input())

import re

def nchars(s, n):
    assert n > 0
    reg = re.compile("(.)\\1{%d,}" % (n - 1))
    while True:
        m = reg.search(s)
        if not m:
            break
        yield m.group(0)
        s = s[m.end():]

if S[0]!=S[-1]:
  S_l = list(nchars(S,2))
  answer = 0
  for s in S_l:
    answer += len(s)//2
  print(answer*K)

else:
  if (S[0]!=S[1])&(S[-1]!=S[-2]):
    answer = 0
    S_lr=0
    S_l = list(nchars(S,2))
    for s in S_l:
      S_lr += len(s)//2

    answer = S_lr + (1+S_lr)*(K-1)
    print(answer)
  
  elif (S[0]!=S[1])&(S[-1]==S[-2]):
    answer = 0
    S_lr=0
    S_l = list(nchars(S,2))
    for s in S_l:
      S_lr += len(s)//2
    
    a=len(S_l[-1])
    answer = S_lr + ((a+1)//2 + (S_lr-a//2))*(K-1)
    print(answer)
  
  elif (S[0]==S[1])&(S[-1]!=S[-2]):
    answer = 0
    S_lr=0
    S_l = list(nchars(S,2))
    for s in S_l:
      S_lr += len(s)//2
    
    a=len(S_l[0])
    answer = S_lr + ((a+1)//2 + (S_lr-a//2))*(K-1)
    print(answer)
    
  else:
    answer = 0
    S_lr=0
    S_l = list(nchars(S,2))
    for s in S_l:
      S_lr += len(s)//2
    
    a=len(S_l[0])
    b=len(S_l[-1])
    answer = S_lr + ((a+b)//2 + (S_lr-a//2-b//2))*(K-1)
    print(answer)

Fixed submission:
S = input()
K = int(input())

import re

def nchars(s, n):
    assert n > 0
    reg = re.compile("(.)\\1{%d,}" % (n - 1))
    while True:
        m = reg.search(s)
        if not m:
            break
        yield m.group(0)
        s = s[m.end():]

if len(S)==1:
  print(K//2)
  
elif S[0]!=S[-1]:
  S_l = list(nchars(S,2))
  answer = 0
  for s in S_l:
    answer += len(s)//2
  print(answer*K)

else:
  if (S[0]!=S[1])&(S[-1]!=S[-2]):
    answer = 0
    S_lr=0
    S_l = list(nchars(S,2))
    for s in S_l:
      S_lr += len(s)//2

    answer = S_lr + (1+S_lr)*(K-1)
    print(answer)
  
  elif (S[0]!=S[1])&(S[-1]==S[-2]):
    answer = 0
    S_lr=0
    S_l = list(nchars(S,2))
    for s in S_l:
      S_lr += len(s)//2
    
    a=len(S_l[-1])
    answer = S_lr + ((a+1)//2 + (S_lr-a//2))*(K-1)
    print(answer)
  
  elif (S[0]==S[1])&(S[-1]!=S[-2]):
    answer = 0
    S_lr=0
    S_l = list(nchars(S,2))
    for s in S_l:
      S_lr += len(s)//2
    
    a=len(S_l[0])
    answer = S_lr + ((a+1)//2 + (S_lr-a//2))*(K-1)
    print(answer)
    
  else:
    answer = 0
    S_lr=0
    S_l = list(nchars(S,2))
    if len(S_l)==1:
      print(len(S)*K//2)
    else:
      for s in S_l:
        S_lr += len(s)//2

      a=len(S_l[0])
      b=len(S_l[-1])
      answer = S_lr + ((a+b)//2 + (S_lr-a//2-b//2))*(K-1)
      print(answer)
Buggy python submission (verdict: Time Limit Exceeded):
A,B = map(int,input().split())
import math
def cf(x1,x2):
    l=[]
    min_x = min(x1,x2)
    for i in range(2,math.ceil(min_x/2)+1):
        if x1 % i == 0 and x2 % i == 0:
            l.append(i)
    return l


def is_prime(n):
    if n == 1:
      return False
    elif n==2:
      True
    elif n%2==0:
      False

    for k in range(3, int(math.sqrt(n)) + 1,2):
        if n % k == 0:
            return False

    return True

cf_l = cf(A,B)
answer = 0
while cf_l:
  cf_0 = cf_l[0]
  cf_l = cf_l[1::]
  if is_prime(cf_0):
    answer += 1
    cf_l = list(filter(lambda x:x%cf_0!=0,cf_l))
print(answer+1)

Fixed submission:
A,B = map(int,input().split())
import math
import fractions
def factorization(n):
    arr = []
    temp = n
    if n!=1:
      for i in range(2, int(-(-n**0.5//1))+1):
          if temp%i==0:
              cnt=0
              while temp%i==0:
                  cnt+=1
                  temp //= i
              arr.append([i, cnt])

      if temp!=1:
          arr.append([temp, 1])

      if arr==[]:
          arr.append([n, 1])

      return len(arr)
    else:
      return 0
print(factorization(fractions.gcd(A,B))+1)
Buggy python submission (verdict: Runtime Error):
N, K = map(int, input().split())
Ss = input()
 
num = Ss.count('RL')*2
if list(Ss)[-1]=='L':
  num += 1
if list(Ss)[0]=='L':
  num += 1
ans = N - max(1, num-2*K)
print(ans)

Fixed submission:
N = int(input())
print(N**3)
Buggy python submission (verdict: Runtime Error):
N,Q = map(int,input().split())
ab = [list(map(int,input().split())) for _ in range(N-1)]
px = [list(map(int,input().split())) for _ in range(Q)]
tree = [[] for i in range(N)]
ans = [0]*N
ad = [0]*N
for a,b in ab:
  tree[a-1].append(b-1)
  

for i in range(N-1,-1,-1):
  x = tree[i].copy()
  for j in x:
    tree[i]+=tree[j]

for p,x in px:
  ad[p-1]+=x
  

for i,a in enumerate(ad):
  ans[i]+=a
  x=tree[i].copy()
  for j in x:
    ans[j]+=a
    
print(' '.join(map(str,ans)))

Fixed submission:
from collections import deque
N, Q = map(int, input().split())
ab = [list(map(int,input().split())) for _ in range(N-1)]
px = [list(map(int,input().split())) for _ in range(Q)]
tree = [[] for _ in range(N)]
ans = [0]*N
for a,b in ab:
  tree[a-1].append(b-1)
  tree[b-1].append(a-1)
  
for p,x in px:
  ans[p-1]+=x
  
q = deque([0])
judge = [False]*N
while q:
  a=q.pop()
  judge[a]=True
  for i in tree[a]:
    if judge[i]:
      continue
    ans[i]+=ans[a]
    q.append(i)
    
print(' '.join(map(str,ans)))
Buggy python submission (verdict: Time Limit Exceeded):
N = int(input())
a = list(map(int,input().split()))
ans = []
def divisor(n):
  ret = [0]
  for i in range(2,int(n**(1/2))+1):
    if n%i==0:
      ret.append(i-1)
      
      comp=n//i
      if i!=comp:
        ret.append(comp-1)
      
  return ret

for i in reversed(range(N)):
  if a[i]:
    ans.append(i+1)
    lis = divisor(i+1)
    for j in lis:
      a[j]^=1
      
l = len(ans)
if l>0:
  print(l)
  print(*ans)
else:
  print(l)

Fixed submission:
N = int(input())
a = list(map(int,input().split()))
ans = []
def divisor(n):
  ret = [0]
  for i in range(2,int(n**(1/2))+1):
    if n%i==0:
      ret.append(i-1)
      
      comp=n//i
      if i!=comp:
        ret.append(comp-1)
      
  return ret

for i in reversed(range(N)):
  if a[i]:
    ans.append(i+1)
    lis = divisor(i+1)
    for j in lis:
      a[j]^=1
      
l = len(ans)
if l>0:
  print(l)
  print(*ans)
else:
  print(l)
Buggy python submission (verdict: Runtime Error):
N,P = map(int,input().split())
i = round(P**(1/N))
res = []
if N == 1:
  print(P)
elif P == 1|N>=40:
  print(1)
else:
  for i in range(i,0,-1):
    if P%i**N==0:
      print(i)
      break

Fixed submission:
N = map(str,input())
M = [M for M in N]
print(M.count("2"))

Buggy python submission (verdict: Runtime Error):
import functools
import operator

N,P = map(int,input().split())

i = 2
res = []
i_2 = i**N
while i * i<=P:
  while P%i_2==0:
    P/=i_2
    res.append(i)
  else:
    i += 1
    
res.append(1)
result = functools.reduce(operator.mul, res)
print(result)

Fixed submission:
N = map(str,input())
M = [M for M in N]
print(M.count("2"))

Buggy python submission (verdict: Runtime Error):
import collections
from functools import reduce
from operator import mul
N,P = map(int,input().split())

def prime_decomposition(n):
  i = 2
  table = []
  while i * i <= n:
    while n % i == 0:
      n /= i
      table.append(i)
    i += 1
  if n > 1:
    table.append(n)
  return table

P = prime_decomposition(P)
c = collections.Counter(P)
temp = [i[0] for i in c.items() if i[1] >= N]
 
temp.append(1)
 
print(int(reduce(mul,temp)))

Fixed submission:
N = map(str,input())
M = [M for M in N]
print(M.count("2"))

Buggy python submission (verdict: Runtime Error):
N = map(str,input())
M = [M for M in N]
print(M.count("2")


Fixed submission:
N = map(str,input())
M = [M for M in N]
print(M.count("2"))
Buggy python submission (verdict: Runtime Error):
N,K = map(int,input().split())
N_d = N*2
ans = 0
kl = [K*x for x in range(1,N_d//K+1)]
s=kl[-1]
t=kl[-2]
if K%2==1:
  a=s//K
  if a%2==0:
    b = a//2
    ans = pow(b,3)
    
  else:
    b=a//2
    ans = pow(b,3)+3
    
else:
  half_K = K//2
  a = s//K
  if a%2==0:
    b = a//2
    ans+=pow(b,3)
  else:
    b=a//2
    ans += pow(b,3)+3
    
  b = t//K
  if b%2==0:
    c = b//2
    ans+=pow(c,3)
  else:
    c=b//2
    ans+=pow(b,3)+3
  
print(ans)

Fixed submission:
N,K = map(int,input().split())
ans = 0
if K%2==1:
  ans = (N//K) ** 3
else:
  half_K = K//2
  a = N//K
  b = N//half_K - a
  ans = a**3+b**3

print(ans)
Buggy python submission (verdict: Runtime Error):
N=int(input())
S=input()
sl=list(S)
change=[0]
for i in range(1,N):
  if (sl[i-1]==')')and(sl[i]=='('):
    change.append(i)

change.append(N)
r_add=0
l_add=0
for i in range(len(change)-1):
  A=sl[change[i]:change[i+1]]
  r=0
  l=0
  for a in A:
    if a=='(':
      l+=1
    else:
      r+=1
      
  if r==l:
    continue
  elif r>l:
    l_add+=r-l
    r_add=max(0,r_add-(r-l))
  else:
    r_add+=l-r
      
print('('*l_add+S+')'*r_add)print('('*l_add+S+')'*r_add)

Fixed submission:
N=int(input())
S=input()
sl=list(S)
change=[0]
for i in range(1,N):
  if (sl[i-1]==')')and(sl[i]=='('):
    change.append(i)

change.append(N)
r_add=0
l_add=0
for i in range(len(change)-1):
  A=sl[change[i]:change[i+1]]
  r=0
  l=0
  for a in A:
    if a=='(':
      l+=1
    else:
      r+=1
      
  if r==l:
    continue
  elif r>l:
    if r_add>0:
      if r_add>=r-l:
        r_add-=r-l
      else:
        l_add+=r-l-r_add
        r_add=0
        
    else:
      l_add+=r-l
      
  else:
    r_add+=l-r
      
print('('*l_add+S+')'*r_add)

Buggy python submission (verdict: Runtime Error):
N=int(input())
S=input()
sl=list(S)
change=[0]
ans=''
for i in range(N+1):
  if (sl[i-1]==')')and(sl[i]=='('):
    change.append(i)

change.append(N)
for i in range(len(change)-1):
  A=sl[change[i]:change[i+1]]
  r=0
  l=0
  for a in A:
    if a=='(':
      l+=1
    else:
      r+=1
      
  if r==l:
    ans+=''.join(A)
  elif r>l:
    ans+='('*(r-l)+''.join(A)
  else:
    ans+=''.join(A)+')'*(l-r)
      
print(ans)

Fixed submission:
N=int(input())
S=input()
sl=list(S)
change=[0]
for i in range(1,N):
  if (sl[i-1]==')')and(sl[i]=='('):
    change.append(i)

change.append(N)
r_add=0
l_add=0
for i in range(len(change)-1):
  A=sl[change[i]:change[i+1]]
  r=0
  l=0
  for a in A:
    if a=='(':
      l+=1
    else:
      r+=1
      
  if r==l:
    continue
  elif r>l:
    if r_add>0:
      if r_add>=r-l:
        r_add-=r-l
      else:
        l_add+=r-l-r_add
        r_add=0
        
    else:
      l_add+=r-l
      
  else:
    r_add+=l-r
      
print('('*l_add+S+')'*r_add)
Buggy python submission (verdict: Time Limit Exceeded):
a,b,x = map(int,input().split())
ans = 0
for i in range(a,b+1):
  if i%x==0:
    ans+=1
    
print(ans)

Fixed submission:
a,b,x = map(int,input().split())
ans = 0
if a==0:
  ans=b//x+1
  
else:
  ans = b//x - (a-1)//x
  
print(ans)

Buggy python submission (verdict: Time Limit Exceeded):
a,b,x = map(int,input().split())
ans = 0
for i in range(a,b+1):
  if i%x==0:
    ans+=1
    
print(ans)

Fixed submission:
a,b,x = map(int,input().split())
ans = 0
if a==0:
  ans=b//x+1
  
else:
  ans = b//x - (a-1)//x
  
print(ans)
Buggy python submission (verdict: Time Limit Exceeded):
n, x, m = [int(x) for x in input().split()]
A = [x]
while len(A) < n:
    a = (A[-1] * A[-1]) % m
    if a not in A:
        A.append(a)
    else:
        i = A.index(a)
        loop_len = len(A) - i
        print(sum(A[:i]) + sum(A[i:]) * ((n - i) // loop_len) + sum(A[i:i + ((n - i) % loop_len)]))
        break
else:
    print(sum(A))


Fixed submission:
n, x, m = [int(x) for x in input().split()]
A = [x]
while len(A) < n:
    a = (A[-1] * A[-1]) % m
    if a not in A:
        A.append(a)
    else:
        i = A.index(a)
        loop_len = len(A) - i
        print(sum(A[:i]) + sum(A[i:]) * ((n - i) // loop_len) + sum(A[i:i + ((n - i) % loop_len)]))
        break
else:
    print(sum(A))
Buggy python submission (verdict: Time Limit Exceeded):
n = int(input())
A = [int(x) for x in input().split()]

A.sort(reverse=True)

line = [A[0]]
comfort = 0
for a in A[1:]:
    diff_comfort = [min(line[(i + 1) % len(line)], line[i])
                    for i in range(len(line))]
    pos = min(range(len(line)), key=lambda i: diff_comfort[i])
    comfort += diff_comfort[pos]
    line.insert(pos + 1 if pos < len(line) - 1 else 0, a)
print(comfort)


Fixed submission:
n = int(input())
A = [int(x) for x in input().split()]
A.sort(reverse=True)
print(A[0] + sum(A[1:(n - 2) // 2 + 1]) * 2 +
      (0 if n % 2 == 0 else A[(n - 1) // 2]))
Buggy python submission (verdict: Runtime Error):
n = int(input())
cur = 0
best = 0
for _ in range(n):
  	a, b = input().split()
    if a == b:
        cur += 1
        best = max(best, cur)
    else:
      	cur = 0
if best >= 3:
  	print("Yes")
else:
  	print("No")

Fixed submission:
n = int(input())
cur = 0
best = 0
for _ in range(n):
        a, b = input().split()
        if a == b:
                cur += 1
                best = max(best, cur)
        else:
                cur = 0
if best >= 3:
        print("Yes")
else:
        print("No")