Harryxun/testdata huggingface dataset:
Buggy python submission (verdict: Time Limit Exceeded):
import math


def combinations_count(n, r):
    return math.factorial(n) // (math.factorial(n - r) * math.factorial(r))


N = int(input())
a = list(map(int, input().split()))
a.sort(reverse=True)

b = []
for i in range(N - 1):
    x = a[i] // 2
    l = i + 1
    r = N - 1
    while r - l > 1:
        mid = l + (r - l) // 2
        if a[mid] < x:
            r = mid
        else:
            l = mid
    if abs(x - a[l]) <= abs(x - a[r]):
        b.append([a[i], a[l]])
    else:
        b.append([a[i], a[r]])

t = 0
ans = 0

for i in range(len(b)):
    tmp = combinations_count(b[i][0], b[i][1])
    if t < tmp:
        t = tmp
        ans = i

print(b[ans][0], b[ans][1])


Fixed submission:
N = int(input())
a = list(map(int, input().split()))
a.sort(reverse=True)

x = a[0] // 2
l = 1
r = N - 1
while r - l > 1:
    mid = l + (r - l) // 2
    if a[mid] < x:
        r = mid
    else:
        l = mid
if abs(x - a[l]) <= abs(x - a[r]):
    print(a[0], a[l])
else:
    print(a[0], a[r])

Buggy python submission (verdict: Time Limit Exceeded):
import math


def combinations_count(n, r):
    return math.factorial(n) // (math.factorial(n - r) * math.factorial(r))


N = int(input())
a = list(map(int, input().split()))
a.sort(reverse=True)

b = []
for i in range(N - 1):
    x = a[i] // 2
    l = i + 1
    r = N - 1
    while r - l > 1:
        mid = l + (r - l) // 2
        if a[mid] < x:
            r = mid
        else:
            l = mid
    if abs(x - a[l]) <= abs(x - a[r]):
        b.append([a[i], a[l]])
    else:
        b.append([a[i], a[r]])

t = 0
ans = 0

for i in range(len(b)):
    tmp = combinations_count(b[i][0], b[i][1])
    if t < tmp:
        t = tmp
        ans = i

print(b[ans][0], b[ans][1])


Fixed submission:
N = int(input())
a = list(map(int, input().split()))
a.sort(reverse=True)

x = a[0] // 2
l = 1
r = N - 1
while r - l > 1:
    mid = l + (r - l) // 2
    if a[mid] < x:
        r = mid
    else:
        l = mid
if abs(x - a[l]) <= abs(x - a[r]):
    print(a[0], a[l])
else:
    print(a[0], a[r])
Buggy python submission (verdict: Time Limit Exceeded):
import itertools

n, k = map(int, input().split())
p_list = [[0] * 2 for i in range(n)]

for i in range(n):
    x, y = map(int, input().split())
    p_list[i] = [x, y]

k_list = list(itertools.combinations(range(n), k))
min_area = ((10 ** 9) * 2) ** 2

for ki in k_list:
    x_list = []
    y_list = []
    for i in ki:
        x_list.append(p_list[i][0])
        y_list.append(p_list[i][1])
    x_max = max(x_list)
    x_min = min(x_list)
    y_max = max(y_list)
    y_min = min(y_list)
    area = abs(x_max - x_min) * abs(y_max - y_min)
    if area < min_area:
        min_area = area

print(min_area)



Fixed submission:
N, K = map(int, input().split())
p_list = [[0] * 2 for i in range(N)]
for i in range(N):
    x, y = map(int, input().split())
    p_list[i] = [x, y]

p_list.sort()
ans = float('inf')
for i in range(N - K + 1):
    for j in range(i + K - 1, N):
        x = abs(p_list[j][0] - p_list[i][0])
        y_list = []
        for k in range(i, j + 1):
            y_list.append((p_list[k][1]))
        y_list.sort()
        for k in range(len(y_list) - K + 1):
            ans = min(ans, x * abs(y_list[k + K - 1] - y_list[k]))

print(ans)
Buggy python submission (verdict: Time Limit Exceeded):
import math
n = int(input())
res=0
for i in range(1,n):

    cnt=0
    for j in range(1,int(math.sqrt(i))+1):
        if i%j==0:
            cnt+=2
    if math.sqrt(i)==int(math.sqrt(i)):
        cnt-=1
    res+=cnt
print(res)
    
    

Fixed submission:

n = int(input())
res=0
for i in range(1,n-1):
    res+=(n-1)//i
print(res+1)
Buggy python submission (verdict: Runtime Error):
import math
n, k = map(int,input().split())
g={}
for i in range(n):
    g[i]=[]
for i in range(k):
    a,b= map(int,input().split())
    g[a-1].append(b-1)
    g[b-1].append(a-1)
ans = [-1] * n
queue = [0]
visited = [False] * n
 

while queue:
    x = queue.pop(0)
    for n in g[x]:
        if visited[n] == False: 
            queue.append(n)
            if ans[n] == -1: 
                ans[n] = x
                visited[n] = True
 
if -1 in ans[1:]:
    print('No')
else:
    print('Yes')
    for a in ans[1:]:
        print(a+1)

Fixed submission:
n = (input())
s=int(n[-1])
if s in (2,4,5,7,9):
  print("hon")
elif s in (1,6,8,0):
  print("pon")
else:
  print("bon")

Buggy python submission (verdict: Runtime Error):
import math
n, k = map(int,input().split())
g={}
for i in range(n):
    g[i]=[]
for i in range(k):
    a,b= map(int,input().split())
    g[a-1].append(b-1)
    g[b-1].append(a-1)
ans = [-1] * n
queue = [0]
visited = [False] * n
 

while queue:
    x = queue.pop(0)
    for n in g[x]:
        if visited[n] == False: 
            queue.append(n)
            if ans[n] == -1: 
                ans[n] = x
                visited[n] = True
 
if -1 in ans[1:]:
    print('No')
else:
    print('Yes')
    for a in ans[1:]:
        print(a+1)

Fixed submission:
n = (input())
s=int(n[-1])
if s in (2,4,5,7,9):
  print("hon")
elif s in (1,6,8,0):
  print("pon")
else:
  print("bon")
Buggy python submission (verdict: Time Limit Exceeded):
import math
n, k = map(int,input().split())
g={}
for i in range(n):
    g[i]=[]
for i in range(k):
    a,b= map(int,input().split())
    g[a-1].append(b-1)
    g[b-1].append(a-1)
ans = [-1] * n
queue = [0]
visited = [False] * n
 

while queue:
    x = queue.pop(0)
    for n in g[x]:
        if visited[n] == False: 
            queue.append(n)
            if ans[n] == -1: 
                ans[n] = x
                visited[n] = True
 
if -1 in ans[1:]:
    print('No')
else:
    print('Yes')
    for a in ans[1:]:
        print(a+1)

Fixed submission:
import math
n, k = map(int,input().split())
g={}
for i in range(n):
    g[i]=[]
for i in range(k):
    a,b= map(int,input().split())
    g[a-1].append(b-1)
    g[b-1].append(a-1)
ans = [-1] * n
queue = [0]
visited = [False] * n
 

while queue:
    x = queue.pop(0)
    for n in g[x]:
        if visited[n] == False: 
            queue.append(n)
            if ans[n] == -1: 
                ans[n] = x
                visited[n] = True
 
if -1 in ans[1:]:
    print('No')
else:
    print('Yes')
    for a in ans[1:]:
        print(a+1)
Buggy python submission (verdict: Runtime Error):
n,k = map(int,input().split())
l =[0]+ list(map(int,input().split()))
q=l[1]
cnt=1
d=[]
d.append(q)
while True and cnt<=n:
    q=l[q]
    cnt+=1
    if q in d:
        d.append(q)
        break
    else:
        d.append(q)
a=d.index(d[-1])
la=len(d)-1
cir=la-a
k=k-a
k=k%cir

print(d[a+k-1])
    

Fixed submission:
from math import sqrt
s = input()
t= input()

if t==(s+t[-1]):
    print("Yes")
else:
    print("No")
Buggy python submission (verdict: Runtime Error):
n,k = map(int,input().split())
s=[]
for i in range(k):
  s= int(input())
  l=list(map(int,input().split()))
  s=s+l
r=set(s)
print(n-len(r))
  

Fixed submission:
n,k = map(int,input().split())
e=[]
for i in range(k):
  s= int(input())
  l=list(map(int,input().split()))
  e=e+l
r=set(e)
print(n-len(r))
Buggy python submission (verdict: Runtime Error):

n= int(input())
x=0
while True:
    if int((n-(x**5))**(1/5))==(n-(x**5))**(1/5):
        print(-x,int((n+(x**5))**(1/5)))
        break
    if  int((n+(x**5))**(1/5))==(n+(x**5))**(1/5):
        print(x,int((n+(x**5))**(1/5)))
    x=x+1

Fixed submission:
x = int(input())
for i in range(-1000,1000):
    for j in range(-1000,1000):
        if x == i**5 - j ** 5:
            print(i,j)
            exit()
Buggy python submission (verdict: Time Limit Exceeded):

n= int(input())
l=[0]+list(map(int,input().split()))

d=[0]*(n+1)
for i in range(1,n+1):
    for k in range(i+1,n+1):
        if k-i==l[k]+l[i]:
            d[k-i]+=1
print(sum(d))

Fixed submission:
n= int(input())
l=list(map(int,input().split()))
d={}
ans=0
for i in range(n):
    
    if i-l[i] in d:
        ans+=d[i-l[i]]
    if i+l[i] in d:
        d[i+l[i]]+=1
    else:
        d[i+l[i]]=1
print(ans)
Buggy python submission (verdict: Time Limit Exceeded):
n= input()
ans=0
for i in range(len(n)):
    for s in range(i+3,len(n)):
        if int(n[i:s+1])%2019 ==0:
            
            ans=ans+1
print(ans)

Fixed submission:
s= input()[::-1]
mods= [0] * 2019
mods[0] = 1
num=0
d = 1
for c in s:
    num += int(c) * d
    num %= 2019
    d *= 10
    d %= 2019
    mods[num] += 1

ans = 0
for cnt in mods:
    ans += cnt * (cnt - 1) // 2

print(ans)

Buggy python submission (verdict: Time Limit Exceeded):
n= input()
ans=0
for i in range(len(n)):
    for s in range(i+1,len(n)):
        if int(n[i:s+1])%2019 ==0:
            
            ans=ans+1
print(ans)



Fixed submission:
s= input()[::-1]
mods= [0] * 2019
mods[0] = 1
num=0
d = 1
for c in s:
    num += int(c) * d
    num %= 2019
    d *= 10
    d %= 2019
    mods[num] += 1

ans = 0
for cnt in mods:
    ans += cnt * (cnt - 1) // 2

print(ans)
Buggy python submission (verdict: Runtime Error):
f=t//5
tt=t//3
ff=t//15
f=(f*(f+1)//2 )*5
tt=(tt*(tt+1)//2 )*3
ff =(ff*(ff+1)//2 )*15
print(t*(t+1)//2 - f -tt +ff)


Fixed submission:
t = int(input())
f=t//5
tt=t//3
ff=t//15
f=(f*(f+1)//2 )*5
tt=(tt*(tt+1)//2 )*3
ff =(ff*(ff+1)//2 )*15
print(t*(t+1)//2 - f -tt +ff)
Buggy python submission (verdict: Runtime Error):
n,m= map(int,input().split())
l = list(map(int,input().split()))
s = sum(l)
r=s/(4*m)
cnt=0
for i in l:
    
    if i>=r:
        cnt=cnt+1

if cnt>=m:
    print("Yes")
else:
    print("No")
            

Fixed submission:
a,b,c= map(int,input().split())
print(c,a,b)
Buggy python submission (verdict: Runtime Error):
n = input()
if s[2]==s[3] and s[4]==s[5]:
  print("Yes")
else:
  print("No")

Fixed submission:
s = input()
if s[2]==s[3] and s[4]==s[5]:
  print("Yes")
else:
  print("No")
Buggy python submission (verdict: Runtime Error):
from collections import Counter
 
N = int(input())
A = sorted(list(map(int,input().split())))
 
edible = sum(i-1 for i in Counter(A).values())
print(len(set(A))-edible%2)

Fixed submission:
x=int(input())
if x<1200:
  print("ABC")
else:
  print("ARC")
Buggy python submission (verdict: Runtime Error):
s =input()
print(s[:5]+" "+s[6:13]+" "+s[14:] 

Fixed submission:
s =input()
print(s[:5]+" "+s[6:13]+" "+s[14:])
Buggy python submission (verdict: Runtime Error):
    x = int(input())
    if x == 0:
        print(1)
    else:
        print(0)

Fixed submission:
x = int(input())
if x == 0:
    print(1)
else:
    print(0)
Buggy python submission (verdict: Runtime Error):
n = int(input())
arr = list(map(int, input().split()))

while len(arr) > 1:
    m = len(arr)
    if m & 1:
        arr.append(1)
        m += 1

    left, right = arr[:n // 2], arr[n // 2:]
    arr = [x * y for x, y in zip(left, right)]

x = arr[0]
if x > 10 ** 18:
    print(-1)
else:
    print(x)


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

while len(arr) > 1:
    m = len(arr)
    if m & 1:
        arr.append(1)
        m += 1

    left, right = arr[:m // 2], arr[m // 2:]
    arr = [x * y for x, y in zip(left, right)]

x = arr[0]
if x > 10 ** 18:
    print(-1)
else:
    print(x)
Buggy python submission (verdict: Runtime Error):
n, k = map(int, input().split())

arr = []
for _ in range(k):
.    d = int(input())
    a = list(map(int, input().split()))
    arr.append(a)

oks = [False] * n
for xs in arr:
    for x in xs:
        oks[x - 1] = True

ans = 0
for x in oks:
    if x == False:
        ans += 1

print(ans)


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

arr = []
for _ in range(k):
    d = int(input())
    a = list(map(int, input().split()))
    arr.append(a)

oks = [False] * n
for xs in arr:
    for x in xs:
        oks[x - 1] = True

ans = 0
for x in oks:
    if x == False:
        ans += 1

print(ans)
Buggy python submission (verdict: Runtime Error):
n, k = map(int, input().split())

def gcd(a,b):
    while b!=0:
        a,b=b,a%b
    return a

x = gcd(max(k, n), min(k, n))
if n % k == 0:
    print(0)
elif n < k:
    print(min(n, abs(n - k)))
else:
    exit(1)
    print(1)


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

print(min(n % k, k - (n % k)))

Buggy python submission (verdict: Runtime Error):
n, k = map(int, input().split())

def gcd(a,b):
    while b!=0:
        a,b=b,a%b
    return a

x = gcd(max(k, n), min(k, n))
if n % k == 0:
    print(0)
elif n < k:
    exit(1)
    print(min(n, abs(n - k)))
else:
    print(1)


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

print(min(n % k, k - (n % k)))
Buggy python submission (verdict: Time Limit Exceeded):
n, x, y = map(int, input().split())

inf = 1000000000
edges = [[inf] * n for _ in range(n)]
for i in range(n - 1):
    edges[i][i + 1] = 1
    edges[i + 1][i] = 1

edges[x - 1][y - 1] = 1

for k in range(n):
    for i in range(n):
        for j in range(n):
            edges[i][j] = min(edges[i][j], edges[i][k] + edges[k][j])

cnts = [0] * (n - 1)
for i in range(n - 1):
    for j in range(i + 1, n):
        cnts[edges[i][j] - 1] += 1

for x in cnts:
    print(x)


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

ans = [0] * n
for i in range(1, n + 1):
    for j in range(i + 1, n + 1):
        ans[min(j - i, min(abs(i - x) + 1 + abs(y - j),
                           abs(i - y) + 1 + abs(x - j)))] += 1

for x in ans[1:]:
    print(x)
Buggy python submission (verdict: Time Limit Exceeded):
import sys

sys.setrecursionlimit(10**9)

input = sys.stdin.readline

N = int(input())
A = list(map(int, input().split()))
put = []

for i in reversed(range(N)):
    if A[i]:
        put.append(i + 1)

        tmp = 1
        n = i + 1
        while tmp * tmp <= n:
            if n % tmp == 0:
                A[tmp - 1] ^= 1
                if tmp != n // tmp:
                    A[n // tmp - 1] ^= 1
            tmp += 1

if len(put) > 0:
    print(len(put))
    print(*put)
else:
    print(0)


Fixed submission:
import sys

sys.setrecursionlimit(10**9)

input = sys.stdin.readline

N = int(input())
A = list(map(int, input().split()))
put = []

for i in reversed(range(N)):
    if A[i]:
        put.append(i + 1)

        tmp = 1
        n = i + 1
        while tmp * tmp <= n:
            if n % tmp == 0:
                A[tmp - 1] ^= 1
                if tmp != n // tmp:
                    A[n // tmp - 1] ^= 1
            tmp += 1

if len(put) > 0:
    print(len(put))
    print(*put)
else:
    print(0)
Buggy python submission (verdict: Runtime Error):
from collections import*
from bisect import*
n=int(input())
a=list(map(int,input().split()))
b=list(map(int,input().split()))
ca=Counter(a)
cb=Counter(b)
for i in a:
  if ca[i]+cb[i]>n:
    print('No')
    exiit()
print('Yes')
ba=[bisect(a,i+1) for i in range(n)]
bb=[bisect_left(b,i+1) for i in range(n)]
i=0
for x,y in zip(ba,bb):
  i=max(i,abs(x-y))
ans=b[i:]+b[:i]
print(*ans)

Fixed submission:
from collections import*
from bisect import*
n=int(input())
a=list(map(int,input().split()))
b=list(map(int,input().split()))
ca=Counter(a)
cb=Counter(b)
for i in a:
  if ca[i]+cb[i]>n:
    print('No')
    exit()
print('Yes')
ba=[bisect(a,i+1) for i in range(n)]
bb=[bisect_left(b,i+1) for i in range(n)]
i=0
for x,y in zip(ba,bb):
  i=max(i,x-y)
ans=b[n-i:]+b[:n-i]
print(*ans)

Buggy python submission (verdict: Time Limit Exceeded):
from collections import*
n=int(input())
a=list(map(int,input().split()))
b=Counter(list(map(int,input().split())))
c=Counter(a)
d=Counter()
for i in c.keys():
  if n-b[i]<c[i]:
    print('No')
    exit()
print('Yes')
i=n-1
while i>=0:
  x=a[i]
  for y in b.keys():
    if x==y:continue
    for j in range(min(b[y],c[x])):
      a[i]=y
      d+=Counter({y:1})
      i-=1
    c[x]-=j+1
  b-=d
print(*a)

Fixed submission:
from collections import*
from bisect import*
n=int(input())
a=list(map(int,input().split()))
b=list(map(int,input().split()))
ca=Counter(a)
cb=Counter(b)
for i in a:
  if ca[i]+cb[i]>n:
    print('No')
    exit()
print('Yes')
ba=[bisect(a,i+1) for i in range(n)]
bb=[bisect_left(b,i+1) for i in range(n)]
i=0
for x,y in zip(ba,bb):
  i=max(i,x-y)
ans=b[n-i:]+b[:n-i]
print(*ans)
Buggy python submission (verdict: Runtime Error):
n,k=map(int,input().split())
p=[0]+list(map(int,input().split()))
c=[0]+list(map(int,input().split()))
ans=-10**18
for i in range(1,n+1):
  vis=set()
  now=i
  a=[0]
  m=k
  while m:
    vis.add(now)
    now=p[now]
    a+=[c[now]+a[-1]]
    m-=1
    if now in vis:break
  if m==0 or a[-1]<=0:
    cnt=max(a[1:])
  else:
    cnt=k//(k-m)*a[-1]+max(a[1:k%(k-m)+1])
  ans=max(ans,cnt)
print(ans) 

Fixed submission:
n,k=map(int,input().split())
p=[0]+list(map(int,input().split()))
c=[0]+list(map(int,input().split()))
ans=-10**18
for i in range(1,n+1):
  vis=set()
  now=i
  a=[0]
  m=k
  while m:
    vis.add(now)
    now=p[now]
    a+=[c[now]+a[-1]]
    m-=1
    if now in vis:break
  if m==0 or a[-1]<=0:
    cnt=max(a[1:])
  else:
    cnt=(k//(k-m))*a[-1]
    if k%(k-m):cnt+=max(a[1:k%(k-m)+1])
    elif max(a[1:])>a[-1]:
      cnt=cnt=(k//(k-m)-1)*a[-1]+max(a[1:])
  ans=max(ans,cnt)
print(ans)
Buggy python submission (verdict: Time Limit Exceeded):
h,w,k=map(int,input().split())
dp=[[[0]*4 for _ in range(w+2)] for _ in range(h+2)]
f=[[0]*(w+1) for _ in range(h+1)]
for i in range(1,k+1):
  r,c,v=map(int,input().split())
  f[r][c]=v
for i in range(1,h+1):
  for j in range(1,w+1):
    for k in range(3,-1,-1):
      if k:dp[i][j][k]=max(dp[i][j][k],dp[i][j][k-1]+f[i][j])
      dp[i+1][j][0]=max(dp[i+1][j][0],dp[i][j][k])
      dp[i][j+1][k]=max(dp[i][j+1][k],dp[i][j][k])
print(max(dp[h][w]))

Fixed submission:
h,w,k=map(int,input().split())
dp=[[[0]*(w+2) for _ in range(h+2)] for _ in range(4)]
f=[[0]*(w+1) for _ in range(h+1)]
for _ in range(k):
  r,c,v=map(int,input().split())
  f[r][c]=v
for i in range(1,h+1):
  for j in range(1,w+1):
    for k in range(3,-1,-1):
      if k:dp[k][i][j]=max(dp[k][i][j],dp[k-1][i][j]+f[i][j])
      dp[0][i+1][j]=max(dp[0][i+1][j],dp[k][i][j])
      dp[k][i][j+1]=max(dp[k][i][j+1],dp[k][i][j])
print(max(dp[k][h][w] for k in range(4)))

Buggy python submission (verdict: Runtime Error):
h,w,n=map(int,input().split())
dp=[[[0]*4 for _ in range(w+1)] for _ in range(h+1)]
v=[[0]*(w+1) for _ in range(h+1)]
for _ in range(n):
  r,c,f=map(int,input().split())
  v[r][c]=f
for i in range(1,h+1):
  for x in 0,1,2:
    for j in range(1,w+1):
      dp[i][j][x+1]=max(dp[i][j][x],max(dp[i][j+1][x],(x<1)*dp[i+1][j][3])+v[i][j],dp[i+1][j][x+1])
print(dp[-1][-1][-1])

Fixed submission:
h,w,k=map(int,input().split())
dp=[[[0]*(w+2) for _ in range(h+2)] for _ in range(4)]
f=[[0]*(w+1) for _ in range(h+1)]
for _ in range(k):
  r,c,v=map(int,input().split())
  f[r][c]=v
for i in range(1,h+1):
  for j in range(1,w+1):
    for k in range(3,-1,-1):
      if k:dp[k][i][j]=max(dp[k][i][j],dp[k-1][i][j]+f[i][j])
      dp[0][i+1][j]=max(dp[0][i+1][j],dp[k][i][j])
      dp[k][i][j+1]=max(dp[k][i][j+1],dp[k][i][j])
print(max(dp[k][h][w] for k in range(4)))

Buggy python submission (verdict: Runtime Error):
h,w,n=map(int,input().split())
dp=[[[0]*4 for _ in range(w+1)] for _ in range(h+1)]
v=[[0]*(w+1) for _ in range(h+1)]
for _ in range(n):
  r,c,f=map(int,input().split())
  v[r][c]=f
for i in range(h):
  for x in 1,2,3:
    for j in range(w):
      dp[i+1][j+1][x]=max(dp[i+1][j+1][x-1],max(dp[i][j+1][x],(x<2)*dp[i+1][j][3])+v[i+1][j+1],dp[i+1][j][x]
print(dp[-1][-1][-1])

Fixed submission:
h,w,k=map(int,input().split())
dp=[[[0]*(w+2) for _ in range(h+2)] for _ in range(4)]
f=[[0]*(w+1) for _ in range(h+1)]
for _ in range(k):
  r,c,v=map(int,input().split())
  f[r][c]=v
for i in range(1,h+1):
  for j in range(1,w+1):
    for k in range(3,-1,-1):
      if k:dp[k][i][j]=max(dp[k][i][j],dp[k-1][i][j]+f[i][j])
      dp[0][i+1][j]=max(dp[0][i+1][j],dp[k][i][j])
      dp[k][i][j+1]=max(dp[k][i][j+1],dp[k][i][j])
print(max(dp[k][h][w] for k in range(4)))
Buggy python submission (verdict: Time Limit Exceeded):
n,k=map(int,input().split())
a=[1]+list(map(int,input().split()))
b=[]
for i in range(1,n):
  a[i+1]*=a[i]
for i in range(k,n+1):
  b+=[a[i]//a[i-k]]
for i in range(1,n-k+1):
  print(['No','Yes'][b[i]>b[i-1]])

Fixed submission:
n,k=map(int,input().split())
a=list(map(int,input().split()))
for i in range(n-k):
  print(['No','Yes'][a[i+k]>a[i]])

Buggy python submission (verdict: Time Limit Exceeded):
n,k=map(int,input().split())
a=[1]+list(map(int,input().split()))
for i in range(n):
  a[i+1]*=a[i]
for i in range(n-k):
  print(['No','Yes'][a[i+k+1]//a[i+1]>a[i+k]//a[i]])

Fixed submission:
n,k=map(int,input().split())
a=list(map(int,input().split()))
for i in range(n-k):
  print(['No','Yes'][a[i+k]>a[i]])
Buggy python submission (verdict: Runtime Error):
from collections import Counter 
n=int(input())
a=sorted(list(map(int,input().split())))
b=[]
c=[]
for i in list(Counter(a).values()):
  b.append(i)
for i in list(Counter(a).keys()):
  c.append(i)
ans=c.pop()*((b[-1])-1)
m=a[-1]
f=len(b)
for _ in range(f-2,-1,-1):
  if b[-1]>b[i]:
    b[-1]-=b[i]
    b.pop(i)
    c.pop(i)    
    ans+=b[i]*m
  else:
    ans+=m*b[-1]
    b[i]-=b[-1]
    m=c.pop()
    ans+=m*b[i]
    b.pop()
print(ans)

Fixed submission:
n=int(input())
a=sorted(list(map(int,input().split())))[::-1]
ans=0
for i in range(1,n):
  ans+=a[i//2]
print(ans)

Buggy python submission (verdict: Runtime Error):
from collections import Counter 
n=int(input())
a=sorted(list(map(int,input().split())))
b=[]
c=[]
for i in list(Counter(a).values()):
  b.append(i)
for i in list(Counter(a).keys()):
  c.append(i)
ans=c.pop()*((b[-1])-1)
m=a[-1]
f=len(b)
for _ in range(f-2,-1,-1):
  i=-2
  if b[-1]>b[i]:
    b[-1]-=b[i]
    b.pop(i)
    c.pop(i)    
    ans+=b[i]*m
  else:
    ans+=m*b[-1]
    b[i]-=b[-1]
    m=c.pop()
    ans+=m*b[i]
    b.pop()
print(ans)

Fixed submission:
n=int(input())
a=sorted(list(map(int,input().split())))[::-1]
ans=0
for i in range(1,n):
  ans+=a[i//2]
print(ans)
Buggy python submission (verdict: Time Limit Exceeded):
from collections import Counter 
n=int(input())
a=list(map(int,input().split()))
a=Counter(a)
q=int(input())
for i in range(q):
  b,c=map(int,input().split())
  if a[c]:
    a[c]+=a[b]
  else:a[c]=a[b]
  a[b]=0
  print(sum(a.elements()))
  

Fixed submission:
from collections import Counter 
n=int(input())
a=list(map(int,input().split()))
sm=sum(a)
a=Counter(a)
q=int(input())
for _ in range(q):
  b,c=map(int,input().split())
  i=a[b]
  if a[c]:
    a[c]+=i
  else:a[c]=i
  sm+=(c-b)*i
  print(sm)
  a[b]=0

Buggy python submission (verdict: Time Limit Exceeded):
from collections import Counter 
n=int(input())
a=list(map(int,input().split()))
a=Counter(a)
q=int(input())
for i in range(q):
  b,c=map(int,input().split())
  if a[c]:
    a[c]+=a[b]
  else:a[c]=a[b]
  a[b]=0
  print(sum(sorted(a.elements())))
  

Fixed submission:
from collections import Counter 
n=int(input())
a=list(map(int,input().split()))
sm=sum(a)
a=Counter(a)
q=int(input())
for _ in range(q):
  b,c=map(int,input().split())
  i=a[b]
  if a[c]:
    a[c]+=i
  else:a[c]=i
  sm+=(c-b)*i
  print(sm)
  a[b]=0
Buggy python submission (verdict: Time Limit Exceeded):
n=int(input())
a=sorted(list(map(int,input().split())))[::-1]
ans=0
d={}
for i in a:
  if d.get(i):d[i]+=1
  else:d[i]=1
for i in range(n):
  if d[a[i]]!=1:continue
  for j in range(i+1,n):
    if a[i]%a[j]==0:break
  else:ans+=1
print(ans)

Fixed submission:
def sieve(n=10**6):
  p=[-1]*(n+1)
  for i in a:
    if p[i]==-1:
      p[i]=1
      for j in range(2*i,n+1,i):p[j]=0
    elif p[i]==1:
      p[i]=0
  return p
n=int(input())
a=sorted(list(map(int,input().split())))
p=sieve()
ans=0
for i in a:
  ans+=p[i]
print(ans)

Buggy python submission (verdict: Runtime Error):
n=int(input())
a=list(map(int,input().split()))
a=sorted(a)
dp=[True]*a[-1]
for i in a:
  for j in range(i,a[-1]):
    if j%i==0:
      dp=False
cnt=0
for i in a:
  if dp[i]:
    cnt+=1
print(cnt)

Fixed submission:
def sieve(n=10**6):
  p=[-1]*(n+1)
  for i in a:
    if p[i]==-1:
      p[i]=1
      for j in range(2*i,n+1,i):p[j]=0
    elif p[i]==1:
      p[i]=0
  return p
n=int(input())
a=sorted(list(map(int,input().split())))
p=sieve()
ans=0
for i in a:
  ans+=p[i]
print(ans)