Harryxun/testdata huggingface dataset:
Buggy python submission (verdict: Runtime Error):
N, K = map(int, input().split())
A = list(map(int, input().split()))
max_A = max(A)
A.sort()

if(max_A < K):
    print("IMPOSSIBLE")
else:
    num = 10**10
    for i in range(N-1):
        num = min(num, abs(A[i]-A[i+1]))

    for i in range(N):
        if(A[i] < K):
            continue
        if((K-A[i])%num == 0):
            print("POSSIBLE")
            break
    else:
        print("IMPOSSIBLE")

Fixed submission:
N, K = map(int, input().split())
A = list(map(int, input().split()))
max_A = max(A)
A.sort()

if(max_A < K):
    print("IMPOSSIBLE")
else:
    num = 10**10
    for i in range(N-1):
        if(min(num, abs(A[i]-A[i+1]))):
            num = min(num, abs(A[i]-A[i+1]))

    for i in range(N):
        if(A[i] < K):
            continue
        if((K-A[i])%num == 0):
            print("POSSIBLE")
            break
    else:
        print("IMPOSSIBLE")
Buggy python submission (verdict: Time Limit Exceeded):
n = int(input())
a = list(map(int, input().split()))

b = []

for i in range(n):
    b.append(a[i])
    b = b[::-1]

print(' '.join(map(str, b)))

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

if(len(a)%2 == 0):
    b = a[1::2][::-1]+a[0::2]
    print(' '.join(map(str, b)))
else:
    b = a[0::2][::-1]+a[1::2]
    print(' '.join(map(str, b)))
Buggy python submission (verdict: Time Limit Exceeded):
N = int(input())
s = [int(input()) for _ in range(N)]

ans = 0
for i in range(2**N+1):
    sum_s = 0
    for j in range(N):
        if((i >> j) & 1):
            sum_s += s[j]
    if(sum_s%10==0):
        sum_s = 0
    ans = max(ans, sum_s)

print(ans)

Fixed submission:
N = int(input())
s = [int(input()) for _ in range(N)]

s.sort()
ans = sum(s)
cnt = []
Flg = False
if(ans%10 != 0):
    print(ans)
else:
    for i in range(N):
        if(s[i]%10 != 0):
            cnt.append(s[i])
            Flg = True
    if(Flg):
        cnt.sort()
        print(ans-cnt[0])
    else:
        print(0)
Buggy python submission (verdict: Runtime Error):
N, K = map(int, input().split())
L = []
for i in range(N):
    a, b = map(int, input().split())
    L.append(a)
    L.append(b)
    
L = sorted(L)
print(L[K+1])

Fixed submission:
N, K = map(int, input().split())
d = [0]*(10**5+1)
sum_d = 0

for _ in range(N):
    a, b = map(int, input().split())
    d[a] += b

for i in range(1, 10**5+1):
    sum_d += d[i]
    if(sum_d >= K):
        print(i)
        break
Buggy python submission (verdict: Runtime Error):
import copy

N, K = map(int, input().split())
a = list(map(int, input().split()))

ans = []
for i in range(2**N):
    s = a.copy()
    cnt = 0
    tmp = 0
    henkou = [False for _ in range(N)]
    for j in range(N):
        if((i >> j)&1):
            henkou[j] = True
    bill = s[0]
    for k in range(1, N):
        if(henkou[k]):
            if(bill >= s[k]):
                cnt += bill-s[k]+1
                s[k] = bill+1
                bill = s[k]
        else:
            if(bill >= s[k]):
                tmp += 1
            else:
                bill = s[k]
    if(N-tmp >= K):
        ans.append(cnt)
print(min(ans))

Fixed submission:
import copy

N, K = map(int, input().split())
a = list(map(int, input().split()))

ans = []
for i in range(2**N):
    s = a.copy()
    cnt = 0
    tmp = 1
    henkou = [False for _ in range(N)]
    for j in range(N):
        if((i >> j)&1):
            henkou[j] = True
    bill = s[0]
    for k in range(1, N):
        if(henkou[k]):
            if(bill >= s[k]):
                cnt += bill-s[k]+1
                s[k] = bill+1
                bill = s[k]
                tmp += 1
            else:
                bill = s[k]
                tmp += 1
        else:
            if(bill < s[k]):
                bill = s[k]
                tmp += 1
    if(tmp >= K):
        ans.append(cnt)
print(min(ans), end='\n')
Buggy python submission (verdict: Time Limit Exceeded):
import numpy as np

N = int(input())
A = list(map(int, input().split()))
a = sorted(A)
res = list(np.cumsum(a))

ans = 0
for i in range(len(res)):
    num = res[i]
    idx = i+1
    
    while(num*2 >= a[idx]):
        num += a[idx]
        idx += 1
        
        if(idx >= len(res)-1):
            break
       
    if(idx >= len(res)-1):
        print(N-i)
        break

Fixed submission:
import numpy as np

N = int(input())
A = list(map(int, input().split()))
a = sorted(A)
res = list(np.cumsum(a))

ans = 0
idx = 1
for i in range(len(res)):
    num = res[i]
    if(idx <= i):
        idx = i+1
    while(num*2 >= a[idx]):
        num += a[idx]
        idx += 1
        
        if(idx >= len(res)-1):
            break
       
    if(idx >= len(res)-1):
        print(N-i)
        break
Buggy python submission (verdict: Time Limit Exceeded):
n = int(input())
pw = 1

for i in range(n):
    pw *= i+1
    
print(pw%(10**9+7))

Fixed submission:
import math

n = int(input())

pw = math.factorial(n)
    
print(pw%(10**9+7))
Buggy python submission (verdict: Runtime Error):
N, M = map(int, input().split())

if(2*N <= M):
    m = M-2*N
    print(N+m//4)
else:
    print(m//2)

Fixed submission:
N, M = map(int, input().split())

if(2*N <= M):
    m = M-2*N
    print(N+m//4)
else:
    print(M//2)
Buggy python submission (verdict: Runtime Error):
N, M = map(int, input().split())
dict = {i+1:[] for i in range(M)}
for _ in range(M):
    a, b = map(int, input().split())
    dict[a].append(b)
    dict[b].append(a)
    
def DFS(visited, sight, cnt):
    if(len(visited) == N):
        return cnt+1
    for num in dict[sight]:
        if num in visited:
            continue
        cnt = DFS(visited+[num], num, cnt)
    return cnt

print(DFS([1], 1, 0))

Fixed submission:
N, M = map(int, input().split())
graph ={i+1:[] for i in range(N)}
for _ in range(M):
    a, b = map(int, input().split())
    graph[a].append(b)
    graph[b].append(a)
    
def dfs(path, n, cnt):
    if(len(path) == N):
        return cnt+1
    for j in graph[n]:
        if(j in path):
            continue
        cnt = dfs(path+[j], j, cnt)
    return cnt
print(dfs([1], 1, 0))

Buggy python submission (verdict: Runtime Error):
N, M = map(int, input().split())
graph ={i+1:[] for i in range(N)}
for _ in range(N):
    a, b = map(int, input().split())
    graph[a].append(b)
    graph[b].append(a)
    
def DFS(graph, start, end):
    stack = [start]
    visited = []
    cnt = 0
    while stack:
        label = stack.pop(0)
        if label == end:
            visited.append(label)
            cnt += 1
        if label not in visited:
            visited.append(label)
            stack = graph.get(label, [])+stack
    return cnt
print(DFS(graph, 1, N))

Fixed submission:
N, M = map(int, input().split())
graph ={i+1:[] for i in range(N)}
for _ in range(M):
    a, b = map(int, input().split())
    graph[a].append(b)
    graph[b].append(a)
    
def dfs(path, n, cnt):
    if(len(path) == N):
        return cnt+1
    for j in graph[n]:
        if(j in path):
            continue
        cnt = dfs(path+[j], j, cnt)
    return cnt
print(dfs([1], 1, 0))
Buggy python submission (verdict: Time Limit Exceeded):
N, Ma, Mb = map(int, input().split())
a = [[0, 0, 0] for _ in range(N)]
sa = 0
sb = 0
for i in range(N):
    a[i][0], a[i][1], a[i][2] = map(int, input().split())
    sa += a[i][0]
    sb += a[i][1]
INF = 1000000  

DP = [[[INF for _ in range(sb+1)] for _ in range(sa+1)] for _ in range(N+1)]
DP[0][0][0] = 0

for i in range(N):
    for j in range(sa+1):
        for k in range(sb+1):
            if(j >= a[i][0] and k >= a[i][1]):
                DP[i+1][j][k] = min(DP[i][j-a[i][0]][k-a[i][1]] + a[i][2], DP[i][j][k])
            else:
                DP[i+1][j][k] = DP[i][j][k]
ans = INF
for i in range(1, min(sa//Ma, sb//Mb)+1):
    ans = min(ans, DP[N][Ma*i][Mb*i])
    
if(ans == INF):
    print(-1)
else:
    print(ans)

Fixed submission:
def main():
    N, Ma, Mb = map(int, input().split())
    yakuhin = []
    sa = 0
    sb = 0
    for i in range(N):
        yakuhin.append(list(map(int, input().split())))
        sa += yakuhin[i][0]
        sb += yakuhin[i][1]
    
    INF = 10**15
    DP = [[[INF for _ in range(sb+1)] for _ in range(sa+1)] for _ in range(N+1)]
    
    for i in range(N):
        DP[i][0][0] = 0
    
    for i in range(N):
        for j in range(sa+1):
            for k in range(sb+1):
                if(j >= yakuhin[i][0] and k >= yakuhin[i][1]):
                    DP[i+1][j][k] = min(DP[i][j][k], DP[i][j-yakuhin[i][0]][k-yakuhin[i][1]]+yakuhin[i][2])
                else:
                    DP[i+1][j][k] = min(DP[i+1][j][k], DP[i][j][k])
        
    ans = INF
    for i in range(1, N+1):
        for j in range(1, sa+1):
            for k in range(1, sb+1):
                if(j*Mb == k*Ma):
                    ans = min(ans, DP[i][j][k])    
        
    print(ans if ans != INF else -1)
    
main()
Buggy python submission (verdict: Runtime Error):
from collections import Counter
N = int(input())
A = list(map(int, input().split()))

#a = Counter(A)
l_a = len(a)
if(l_a%2 == 0):
     print(l_a-1)
else:
    print(l_a)

Fixed submission:
from collections import Counter
N = int(input())
A = list(map(int, input().split()))

a = Counter(A)
l_a = len(a)
if(l_a%2 == 0):
     print(l_a-1)
else:
    print(l_a)
Buggy python submission (verdict: Time Limit Exceeded):
k, s = map(int, input().split())
x = [n for n in range(0, k+1)]
y = [m for m in range(0, k+1)]
z = [l for l in range(0, k+1)]
cnt = 0

for i in range(k+1):
    for j in range(k+1):
        for t in range(k+1):
            if(x[i] + y[j] + z[t] == s):
                cnt += 1
print(cnt)

Fixed submission:
k, s = map(int, input().split())
cnt = 0

for x in range(k+1):
    for y in range(k+1):
        z = s - (x+y)
        if(z >= 0 and z <= k):
            cnt += 1
print(cnt)
Buggy python submission (verdict: Runtime Error):
from string import *
h,w=map(int,input().split())

s =[None] * h
for i in range(h):
    s[i] = [None] * w
    for j in range(w):
        s[i][j] = input()

for i in range(h):
    for j in range(w):
        if(s[i][j]=='snuke'):
            idx1=ascii_lowercase[i].swapcase()
            idx2=str(j+1)
            print(idx1+idx2)
            break

Fixed submission:
from string import *
h,w=map(int,input().split())

s = [input().split() for _ in range(h)]

for i in range(h):
    for j in range(w):
        if(s[i][j]=='snuke'):
            idx1=ascii_lowercase[j].swapcase()
            idx2=str(i+1)
            print(idx1+idx2)
            exit()
Buggy python submission (verdict: Runtime Error):
w, h, n=map(int,input().split())

mat = [list(map(int, input().split())) for _ in range(n)]

w1 = 0
w2 = w
h1 = 0
h2 = h

for i in range(n):
    if(mat[i][2] == 1 and w1 < mat[i][0]):
        w1 = mat[i][0]
    elif(mat[i][2] == 2 and w2 > mat[i][0]):
        w2 = mat[i][0]
    elif(mat[i][2] == 3 and w3 < mat[i][1]):
        h1 = mat[i][1]
    elif(mat[i][2] == 4 and w4 > mat[i][1]):
        h2 = mat[i][1]
        
print((w2-w1)*(h2-h1) if w2 >= w1 and h2 >= h1 else 0)

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

mat = [list(map(int, input().split())) for _ in range(n)]

w1 = 0
w2 = w
h1 = 0
h2 = h

for i in range(n):
    if(mat[i][2] == 1 and w1 < mat[i][0]):
        w1 = mat[i][0]
    elif(mat[i][2] == 2 and w2 > mat[i][0]):
        w2 = mat[i][0]
    elif(mat[i][2] == 3 and h1 < mat[i][1]):
        h1 = mat[i][1]
    elif(mat[i][2] == 4 and h2 > mat[i][1]):
        h2 = mat[i][1]
        
print((w2-w1)*(h2-h1) if w2 >= w1 and h2 >= h1 else 0)
Buggy python submission (verdict: Runtime Error):
a = input().split()
num = 3

if a[0] == a[1]:
    num = num - 1
    if a[0] == a[2]:
        num = num - 1:
elif a[0] == a[2]:
    num = num - 1
elif a[1] == a[2]:
    num = num - 1
    
print(num)

Fixed submission:
a = input().split()
num = 3

if a[0] == a[1]:
    num = num - 1
    if a[0] == a[2]:
        num = num - 1
elif a[0] == a[2]:
    num = num - 1
elif a[1] == a[2]:
    num = num - 1
    
print(num)

Buggy python submission (verdict: Runtime Error):
a = input().split()
num = 3

if a[0] == a[1]:
    num = num - 1
    if a[1] == a[2]:
        num = num - 1:
elif a[0] == a[2]:
    num = num - 1
elif a[1] == a[2]:
    num = num - 1
    
print(num)

Fixed submission:
a = input().split()
num = 3

if a[0] == a[1]:
    num = num - 1
    if a[0] == a[2]:
        num = num - 1
elif a[0] == a[2]:
    num = num - 1
elif a[1] == a[2]:
    num = num - 1
    
print(num)

Buggy python submission (verdict: Runtime Error):
a = int(input())
b = int(input())
c = int(input())

num = 3

if a == b:
    num = num - 1
    if b == c:
        num = num - 1
elif b == c:
    num = num - 1
    
print('num')

Fixed submission:
a = input().split()
num = 3

if a[0] == a[1]:
    num = num - 1
    if a[0] == a[2]:
        num = num - 1
elif a[0] == a[2]:
    num = num - 1
elif a[1] == a[2]:
    num = num - 1
    
print(num)

Buggy python submission (verdict: Runtime Error):
a = int(input())
b = int(input())
c = int(input())

num = 3

if a == b:
    num = num - 1
    if b == c:
        num = num - 1
elif b == c:
    num = num - 1
    
print(num)

Fixed submission:
a = input().split()
num = 3

if a[0] == a[1]:
    num = num - 1
    if a[0] == a[2]:
        num = num - 1
elif a[0] == a[2]:
    num = num - 1
elif a[1] == a[2]:
    num = num - 1
    
print(num)
Buggy python submission (verdict: Runtime Error):
dict = {ch: list(input()) for ch in "abc"}
ch = "a"

While (dict[ch]):
    ch = dict[ch].pop(0)

print(ch.upper())

Fixed submission:
S = {i:list(input()) for i in "abc"}
s = "a"
while S[s]:
    s = S[s].pop(0)
print(s.upper())
Buggy python submission (verdict: Runtime Error):
from collections import Counter

s = input()

flg = False
lst = []
for i in range(len(s)-2):
    if(s[i] == s[i+1]):
        flg = True
        lst.append(i+1)
        lst.append(i+2)
        break
    elif(s[i] == s[i+2]):
        flg = True
        lst.append(list(i+1, i+3))
        break
if(flg):
    print(*lst)
else:
    print(-1, -1)

Fixed submission:
from collections import Counter

s = input()

flg = False
lst = []

for i in range(len(s)-2):
    if(s[i] == s[i+1]):
        flg = True
        lst.append(i+1)
        lst.append(i+2)
        break
    elif(s[i] == s[i+2]):
        flg = True
        lst.append(i+1)
        lst.append(i+3)
        break

if not(lst):     
    if(s[len(s)-1] == s[len(s)-2]):
        lst.append(len(s)-1)
        lst.append(len(s))
        flg = True

if(flg):
    print(*lst)
else:
    print(-1, -1)
Buggy python submission (verdict: Runtime Error):
s = input()
a = []

for i in range(len(s)):
    if (s[i] == "B"):
        if(len(a) == 0):
            continue
        else:
            a.remove(a[i-1])
    else:
        a.append(s[i])
print(''.join(a))

Fixed submission:
s = input()
a = []

for i in range(len(s)):
    if (s[i] == "B"):
        if(len(a) <= 0):
            continue
        else:
            a.pop()
    else:
        a.append(s[i])
print(''.join(a))
Buggy python submission (verdict: Time Limit Exceeded):
a, b = map(int, input().split())
ans = 1

for i in range(a, b+1):
    ans *= i
if(ans != 0):
    print("Positive" if ans > 0 else "Negative")
else:
    print("Zero")

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

if(a > 0):
    print("Positive")
elif(a < 0 and b >= 0):
    print("Zero")
elif(a < 0 and b < 0):
    if((abs(a-b)+1)%2 == 0):
        print("Positive")
    else:
        print("Negative")
Buggy python submission (verdict: Time Limit Exceeded):
N,M = map(int,input().split())
AB = [list(map(int,input().split())) for _ in range(M)]

group = [set([i]) for i in range(N)]
syozoku = [i for i in range(N)]


for a,b in AB:
  a -= 1
  b -= 1
  group[syozoku[a]] = group[syozoku[a]] | group[syozoku[b]]
  x = group[syozoku[b]].copy()
  if syozoku[a]!=syozoku[b]:
  	group[syozoku[b]] = set([])
  for i in x:
    syozoku[i] = syozoku[a]
  
ans = 0
for i in range(N):
  ans = max(len(group[i]),ans)
  
print(ans)

Fixed submission:
N,M = map(int,input().split())
AB = [list(map(int,input().split())) for _ in range(M)]
from collections import deque
friends = [deque() for _ in range(N)]
ans = 0

for a,b in AB:
  a -= 1
  b -= 1
  friends[a].append(b)
  friends[b].append(a)
  
flag = [False] * N
for i in range(N):
  if flag[i]:
    continue
  else:
    x = friends[i]
    tmp = 1
    flag[i] = True
    while len(x)!=0:
      y = x.pop()
      if flag[y]:
        continue
      else:
        tmp += 1
        for j in friends[y]:
          x.append(j)
        flag[y] = True
    ans = max(tmp,ans)
    
print(ans)
Buggy python submission (verdict: Runtime Error):
N = int(input())
A = list(map(int,input().split()))
from fractions import gcd

setwise = A[0]

A = sorted(A,reverse = True)
prime = [0] * (10**6+1)
judge = True

for a in A:
  setwise = gcd(setwise,a)
  if prime[a]:
    continue
  else:
    prime[a] += 1
    if a%2==0:
      if prime[2]:
        judge = False
      prime[2] += 1
      a//=2
      if (a!=2)and(prime[a]):
        judge = False
      prime[a] += 1
    
    for i in range(3,int((a)**(1/2))+1,2):
      if a%i==0:
        if prime[i]:
          judge = False
        prime[i] += 1
        
if judge:
  print(ans)
  
elif setwise==1:
  print('setwise coprime')
else:
  print('not coprime')

Fixed submission:
N = int(input())
A = list(map(int,input().split()))

A = sorted(A,reverse = True)
prime = [0] * (10**6+1)
eratos = [True] * (A[0] + 1)
D = [0] * (A[0]+1)
D[1] = 1
for i in range(2,A[0] + 1):
  if not eratos[i]:
    continue
  else:
    for j in range(i,A[0] + 1,i):
      if not D[j]:
        D[j] = i
      if j!=i:
      	eratos[j] = False
  
for a in A:
  while a!=1:
    x = D[a]
    while a%x==0:
      a//=x
    prime[x] += 1

if max(prime)<=1:
  print('pairwise coprime')
  
elif max(prime)!=N:
  print('setwise coprime')
else:
  print('not coprime')
Buggy python submission (verdict: Time Limit Exceeded):
from heapq import heapify,heappop,heappush
import math
N,K = map(int,input().split())
A = list(map(int,input().split()))

for i in range(N):
  A[i] = [-A[i],A[i],0]
  
heapify(A)
for i in range(K):
  a = heappop(A)
  x = a[2] + 1
  a[2] = x
  a[0] = -(a[1] / (x + 1))
  heappush(A, a)
  
ans = -heappop(A)[0]
print(math.ceil(ans))

Fixed submission:
import math
N,K = map(int,input().split())
A = list(map(int,input().split()))

left = 0
right = max(A) + 1

while left+1!=right:
  mid = (left + right)//2
  x = 0
  for a in A:
    x += math.ceil(a/mid) - 1
  if x<=K:
    right = mid
  else:
    left = mid
  
print(right)
Buggy python submission (verdict: Runtime Error):
N = int(input())
A = map(int,input().split())
ans = 0
for i in range(0,N,2):
  if A[i]%2==1:
    ans+=1
    
print(ans)

Fixed submission:
N = int(input())
A = list(map(int,input().split()))
ans = 0
for i in range(0,N,2):
  if A[i]%2==1:
    ans+=1
    
print(ans)
Buggy python submission (verdict: Runtime Error):
N,M,K = map(int,input().split())
A = list(map(int,input().split()))
B = list(map(int,input().split()))

S_A = [0] * (N + 1)
S_B = [0] * (N + 1)
for i in range(N):
  S_A[i+1] = S_A[i] + A[i]

for i in range(M):
  S_B[i+1] = S_B[i] + B[i]
  
ans = 0
a = 0
for i in range(M, -1, -1):
  s = S_B[i]
  while a<N:
    if s + S_A[a + 1]<=K:
      a += 1
    else:
      break
  ans = max(ans, i + a)
print(ans)

Fixed submission:
N,M,K = map(int,input().split())
A = list(map(int,input().split()))
B = list(map(int,input().split()))
S = 0
ans = 0
for i in range(M):
  S += B[i]
  if S > K:
    b = i - 1
    S -= B[i]
    break
  else:
    ans += 1
    if i==M-1:
      b = M-1
if b==0:
  ans = 0
  S = 0
  for a in A:
    if S + a <= K:
      S += a
      ans += 1
    else:
      break
  if S + B[0]<=K:
    ans+=1
  print(ans)
else:
  a = 0
  max_ans = ans
  while a<N:
    if S + A[a] <= K:
      S += A[a]
      ans += 1
      a += 1
    else:
      break
  max_ans = max(max_ans, ans)
  for j in range(b, -1, -1):
    S -= B[j]
    ans -= 1
    while a<N:
      if S + A[a] <= K:
        S += A[a]
        ans += 1
        a += 1
      else:
        break
      
    max_ans = max(max_ans, ans)
  print(max_ans)
Buggy python submission (verdict: Time Limit Exceeded):
def main():
  N = int(input())
  def count(n):
    ret = 0
    i = 1
    while i*i <= n:
      if n % i == 0:
        ret += 1
        if i != n // i:
          ret += 1
      i += 1
    return ret


  ans = 1
  if N==1:
    print(ans)
  else:
    for i in range(2,N+1):
      x = count(i)
      ans += x * i

    print(ans)
    
main()

Fixed submission:
N = int(input())
ans = 0
for i in range(1, N + 1):
  x = N//i
  ans += i * x * (x + 1) // 2
  
print(ans)

Buggy python submission (verdict: Runtime Error):
def main():
  N = int(input())
  def count(n):
    ret = 0
    i = 1
    while i*i <= n:
      if n % i == 0:
        ret += 1
        if i != n // i:
          ret += 1
      i += 1
    return ret


  ans = 1
  l[0] = True
  l[1] = True
  if N==1:
    print(ans)
  else:
    for i in range(2,N+1):
      x = count(i)
      ans += x * i

    print(ans)
    
main()

Fixed submission:
N = int(input())
ans = 0
for i in range(1, N + 1):
  x = N//i
  ans += i * x * (x + 1) // 2
  
print(ans)

Buggy python submission (verdict: Time Limit Exceeded):
N = int(input())
l = [False] * (N + 1)
def count(n):
  ret = 0
  i = 1
  while i*i <= n:
    if n % i == 0:
      ret += 1
      if i != n // i:
        ret += 1
    i += 1
  return ret

num = [0] * (10**5 + 1)
for i in range(1, 10**5):
  num[i] = count(i)


ans = 1
l[0] = True
l[1] = True
if N==1:
  print(ans)
else:
  for i in range(2,N+1):
    if l[i]:
      continue
    if i<=10**5:
      ans += num[i] * i
    else:
      x = int(i**(1/2)) + 1
      a = 1
      while x>1:
        if num[x]!=2:
          continue
          x -= 1
        else:
          y = i
          while True:
            if y%x==0:
              y//=x
              a += 1
            else:
              break
          if y<=10**5:
            ans += a * num[y]
            break
          else:
            x -= 1
            continue
              

  print(ans)

Fixed submission:
N = int(input())
ans = 0
for i in range(1, N + 1):
  x = N//i
  ans += i * x * (x + 1) // 2
  
print(ans)

Buggy python submission (verdict: Time Limit Exceeded):
N = int(input())
l = [False] * (N + 1)
import collections
def count(n):
  ret = 0
  i = 1
  while i*i <= n:
    if n % i == 0:
      ret += 1
      if i != n // i:
        ret += 1
    i += 1
  return ret


ans = 1
l[0] = True
l[1] = True
if N==1:
  print(ans)
else:
  for i in range(2,N+1):
    if l[i]:
      continue
    x = count(i)
    ans += x * i
    l[i] = True

  print(ans)

Fixed submission:
N = int(input())
ans = 0
for i in range(1, N + 1):
  x = N//i
  ans += i * x * (x + 1) // 2
  
print(ans)
Buggy python submission (verdict: Runtime Error):
K = int(input())
S = input()
MOD = 10**9 + 7

length = len(S)
length_all = K + length
ans = 0
list_25 = [1] * (10**6 + 5)
list_26 = [1] * (10**6 + 5)
for i in range(1,10**6 + 5):
  list_25[i] = list_25[i - 1] * 25 % MOD
  list_26[i] = list_26[i - 1] * 26 % MOD
  
fact = [1] * (10**6 + 5)
fact_inv = [1] * (10**6 + 5)
inv = [1] * (10**6 + 5)
for i in range(1, 10**6 + 5):
  fact[i] = fact[i-1] * i % MOD
  fact_inv[i] = fact_inv[i - 1] * pow(i, MOD - 2, MOD) % MOD
for i in range(K + 1):
  ans += list_26[i] * list_25[K - i] % MOD * fact[length_all - i - 1] * fact_inv[length - 1] * fact_inv[K - i] % MOD

print(ans % MOD)

Fixed submission:
K = int(input())
S = input()
MOD = 10**9 + 7

length = len(S)
length_all = K + length
ans = 0
list_25 = [1] * (10**6 + 5)
list_26 = [1] * (10**6 + 5)
for i in range(1,10**6 + 5):
  list_25[i] = list_25[i - 1] * 25 % MOD
  list_26[i] = list_26[i - 1] * 26 % MOD
  
fact = [1] * (2 * 10**6 + 5)
fact_inv = [1] * (2 * 10**6 + 5)
for i in range(1, 2 * 10**6 + 5):
  fact[i] = fact[i-1] * i % MOD
  fact_inv[i] = fact_inv[i - 1] * pow(i, MOD - 2, MOD) % MOD

for i in range(K + 1):
  ans += list_26[i] * list_25[K - i] % MOD * fact[length_all - i - 1] * fact_inv[length - 1] * fact_inv[K - i] % MOD

print(ans % MOD)