Harryxun/testdata huggingface dataset:
Buggy python submission (verdict: Time Limit Exceeded):
N = int(input())
A = list(map(int,input().split()))

flag = True

if N % 2 != 0:
    for i in range(0,N,2):
        if i == 0:
            if A.count(0) != 1:
                flag = False
                break
        else:
            if A.count(i) != 2:
                flag = False
                break
else:
    for i in range(1,N,2):
        if A.count(i) != 2:
            flag = False
            break
            
if flag == False:
    print(0)
else:
    print(pow(2,N//2,10**9+7))

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

from collections import Counter
MOD = 10**9 + 7
c = Counter(a)

ans = 0

if n % 2 == 1:
    for i in range(2, n, 2):
        if c[i] != 2:
            print(0)
            exit()
    if c[0] == 1:
        ans = pow(2, n // 2, MOD)
else:
    for i in range(1, n, 2):
        if c[i] != 2:
            print(0)
            exit()
    ans = pow(2, n // 2, MOD)
print(ans)

Buggy python submission (verdict: Time Limit Exceeded):
N = int(input())
A = list(map(int,input().split()))

flag = True

if N % 2 != 0:
    for i in range(0,N,2):
        if i == 0:
            if A.count(0) != 1:
                flag = False
        else:
            if A.count(i) != 2:
                flag = False
else:
    for i in range(1,N,2):
        if A.count(i) != 2:
            flag = False
            
if flag == False:
    print(0)
else:
    print(pow(2,N//2,10**9+7))

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

from collections import Counter
MOD = 10**9 + 7
c = Counter(a)

ans = 0

if n % 2 == 1:
    for i in range(2, n, 2):
        if c[i] != 2:
            print(0)
            exit()
    if c[0] == 1:
        ans = pow(2, n // 2, MOD)
else:
    for i in range(1, n, 2):
        if c[i] != 2:
            print(0)
            exit()
    ans = pow(2, n // 2, MOD)
print(ans)
Buggy python submission (verdict: Time Limit Exceeded):
from math import gcd
n = int(input())
a = list(map(int, input().split()))
max_a = max(a)
cnt_a = [0] * (max_a + 1)
for ai in a:
  cnt_a[ai] += 1
ans = 'pairwise'
for i in range(2, max_a + 1):
  cnt = 0
  for j in range(i, max_a + 1, i):
    cnt += cnt_a[j]
  if cnt > 1:
    ans = 'setwise'
g = 0
for ai in a:
  g = gcd(g, ai)

if ans == 'pairwise':
  print(ans, 'coprime')
elif ans == 'setwise' and g == 1:
  print(ans, 'coprime')
else:
  print('not coprime')

Fixed submission:
from math import gcd
n = int(input())
a = list(map(int, input().split()))
max_a = max(a)
cnt_a = [0] * (max_a + 1)
for ai in a:
  cnt_a[ai] += 1
ans = 'pairwise'
for i in range(2, max_a + 1):
  cnt = 0
  for j in range(i, max_a + 1, i):
    cnt += cnt_a[j]
  if cnt > 1:
    ans = 'setwise'
g = 0
for ai in a:
  g = gcd(g, ai)

if ans == 'pairwise':
  print(ans, 'coprime')
elif ans == 'setwise' and g == 1:
  print(ans, 'coprime')
else:
  print('not coprime')
Buggy python submission (verdict: Time Limit Exceeded):
k = int(input())
ans = -1
a = 7
for i in range(k):
    if a % k == 0:
        ans = i + 1
        break
    a = 10*a + 7
print(ans)

Fixed submission:
k = int(input())
ans = -1
a = [7%k] * k
for i in range(k - 1):
    a[i + 1] = (10*a[i] + 7) % k
for i in range(k):
    if a[i] == 0:
        ans = i + 1
        break
print(ans)
Buggy python submission (verdict: Runtime Error):
n = int(input())
ans = [0] * (n + 1)
for x in range(1, n**0.5 + 1):
    for y in range(1, n**0.5 + 1):
        for z in range(1, n**0.5 + 1):
            if x**2 + y**2 + z**2 + x*y + y*z + z*x <= n:
                ans[x**2 + y**2 + z**2 + x*y + y*z + z*x] += 1
print(*ans[1:], sep='\n')

Fixed submission:
n = int(input())
ans = [0] * (n + 1)
for x in range(1, int(n**0.5) + 1):
    for y in range(1, int(n**0.5) + 1):
        for z in range(1, int(n**0.5) + 1):
            if x**2 + y**2 + z**2 + x*y + y*z + z*x <= n:
                ans[x**2 + y**2 + z**2 + x*y + y*z + z*x] += 1
print(*ans[1:], sep='\n')

Buggy python submission (verdict: Time Limit Exceeded):
n = int(input())
ans = [0] * (n + 1)
for x in range(1, n):
    for y in range(1, n):
        for z in range(1, n):
            if x**2 + y**2 + z**2 + x*y + y*z + z*x <= n:
                ans[x**2 + y**2 + z**2 + x*y + y*z + z*x] += 1
print(*ans[1:], sep='\n')

Fixed submission:
n = int(input())
ans = [0] * (n + 1)
for x in range(1, int(n**0.5) + 1):
    for y in range(1, int(n**0.5) + 1):
        for z in range(1, int(n**0.5) + 1):
            if x**2 + y**2 + z**2 + x*y + y*z + z*x <= n:
                ans[x**2 + y**2 + z**2 + x*y + y*z + z*x] += 1
print(*ans[1:], sep='\n')
Buggy python submission (verdict: Runtime Error):
from collections import Counter
n = int(input())
a = list(map(int, input().split()))
s = sum(a)
cnt = Counter(a)
q = int(input())
for i in range(q):
    b, c = map(int, input().split())
    cnt_b = cnt.pop(b)
    cnt[c] += cnt_b
    s += (c - b)*cnt_b
    print(s)

Fixed submission:
from collections import defaultdict
n = int(input())
a = [int(i) for i in input().split()]
dict_a = defaultdict(int)
for i in range(n):
    dict_a[a[i]] += 1
q = int(input())
s = [sum(a)] + [0] * q
for i in range(q):
    b, c = map(int, input().split())
    try:
        cnt_b = dict_a.pop(b)
        dict_a[c] += cnt_b
        s[i + 1] = s[i] + (c - b)*cnt_b
    except KeyError:
        s[i + 1] = s[i]
print(*s[1:], sep='\n')
Buggy python submission (verdict: Runtime Error):
n = int(input())
a = sorted([int(i) for i in input().split()])
cnt_d = [0] * (max(a) + 1)
cnt_nd = 0
for ai in a:
    if cnt_d[ai] >= 1:
        continue
    else:
        cnt_d[ai] += 1
        cnt_nd += 1
    multi = 2
    while ai*multi <= max_a:
        cnt_d[ai*multi] += 1
        multi += 1
print(cnt_nd)

Fixed submission:
n = int(input())
a = sorted([int(i) for i in input().split()])
max_a = max(a)
cnt_d = [0] * (max_a + 1)

for ai in a:
    for multi in range(ai, max_a + 1, ai):
        cnt_d[multi] += 1

cnt_nd = 0
for ai in a:
    if cnt_d[ai] == 1:
        cnt_nd += 1
print(cnt_nd)

Buggy python submission (verdict: Time Limit Exceeded):
n = int(input())
a = sorted([int(i) for i in input().split()])
set_a = set(a)
max_a = max(a)
dup_a = {ai for ai in set_a if a.count(ai) > 1}
nd = [True] * (max_a + 1)
cnt = 0
for ai in sorted(list(set_a)):
    if nd[ai] == True and ai not in dup_a:
        cnt += 1
    elif nd[ai] == False:
        continue
    multi = 2
    while ai*multi <= max_a:
        nd[ai*multi] = False
        multi += 1
print(cnt)

Fixed submission:
n = int(input())
a = sorted([int(i) for i in input().split()])
max_a = max(a)
cnt_d = [0] * (max_a + 1)

for ai in a:
    for multi in range(ai, max_a + 1, ai):
        cnt_d[multi] += 1

cnt_nd = 0
for ai in a:
    if cnt_d[ai] == 1:
        cnt_nd += 1
print(cnt_nd)

Buggy python submission (verdict: Time Limit Exceeded):
n = int(input())
a = sorted([int(i) for i in input().split()])
set_a = set(a)
max_a = max(a)
dup_a = {ai for ai in set_a if a.count(ai) > 1}
nd = [True] * (max_a + 1)
cnt = 0
for ai in sorted(list(set_a)):
    if nd[ai] == True and ai not in dup_a:
        cnt += 1
    elif nd[ai] == False:
        continue
    multi = 2
    while ai*multi <= max_a:
        nd[ai*multi] = False
        multi += 1
print(cnt)

Fixed submission:
n = int(input())
a = sorted([int(i) for i in input().split()])
max_a = max(a)
cnt_d = [0] * (max_a + 1)

for ai in a:
    for multi in range(ai, max_a + 1, ai):
        cnt_d[multi] += 1

cnt_nd = 0
for ai in a:
    if cnt_d[ai] == 1:
        cnt_nd += 1
print(cnt_nd)

Buggy python submission (verdict: Time Limit Exceeded):
n = int(input())
a = sorted([int(i) for i in input().split()])
set_a = set(a)
max_a = max(a)
dup_a = {ai for ai in set_a if a.count(ai) > 1}
nd = [True] * (max_a + 1)
cnt = 0
for ai in sorted(list(set_a)):
    if nd[ai] == True and ai not in dup_a:
        cnt += 1
    multi = 2
    while ai*multi <= max_a:
        nd[ai*multi] = False
        multi += 1
print(cnt)

Fixed submission:
n = int(input())
a = sorted([int(i) for i in input().split()])
max_a = max(a)
cnt_d = [0] * (max_a + 1)

for ai in a:
    for multi in range(ai, max_a + 1, ai):
        cnt_d[multi] += 1

cnt_nd = 0
for ai in a:
    if cnt_d[ai] == 1:
        cnt_nd += 1
print(cnt_nd)
Buggy python submission (verdict: Time Limit Exceeded):
n = int(input())
a = [int(i) for i in input().split()]
ans = 1
for i in range(n):
    ans *= a[i]
print(ans if ans <= 10**18 else -1)

Fixed submission:
def prod(n, A):
    if 0 in A:
        return 0
    p = 1
    for a in A:
        if p * a <= 10**18:
            p *= a
        else:
            return -1
    return p

n = int(input())
A = [int(i) for i in input().split()]
print(prod(n, A))
Buggy python submission (verdict: Runtime Error):
from math import gcd
MOD = 10**9 + 7
n = int(input())
zero = 0
cnt = defaultdict()
for i in range(n):
    x, y = map(int, input().split())
    if x == 0 and y == 0:
        zero += 1
        continue
    g = gcd(x, y)
    x //= g
    y //= g
    if y < 0 or (y == 0 and x < 0):
        x *= -1
        y *= -1
    rot_90 = 1 if x <= 0 else 0
    if rot_90:
        x, y = y, -x
        cnt[(x, y)][rot_90] += 1

ans = 1
for s, t in cnt.values():
    now = 1
    now += (pow(2, s, MOD) - 1) % MOD
    now += (pow(2, t, MOD) - 1) % MOD
    ans *= now
ans -= 1
ans += zero
print(ans % MOD)

Fixed submission:
from math import gcd
MOD = 10**9 + 7
n = int(input())
zero = 0
cnt = dict()
for i in range(n):
    x, y = map(int, input().split())
    if x == 0 and y == 0:
        zero += 1
        continue
    g = gcd(x, y)
    x //= g
    y //= g
    if y < 0 or (y == 0 and x < 0):
        x *= -1
        y *= -1
    rot_90 = 1 if x <= 0 else 0
    if rot_90:
        x, y = y, -x
    try:
        cnt[(x, y)][rot_90] += 1
    except KeyError:
        cnt[(x, y)] = [int(not rot_90), rot_90]

ans = 1
for s, t in cnt.values():
    now = 1
    now += (pow(2, s, MOD) - 1) % MOD
    now += (pow(2, t, MOD) - 1) % MOD
    ans *= now
ans -= 1
ans += zero
print(ans % MOD)

Buggy python submission (verdict: Runtime Error):
from collections import defaultdict
from math import gcd
MOD = 10**9 + 7
n = int(input())
zero = 0
cnt = dict()
for i in range(n):
    x, y = map(int, input().split())
    if x == 0 and y == 0:
        zero += 1
        continue
    g = gcd(x, y)
    x //= g
    y //= g
    if y < 0 or (y == 0 and x < 0):
        x *= -1
        y *= -1
    rot_90 = 1 if x <= 0 else 0
    if rot_90:
        x, y = y, -x
        cnt[(x, y)][rot_90] += 1

ans = 1
for s, t in cnt.values():
    now = 1
    now += (pow(2, s, MOD) - 1) % MOD
    now += (pow(2, t, MOD) - 1) % MOD
    ans *= now
ans -= 1
ans += zero
print(ans % MOD)

Fixed submission:
from math import gcd
MOD = 10**9 + 7
n = int(input())
zero = 0
cnt = dict()
for i in range(n):
    x, y = map(int, input().split())
    if x == 0 and y == 0:
        zero += 1
        continue
    g = gcd(x, y)
    x //= g
    y //= g
    if y < 0 or (y == 0 and x < 0):
        x *= -1
        y *= -1
    rot_90 = 1 if x <= 0 else 0
    if rot_90:
        x, y = y, -x
    try:
        cnt[(x, y)][rot_90] += 1
    except KeyError:
        cnt[(x, y)] = [int(not rot_90), rot_90]

ans = 1
for s, t in cnt.values():
    now = 1
    now += (pow(2, s, MOD) - 1) % MOD
    now += (pow(2, t, MOD) - 1) % MOD
    ans *= now
ans -= 1
ans += zero
print(ans % MOD)
Buggy python submission (verdict: Runtime Error):
from itertools import product
n, m, x = map(int, input().split())
books = [[int(j) for j in input().split()] for i in range(n)]
min_cost = float('inf')
for bit in product([0, 1], repeat=n):
    cost = 0
    skill = [0] * m
    for i, b in enumerate(bit):
        if b == 1:
            cost += books[i][0]
            for j in range(m):
                skill[j] += books[i][j + 1]
    if x <= min(*skill):
        min_cost = min(min_cost, cost)
print(min_cost if min_cost != float('inf') else -1)

Fixed submission:
from itertools import product
n, m, x = map(int, input().split())
books = [[int(j) for j in input().split()] for i in range(n)]
min_cost = float('inf')
for bit in product([0, 1], repeat=n):
    cost = 0
    skill = [0] * m
    for i, b in enumerate(bit):
        if b == 1:
            cost += books[i][0]
            for j in range(m):
                skill[j] += books[i][j + 1]
    if x <= min(i for i in skill):
        min_cost = min(min_cost, cost)
print(min_cost if min_cost != float('inf') else -1)
Buggy python submission (verdict: Time Limit Exceeded):
MOD = 998244353

def C(n, r, m):
    num, den = 1, 1
    for i in range(1, r + 1):
        num = num * (n - i + 1) % m
        den = den * i % m
    return (num * pow(den, m - 2, m)) % m

n, m, k = map(int, input().split())
cnt = 0
for x in range(k + 1):
    cnt += m * pow(m - 1, n - 1 - x, MOD) * C(n - 1, x, MOD)
    cnt %= MOD
print(cnt)

Fixed submission:
MOD = 998244353
n, m, k = map(int, input().split())
c = 1
cnt = 0
for x in range(k + 1):
    cnt += c * m * pow(m - 1, n - 1 - x, MOD) 
    cnt %= MOD
    c *= (n - x - 1) * pow(x + 1, MOD - 2, MOD)
    c %= MOD
print(cnt)
Buggy python submission (verdict: Time Limit Exceeded):
x = int(input())
for a in range(-int(x**0.5), int(x**0.5)):
    for b in range(-int(x**0.5), int(x**0.5)):
        if a**5 - b**5 == x:
            print(a, b)
            break
    else:
        continue
    break

Fixed submission:
x = int(input())
for a in range(-int(x**0.3), int(x**0.3) + 1):
    for b in range(-int(x**0.3), int(x**0.3) + 1):
        if a**5 - b**5 == x:
            print(a, b)
            break
    else:
        continue
    break
Buggy python submission (verdict: Runtime Error):
n, a, b, c = map(int, input().split())
abc = list((a, b, c))
ans = [0] * n
dic = {'A': 0, 'B': 1, 'C': 2}
flag = True
s = [input() for i in range(n)]
for i in range(n):
    if abc[dic[s[i][0]]] == 0 and abc[dic[s[i][1]]] == 0:
        flag = False
        break
    elif sum(abc) == 2 and abc[dic[s[i][0]]] == 1 and abc[dic[s[i][1]]] == 1:
        ps = (set(s[i]) & set(s[i + 1])).pop()
        ms = (set(s[i]) - set(ps)).pop()
        abc[dic[ps]] += 1
        abc[dic[ms]] -= 1
        ans[i] = ps
    elif abc[dic[s[i][0]]] <= abc[dic[s[i][1]]]:
        abc[dic[s[i][0]]] += 1
        abc[dic[s[i][1]]] -= 1
        ans[i] = s[i][0]
    else:
        abc[dic[s[i][0]]] -= 1
        abc[dic[s[i][1]]] += 1
        ans[i] = s[i][1]
if flag:
    print('Yes')
    print(*ans, sep='\n')
else:
    print('No')

Fixed submission:
n, a, b, c = map(int, input().split())
abc = list((a, b, c))
ans = [0] * n
dic = {'A': 0, 'B': 1, 'C': 2}
flag = True
s = [input() for i in range(n)]
for i in range(n):
    if abc[dic[s[i][0]]] == 0 and abc[dic[s[i][1]]] == 0:
        flag = False
        break
    elif sum(abc) == 2 and abc[dic[s[i][0]]] == 1 and abc[dic[s[i][1]]] == 1 and i != n - 1:
        ps = (set(s[i]) & set(s[i + 1])).pop()
        ms = (set(s[i]) - set(ps)).pop()
        abc[dic[ps]] += 1
        abc[dic[ms]] -= 1
        ans[i] = ps
    elif abc[dic[s[i][0]]] <= abc[dic[s[i][1]]]:
        abc[dic[s[i][0]]] += 1
        abc[dic[s[i][1]]] -= 1
        ans[i] = s[i][0]
    else:
        abc[dic[s[i][0]]] -= 1
        abc[dic[s[i][1]]] += 1
        ans[i] = s[i][1]
if flag:
    print('Yes')
    print(*ans, sep='\n')
else:
    print('No')
Buggy python submission (verdict: Runtime Error):
import itertools
n, m, q = map(int, input().split())
A = itertools.product(range(1, m + 1), repeat=m)
quads = [[int(i) for i in input().split()] for j in range(q)]
max_p = 0
for a in A:
    p = 0
    for quad in quads:
        if a[quad[1] - 1] - a[quad[0] - 1] == quad[2]:
            p += quad[3]
    if max_p < p:
        max_p = p
print(max_p)

Fixed submission:
import itertools
n, m, q = map(int, input().split())
A = itertools.combinations_with_replacement(range(1, m+1), n)
quads = [[int(i) for i in input().split()] for j in range(q)]
max_p = 0
for a in A:
    p = 0
    for quad in quads:
        if a[quad[1] - 1] - a[quad[0] - 1] == quad[2]:
            p += quad[3]
    if max_p < p:
        max_p = p
print(max_p)
Buggy python submission (verdict: Time Limit Exceeded):
a, b, n = map(int, input().split())
print(max([(a*i)//b - a*(i//b) for i in range(n + 1)]))

Fixed submission:
a, b, n = map(int, input().split())
if n < b:
    k = n
else:
    k = b - 1
print((a*k)//b - a*(k//b))
Buggy python submission (verdict: Time Limit Exceeded):
s = input()
cnt = 0
for i in range(len(s)):
    for j in range(i + 4, len(s) + 1):
        if int(s[i:j]) % 2019 == 0:
            cnt += 1
print(cnt)

Fixed submission:
M = 2019
s = input()
tot, ten, ans = 0, 1, 0
cnt = [0] * M
for si in s[::-1]:
    cnt[tot] += 1
    tot += int(si) * ten
    tot %= M
    ans += cnt[tot]
    ten *= 10
    ten %= M
print(ans)

Buggy python submission (verdict: Time Limit Exceeded):
s = input()
cnt = 0
for l in range(len(s)):
    r = l + 1
    while r < len(s) and int(s[l:r]) % 2019 != 0:
        r += 1
    if int(s[l:r]) % 2019 == 0:
        cnt += 1
print(cnt)

Fixed submission:
M = 2019
s = input()
tot, ten, ans = 0, 1, 0
cnt = [0] * M
for si in s[::-1]:
    cnt[tot] += 1
    tot += int(si) * ten
    tot %= M
    ans += cnt[tot]
    ten *= 10
    ten %= M
print(ans)

Buggy python submission (verdict: Runtime Error):
s = input()
cnt = 0
for l in range(len(s)):
    r = l + 1
    while r < len(s) and int(s[l:r]) % 2019 != 0:
        r += 1
    if int(s[l:r]) % 2019 == 0:
        cnt += 1
        print(i, j, s[i:j])
print(cnt)       

Fixed submission:
M = 2019
s = input()
tot, ten, ans = 0, 1, 0
cnt = [0] * M
for si in s[::-1]:
    cnt[tot] += 1
    tot += int(si) * ten
    tot %= M
    ans += cnt[tot]
    ten *= 10
    ten %= M
print(ans)

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

Fixed submission:
M = 2019
s = input()
tot, ten, ans = 0, 1, 0
cnt = [0] * M
for si in s[::-1]:
    cnt[tot] += 1
    tot += int(si) * ten
    tot %= M
    ans += cnt[tot]
    ten *= 10
    ten %= M
print(ans)
Buggy python submission (verdict: Runtime Error):
n = int(input())
print(sum(i for i in range(i, n + 1) if i % 3 and i % 5))

Fixed submission:
n = int(input())
sum = 0
for i in range(1, n + 1):
    if i % 3 != 0 and i % 5 != 0:
        sum += i
print(sum)
Buggy python submission (verdict: Time Limit Exceeded):
from math import gcd
k = int(input())
sum = 0
for a in range(k):
    for b in range(k):
        for c in range(k):
            sum += gcd(gcd(a + 1, b + 1), c + 1)
print(sum)

Fixed submission:
def gcd(a, b):
    if a < b:
        a, b = b, a
    while b:
        a, b = b, a % b
    return a

k = int(input())
sum = 0

for i in range(1, k + 1):
    for j in range(1, k + 1):
        gcd_ij = gcd(i, j)
        for k in range(1, k + 1):
            sum += gcd(gcd_ij, k)
print(sum)

Buggy python submission (verdict: Time Limit Exceeded):
def gcd(a, b):
    if a < b:
        a, b = b, a
    while b:
        a, b = b, a % b
    return a

k = int(input())
sum = 0

for i in range(1, k + 1):
    for j in range(1, k + 1):
        for k in range(1, k + 1):
            sum += gcd(gcd(i, j), k)
print(sum)

Fixed submission:
def gcd(a, b):
    if a < b:
        a, b = b, a
    while b:
        a, b = b, a % b
    return a

k = int(input())
sum = 0

for i in range(1, k + 1):
    for j in range(1, k + 1):
        gcd_ij = gcd(i, j)
        for k in range(1, k + 1):
            sum += gcd(gcd_ij, k)
print(sum)

Buggy python submission (verdict: Time Limit Exceeded):
def gcd(a, b):
    if a < b:
        a, b = b, a
    while b:
        a, b = b, a % b
    return a

k = int(input())
sum = 0
for i in range(1, k + 1):
    for j in range(1, k + 1):
        for k in range(1, k + 1):
            sum += gcd(gcd(i, j), k)
print(sum)

Fixed submission:
def gcd(a, b):
    if a < b:
        a, b = b, a
    while b:
        a, b = b, a % b
    return a

k = int(input())
sum = 0

for i in range(1, k + 1):
    for j in range(1, k + 1):
        gcd_ij = gcd(i, j)
        for k in range(1, k + 1):
            sum += gcd(gcd_ij, k)
print(sum)
Buggy python submission (verdict: Runtime Error):
n, k = map(int, input().split())
p = 10**9 + 7
sg = [0] * (k + 1)
for i in range(k, 0, -1):
    sg[i] += i * pow(k // i, n, p)
    m = 2
    while m*i <= k:
        sg[i] = (sg[i] - sg[m*i]) % p
        m += 1
print(sum(sg) % MOD)

Fixed submission:
MOD = 10**9 + 7
n, k = map(int, input().split())
d = [0] + [pow(k // i, n, MOD) for i in range(1, k + 1)]
for i in range(k, 0, -1):
    for j in range(2*i, k + 1, i):
        d[i] -= d[j]
        d[i] %= MOD
print(sum(i * d[i] % MOD for i in range(1, k + 1)) % MOD)
Buggy python submission (verdict: Time Limit Exceeded):
def calc_divisors(n):
    divisors = []
    for i in range(1, int(n**0.5)+1):
        if n % i == 0:
            divisors.append(i)
            if i != n // i:
                divisors.append(n//i)
    divisors.sort()
    return divisors

def div_or_sub(n, k):
    while k <= n:
        if n % k == 0:
            n //= k
        else:
            n -= k
    return n

n = int(input())
cnt = len(calc_divisors(n - 1)) - 1
n_divisors = calc_divisors(n)
for divisor in n_divisors[1:]:
    if div_or_sub(n, divisor) == 1:
        cnt += 1
print(cnt)

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

def div_or_sub(n, k):
    while k <= n:
        if n % k == 0:
            n //= k
        else:
            n %= k
    return n

n = int(input())
cnt = len(calc_divisors(n - 1)) - 1
n_divisors = calc_divisors(n)
for divisor in n_divisors[1:]:
    if div_or_sub(n, divisor) == 1:
        cnt += 1
print(cnt)
Buggy python submission (verdict: Runtime Error):
k, n = map(int, input().split())
a = list(map(int, input().split())) + [k + a[0]]
print(k - max([a[i + 1] - a[i] for i in range(n)]))

Fixed submission:
k, n = map(int, input().split())
a = [int(i) for i in input().split()]
diff_a = [0] * n
diff_a[0] = (a[0] + k) - a[n - 1]
for i in range(1, n):
    diff_a[i] = a[i] - a[i - 1]
print(k - max(diff_a))

Buggy python submission (verdict: Runtime Error):
k, n = map(int, input().split())
a = list(map(int, input().split())) + [k + a[0]]
print(k - max([a[i + 1] - a[i] for i in range(n)]))

Fixed submission:
k, n = map(int, input().split())
a = [int(i) for i in input().split()]
diff_a = [0] * n
diff_a[0] = (a[0] + k) - a[n - 1]
for i in range(1, n):
    diff_a[i] = a[i] - a[i - 1]
print(k - max(diff_a))

Buggy python submission (verdict: Runtime Error):
k, n = map(int, input().split())
a = list(map(int, input().split())) + [k + a[0]]
print(k - max([a[i + 1] - a[i] for i in range(n)]))

Fixed submission:
k, n = map(int, input().split())
a = [int(i) for i in input().split()]
diff_a = [0] * n
diff_a[0] = (a[0] + k) - a[n - 1]
for i in range(1, n):
    diff_a[i] = a[i] - a[i - 1]
print(k - max(diff_a))
Buggy python submission (verdict: Runtime Error):
def is_p(s):
    return s == s[::-1]
s = input()
n = len(s)
l, r = (n - 1)//2, l + 1
print('Yes' if is_p(s) and is_p(s[:l]) and is_p(s[r:]) else 'No')

Fixed submission:
def is_palindrome(s):
    len_s = len(s)
    ans = True
    for i in range(len_s // 2):
        if s[i] != s[-(i + 1)]:
            ans = False
    return ans

s = input()
len_s = len(s)
ans = True
if is_palindrome(s) == False:
    ans = False
if is_palindrome(s[0:(len_s - 1) // 2]) == False or is_palindrome(s[(len_s + 1) // 2:len_s]) == False:
    ans = False
if ans:
    print('Yes')
else:
    print('No')