Buggy python submission (verdict: Runtime Error):
from fractions import gcd

K = int(input())

ans = 0

for a in range(1,K+1) :
    for b in range(1,K+1) :
        for c in range(1,K+1) :
           X = fractions.gcd(a, b)
           Y = fractions.gcd(X, c)
           ans += Y

print(ans)

Fixed submission:
from math import gcd

K = int(input())

ans = 0

for a in range(1,K+1) :
    for b in range(1,K+1) :
        X = gcd(a, b)
        for c in range(1,K+1) :
           Y = gcd(X, c)
           ans += Y

print(ans)

Buggy python submission (verdict: Runtime Error):
import math
import fractions import gcd
import numpy as np
from functools import reduce

def gcd(*numbers):
    return reduce(math.gcd, numbers)

def gcd_list(numbers):
    return reduce(math.gcd, numbers)

K = int(input())

ans = 0

for a in range(1,K+1) :
    for b in range(1,K+1) :
        for c in range(1,K+1) :
           X = fractions.gcd(a, b)
           Y = fractions.gcd(X, c)
           ans += Y

print(ans)

Fixed submission:
from math import gcd

K = int(input())

ans = 0

for a in range(1,K+1) :
    for b in range(1,K+1) :
        X = gcd(a, b)
        for c in range(1,K+1) :
           Y = gcd(X, c)
           ans += Y

print(ans)

Buggy python submission (verdict: Runtime Error):
import math
import fractions
import numpy as np
from functools import reduce

def gcd(*numbers):
    return reduce(math.gcd, numbers)

def gcd_list(numbers):
    return reduce(math.gcd, numbers)

K = int(input())

ans = 0

for a in range(1,K+1) :
    for b in range(1,K+1) :
        for c in range(1,K+1) :
           X = fractions.gcd(a, b)
           Y = fractions.gcd(X, c)
           ans += Y

print(ans)

Fixed submission:
from math import gcd

K = int(input())

ans = 0

for a in range(1,K+1) :
    for b in range(1,K+1) :
        X = gcd(a, b)
        for c in range(1,K+1) :
           Y = gcd(X, c)
           ans += Y

print(ans)

Buggy python submission (verdict: Runtime Error):
import math
import numpy as np
from functools import reduce

def gcd(*numbers):
    return reduce(math.gcd, numbers)

def gcd_list(numbers):
    return reduce(math.gcd, numbers)

K = int(input())

ans = 0

for a in range(1,K+1) :
    for b in range(1,K+1) :
        for c in range(1,K+1) :
           X = math.gcd(a, b)
           Y = math.gcd(X, c)
           ans += Y

print(ans)

Fixed submission:
from math import gcd

K = int(input())

ans = 0

for a in range(1,K+1) :
    for b in range(1,K+1) :
        X = gcd(a, b)
        for c in range(1,K+1) :
           Y = gcd(X, c)
           ans += Y

print(ans)

Buggy python submission (verdict: Time Limit Exceeded):
import math
import numpy as np
from functools import reduce

def gcd(*numbers):
    return reduce(math.gcd, numbers)

def gcd_list(numbers):
    return reduce(math.gcd, numbers)

K = int(input())

ans = 0

for a in range(1,K+1) :
    for b in range(1,K+1) :
        for c in range(1,K+1) :
           X = math.gcd(a, b)
           Y = math.gcd(X, c)
           ans += Y

print(ans)

Fixed submission:
from math import gcd

K = int(input())

ans = 0

for a in range(1,K+1) :
    for b in range(1,K+1) :
        X = gcd(a, b)
        for c in range(1,K+1) :
           Y = gcd(X, c)
           ans += Y

print(ans)

Buggy python submission (verdict: Time Limit Exceeded):
import math
import numpy as np
from functools import reduce

def gcd(*numbers):
    return reduce(math.gcd, numbers)

def gcd_list(numbers):
    return reduce(math.gcd, numbers)

K = int(input())

ans = 0

for a in range(1,K+1) :
    for b in range(1,K+1) :
        for c in range(1,K+1) :
            s = np.gcd.reduce([a, b, c])
            ans += s

print(ans)

Fixed submission:
from math import gcd

K = int(input())

ans = 0

for a in range(1,K+1) :
    for b in range(1,K+1) :
        X = gcd(a, b)
        for c in range(1,K+1) :
           Y = gcd(X, c)
           ans += Y

print(ans)