qyliang/CodeNanoFix huggingface dataset:
Buggy code:
N, X = map(int, input().split())
listx = list(map(int, input().split()))
subx = []

for i in range(N):
  subx.append(abs(listx[i] - X))

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

ans = gcd(subx[0], subx[1])

for i in range(2, N-1):
  ans = gcd(ans, subx[i])
  
print(ans)

Fixed code:
N, X = map(int, input().split())
listx = list(map(int, input().split()))
subx = []

for i in range(N):
  subx.append(abs(listx[i] - X))
if N == 1:
  subx.append(subx[0])

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

ans = gcd(subx[0], subx[1])

if N > 2:
  for i in range(2, N):
    ans = gcd(ans, subx[i])
  
print(ans)
Buggy code:
n, x =  map(int, input().split())
xi = list(map(int, input().strip().split()))
c = [1] * x
xi = [x - y for (x,y) in zip(xi,c)]
def gcd(a, b):
  if b == 0: return a
  return gcd(b, a % b)
d0 = xi[0]
for i in range(n-1):
    d = gcd(xi[i+1],d0)
    d0 = d
print(d)

Fixed code:
n, x =  map(int, input().split())
xi = map(int, input().strip().split())
c = [x] * n
xi = [x - y for (x,y) in zip(xi,c)]
def gcd(a, b):
  if b == 0: return a
  return gcd(b, a % b)
d0 = xi[0]
for i in range(n-1):
    d = gcd(xi[i+1],d0)
    d0 = d
if len(xi) == 1:
  d = xi[0]
print(abs(d))
Buggy code:
import math

def gcd(x, y):
  if y == 0:
    return x
  else:
    return gcd(y, x % y)
      

n, x = map(int,input().split())
li_x = list(map(int,input().split()))

for i in range(len(li_x)):
    if li_x[i] - x < 0:
        li_x[i] =x - li_x[i]
    else:
        li_x[i] = li_x[i] -x

g =gcd(li_x[0],li_x[1])
k=2
while k<len(li_x):
  g=gcd(g,li_x[k])
  k+=1
print(g)


Fixed code:
import math

def gcd(x, y):
  if y == 0:
    return x
  else:
    return gcd(y, x % y)

n, x = map(int,input().split())
li_x = list(map(int,input().split()))

for i in range(len(li_x)):
  if li_x[i] - x < 0:
    li_x[i] =x - li_x[i]
  else:
    li_x[i] = li_x[i] -x

if len(li_x)==1:
  print(li_x[0])

elif len(li_x)==2:
  print(gcd(li_x[0],li_x[1]))

else:
  g =gcd(li_x[0],li_x[1])
  k=2
  while k<len(li_x):
    g=gcd(g,li_x[k])
    k+=1
  print(g)
Buggy code:
from functools import reduce

def gcd(a, b):

    if b == 0:
        return a
    else:
        return gcd(b, a % b)

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

N, X = map(int, input().split(" "))
Xi = [int(a) for a in input().split()]

def minusX(a):
    return a-X

Xi = map(minusX, Xi)

d = gcd_list(Xi)
print (d)

Fixed code:
from functools import reduce

def gcd(a, b):

    if b == 0:
        return a
    else:
        return gcd(b, a % b)

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

N, X = map(int, input().split(" "))
Xi = [int(a) for a in input().split()]

def minusX(a):
    return abs(a-X)

Xi = map(minusX, Xi)

d = gcd_list(Xi)
print (d)
Buggy code:
n, x = map(int, input().split())
c = list(map(int, input().split()))
dis = set()
for i in range(1, n):
    dis.add(abs(c[i] - c[i-1]))
l = min(dis)
for i in range(l, 0, -1):
    d = True
    for item in dis:
        if item % i != 0:
            d = False
    if d:
        print(i)
        break


Fixed code:
n, x = map(int, input().split())
c = list(map(int, input().split()))
c = set([abs(x-c[i]) for i in range(n)])
l = min(c)
for i in range(l+1, 0, -1):
    if l % i == 0:
        d = True
        for item in c:
            if item % i != 0:
                d = False
        if d:
            print(i)
            break
Buggy code:
def make_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 make_codivisors(n):
    divisors = []
    n0divisors = make_divisors(n[0])
    n0len = len(n0divisors)
    for i in n0divisors:
        for j in range(1, len(n)):
            if n[j] % i != 0:
                break
            if j == len(n)-1:
                divisors.append(i)
            
    # divisors.sort()
    return max(divisors)


n, x = list(map(int, input().split()))
a = list(map(int, input().split()))
a.append(x)
a.sort()
b = [a[i]-a[i-1] for i in range(1, n+1)]

print(b)
print(a)

print(make_codivisors(b))

Fixed code:
def make_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 make_codivisors(n):
    divisors = []
    n0divisors = make_divisors(n[0])
    n0len = len(n0divisors)
    for i in n0divisors:
        for j in range(1, len(n)):
            if n[j] % i != 0:
                break
            if j == len(n)-1:
                divisors.append(i)
            
    # divisors.sort()
    return max(divisors)


n, x = list(map(int, input().split()))
a = list(map(int, input().split()))
a.append(x)
a.sort()
b = [a[i]-a[i-1] for i in range(1, n+1)]

#print(b)
#print(a)
if len(b) >= 2:
  print(make_codivisors(b))
else:
  print(b[0])
Buggy code:
def gcd(a, b):
    while b != 0:
        a, b = b, a%b
    return a

N, X = map(int, input().split())
a = [abs(int(i)-X) for i in input().split()]
ans = gcd(a[0], a[1])

if N == 1:
    print(abs(X-a[0]))
else:
    for i in range(N):
        ans = gcd(ans, a[i])
    print(ans)

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

N, X = map(int, input().split())
a = [abs(int(i)-X) for i in input().split()]


if N == 1:
    print(a[0])
else:
    ans = gcd(a[0], a[1])
    for i in range(N):
        ans = gcd(ans, a[i])
    print(ans)
Buggy code:
from math import gcd 
N, X = list(map(int, input().split()))
x = list(map(int, input().split()))
ans = gcd(abs(x[0] - X), abs(x[1] - X))
for i in range(2, N):
  ans = gcd(ans, X[i])
print(ans)

Fixed code:
from math import gcd 
N, X = list(map(int, input().split()))
x = list(map(int, input().split()))
if(N == 1): print(abs(x[0] - X))
else:
  ans = gcd(abs(x[0] - X), abs(x[1] - X))
  for i in range(2, N):
  	ans = gcd(ans, abs(x[i] - X))
    
  print(ans)
Buggy code:
def make_divisors(n):
    lower_divisors , upper_divisors = [], []
    i = 1
    while i*i <= n:
        if n % i == 0:
            lower_divisors.append(i)
            if i != n // i:
                upper_divisors.append(n//i)
        i += 1
    return lower_divisors + upper_divisors[::-1]
    
a = [int(s) for s in input().split()]
N = a[0]
st = a[1]
mini = int(-1)
b = [int(s) for s in input().split()]

for i in range(N):
    if abs(b[i] - st) < mini or mini == -1:
        mini = abs(b[i] - st)

yakulist = make_divisors(mini)
gyakulist = sorted(yakulist, reverse=True)
kazu = len(gyakulist)
print(kazu)
flag = int(0)

for i in range(kazu):
    for j in range(N):
        if abs(b[j] - st) % gyakulist[i] != 0:
            flag = 1
        else:
            pass
    if flag == 0:
        print(gyakulist[i])
        break
    

Fixed code:
def make_divisors(n):
    lower_divisors , upper_divisors = [], []
    i = 1
    while i*i <= n:
        if n % i == 0:
            lower_divisors.append(i)
            if i != n // i:
                upper_divisors.append(n//i)
        i += 1
    return lower_divisors + upper_divisors[::-1]
    
a = [int(s) for s in input().split()]
N = a[0]
st = a[1]
mini = int(-1)
b = [int(s) for s in input().split()]

for i in range(N):
    if abs(b[i] - st) < mini or mini == -1:
        mini = abs(b[i] - st)

yakulist = make_divisors(mini)
gyakulist = sorted(yakulist, reverse=True)
kazu = len(gyakulist)
flag = int(0)

for i in range(kazu):
    for j in range(N):
        if abs(b[j] - st) % gyakulist[i] != 0:
            flag = 1
        else:
            pass
    if flag == 0:
        print(gyakulist[i])
        break
    else:
        flag = 0
Buggy code:
import sys
import math


N, X = map(int, input().split())
A = list(map(int, input().split()))

if N == 1:
    print(A[0]-X)
    sys.exit()

A.append(X)
A = sorted(A)

anslis = [0]*N

for i in range(N):
    anslis[i] = A[i+1] - A[i]

g = anslis.pop(0)
for c in cost_li:
    g = math.gcd(g,c)

print(g)

Fixed code:
import sys
import math


N, X = map(int, input().split())
A = list(map(int, input().split()))

A.append(X)
A = sorted(A)

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

g = anslis.pop(0)
for c in anslis:
    g = math.gcd(g,c)

print(g)
Buggy code:
n,x = map(int,input().split())
X = list(map(int,input().split()))
sort_X = sorted(X)
temp = sort_X[0]
mini = float("inf")
D = 1
if(n==1):
    print(999999999-abs(X[0]-x))
elif(n==2):
    mini = min(X[-1]-x,x-X[0])

    for p in range(1,mini+1):
        point = x%p
        flag = True
        for xx in X:
            if(point != xx%p):
                    flag = False
                    break
        if(flag):
            D = p
    print(D)

else:
    for xx in sort_X[1:]:
        if(mini >= xx-temp):
            mini = xx-temp
        temp = xx
    for p in range(1,mini+1):
        point = x%p
        flag = True
        for xx in X:
            if(point != xx%p):
                    flag = False
                    break
        if(flag):
            D = p

    print(D)



Fixed code:
n,x = map(int,input().split())
X = list(map(int,input().split()))
sort_X = sorted(X)
temp = sort_X[0]
mini = float("inf")
D = 1
if(n==1):
    print(abs(X[0]-x))
elif(n==2):
    mini = min(X[-1]-x,x-X[0])

    for p in range(1,mini+1):
        point = x%p
        flag = True
        for xx in X:
            if(point != xx%p):
                    flag = False
                    break
        if(flag):
            D = p
    print(D)

else:
    for xx in sort_X[1:]:
        if(mini >= xx-temp):
            mini = xx-temp
        temp = xx
    for p in range(1,mini+1):
        point = x%p
        flag = True
        for xx in X:
            if(point != xx%p):
                    flag = False
                    break
        if(flag):
            D = p

    print(D)
Buggy code:
num_str=input().split()
num=list(map(int, num_str))
n=num[0]
x=num[1]
num2_str=input().split()
distance=list(map(int, num2_str))

first_distance=list(map(lambda y:abs(y-x),distance))
min_distance=min(first_distance)

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

gcd=gcd(first_distance[0],first_distance[1])
for i in range(2,n):
    gcd=gcd(gcd,first_distance[i])
print(gcd)

Fixed code:
num_str=input().split()
num=list(map(int, num_str))
n=num[0]
x=num[1]
num2_str=input().split()
distance=list(map(int, num2_str))

first_distance=list(map(lambda y:abs(y-x),distance))
min_distance=min(first_distance)

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


if n==1:
    print(first_distance[0])
else:
    element = gcd(first_distance[0], first_distance[1])
    if n==2:print(element)
    else:
        for i in range(2,n):
            element=gcd(element,first_distance[i])
        print(element)
Buggy code:
headData=[int(n) for n in input().split()]
cityNum=headData[0]
pos_x=int(headData[1])
cityList=[int(n) for n in input().split()]
allList=[]
allList.append(pos_x)
for n in cityList:
    allList.append(n)

allList=sorted(allList)
print(allList)

diffList=[]

for n in range(len(allList)-1):
    diffList.append(allList[n+1]-allList[n])

answer = min(diffList)

while True:
    isAnswer = True
    for n in diffList:
        if n % answer != 0:
            isAnswer = False
            break
    if isAnswer:
        print(answer)
        break
    else:
        answer = answer-1

Fixed code:
headData=[int(n) for n in input().split()]
cityNum=headData[0]
pos_x=int(headData[1])
cityList=[int(n) for n in input().split()]
allList=[]
allList.append(pos_x)
for n in cityList:
    allList.append(n)

allList=sorted(allList)

diffList=[]

for n in range(len(allList)-1):
    diffList.append(allList[n+1]-allList[n])

answer = min(diffList)

while True:
    isAnswer = True
    for n in diffList:
        if n % answer != 0:
            isAnswer = False
            break
    if isAnswer:
        print(answer)
        break
    else:
        answer = answer-1
Buggy code:
from functools import reduce
from math import gcd

n, x = map(int, input().split())
a = [abs(int(A) - x) for A in input().split()]
a.sort()
print(a)
print(reduce(gcd, a))


Fixed code:
from functools import reduce
from math import gcd

n, x = map(int, input().split())
a = [abs(int(A) - x) for A in input().split()]
a.sort()
print(reduce(gcd, a))
Buggy code:
n,x=map(int,input().split())
X=list(map(int,input().split()))
for i in X:
  i=abs(i-x)
def gcd(x,y):
  if y==0:
    return x
  else:
    return(y,x%y)
stack=X[0]
for i in range(n-1):
  stack=gcd(stack,X[i+1])
print(stack)

Fixed code:
n,x=map(int,input().split())
X=list(map(int,input().split()))
for i in range(n):
  X[i]=abs(X[i]-x)
def gcd(p,q):
  if q==0:
    return p
  else:
    return gcd(q,p%q)
stack=X[0]
for i in range(n-1):
  stack=gcd(stack,X[i+1])
print(stack)
Buggy code:
N,X = map(int,input().split())
list = [int(x) for x in input().split()]
list_dist = sorted([abs(x - X) for x in list])

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

print(gcd(list_dist[0],list_dist[1]))

Fixed code:
N,X = map(int,input().split())
list = [int(x) for x in input().split()]
list_dist = sorted([abs(x - X) for x in list])

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

ans = list_dist[0]

for x in list_dist[1:]:
    ans = gcd(ans,x)

print(ans)
Buggy code:
def gcd(a, b):
    if a < b:
        a, b = b, a
    if b == 0:
        return a
    c = a % b
    return gcd(b, c)
  
n,x = map(int,input().split())
xlist = list(map(int,input().split()))
ans = 0
for i in range(n):
    ans = gcd(int(xlist[i]-x),ans)
print(ans)

Fixed code:
def gcd(a, b):
    if a < b:
        a, b = b, a
    if b == 0:
        return a
    c = a % b
    return gcd(b, c)
  
n,x = map(int,input().split())
xlist = list(map(int,input().split()))
ans = 0
for i in range(n):
    ans = gcd(abs(xlist[i]-x),ans)
print(ans)
Buggy code:
def gcd(a,b) :
    if b>0 :
        return gcd(b,a % b)
    elif b == 0:
        return a


N,X = map(int,input().split())
x = list(map(int,input().split()))
if N == 1:
    print(abs(x[0] - X))
else:
    xlen = []
    for i in range(N):
        xlen.append(x[i] - X)
    ans = xlen[0]
    for i in range(1,N):
        ans = gcd(ans,xlen[i])
    print(ans)

Fixed code:
def gcd(a,b) :
    if b>0 :
        return gcd(b,a % b)
    elif b == 0:
        return a


N,X = map(int,input().split())
x = list(map(int,input().split()))
if N == 1:
    print(abs(x[0] - X))
else:
    xlen = []
    for i in range(N):
        xlen.append(abs(x[i] - X))
        #print(xlen[i])
    ans = xlen[0]
    for i in range(1,N):
        ans = gcd(ans,xlen[i])
        #print(ans)
    print(ans)
Buggy code:
def gcd(a,b):
    while b:
        a,b=b,a%b
    return a

N,X=[int(i) for i in input().split()]
a=input().split()
x=[]
for i in range(N):
    x.append(int(a[i]))
if(N==1):
    print(abs(x[0]-X))
    exit()
x=list(map(lambda y:abs(y-X) , x))
x.sort()
print(math.gcd(x[0],x[1]))


Fixed code:
def gcd(a,b):
    while b:
        a,b=b,a%b
    return a

N,X=[int(i) for i in input().split()]
a=input().split()
x=[]
for i in range(N):
    x.append(int(a[i]))
if(N==1):
    print(abs(x[0]-X))
    exit()
x=list(map(lambda y:abs(y-X) , x))
ans=gcd(x[0],x[1])
for i in range(2,N):
    ans=gcd(x[i],ans)
print(ans)
Buggy code:
N,X = map(int, input().split())
target = list(map(int, input().split()))

distances = [abs(i - X) for i in target]

def GCD(x,y):
    if x == 0:
        return y
    else:
        return GCD(y, x % y)
res = 0
for d in distances:
    res = GCD(res, d)
print(res)

Fixed code:
N,X = map(int, input().split())
target = list(map(int, input().split()))

distances = [abs(i - X) for i in target]

def GCD(x,y):
    if y == 0:
        return x
    else:
        return GCD(y, x % y)
res = 0
for d in distances:
    res = GCD(res, d)
print(res)
Buggy code:
def gcd(a,b):
  n,  = max(a, b), min(a, b)
  if n % m == 0:
    return m
  else:
    return gcd(m, n%m)

N, X = [int(item) for item in input().split()]
cities = [int(item) for item in input().split()]
if N == 1:
  print(abs(cities[0]-X))
  exit()

mod = gcd(abs(cities[0] - X), abs(cities[1] - X))
for i in range(2, N):
  mod = gcd(mod, abs(cities[0] - X))
print(mod)

Fixed code:
def gcd(a,b):
  n, m  = max(a, b), min(a, b)
  if n % m == 0:
    return m
  else:
    return gcd(m, n%m)

N, X = [int(item) for item in input().split()]
cities = [int(item) for item in input().split()]
if N == 1:
  print(abs(cities[0]-X))
  exit()

mod = gcd(abs(cities[0] - X), abs(cities[1] - X))
for i in range(2, N):
  mod = gcd(mod, abs(cities[i] - X))
print(mod)
Buggy code:
n, x = map(int, input().split())

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


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


a = [i - x for i in a]
from functools import reduce
print(reduce(gcd, a))


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

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


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


a = [abs(i - x) for i in a]
from functools import reduce
print(reduce(gcd, a))
Buggy code:
import numpy as np
from functools import reduce

def gcd(a, b):
    while b:
        a, b = b, a % b

    return a

def multi_gcd(*numbers):
    return reduce(gcd, numbers)

N, X = map(int, input().split(' '))
city = np.array(list(map(int, input().split(' '))))

city -= X
print(multi_gcd(*city))

Fixed code:
import numpy as np
import math
from functools import reduce

def gcd(a, b):
    while b:
        a, b = b, a % b

    return a

def multi_gcd(*numbers):
    return reduce(gcd, numbers)

N, X = map(int, input().split(' '))
city = np.array(list(map(int, input().split(' '))))

city -= X
print(abs(multi_gcd(*city)))
Buggy code:
N,X = map(int,input().split(" "))
x = list(map(int,input().split(" ")))
x = list(map(lambda y: abs(y - X),x))


# gcd
def gcd (a,b):
    if a < b:
        a,b = b,a
    return a if b == 0 else gcd(b,a%b)

ans = gcd(x[0],x[1])
for i in range(2,N):
    ans = gcd(ans,x[i])

print(ans)


Fixed code:
N,X = map(int,input().split(" "))
x = list(map(int,input().split(" ")))
x = list(map(lambda y: abs(y - X),x))


# gcd
def gcd (a,b):
    if a < b:
        a,b = b,a
    return a if b == 0 else gcd(b,a%b)

if N == 1:
    print(x[0])
    exit(0)
ans = gcd(x[0],x[1])
if N == 2:
    print(ans)
    exit(0)
for i in range(2,N):
    ans = gcd(ans,x[i])

print(ans)
Buggy code:
N,X = map(int,input().split(' '))
L = list(map(int,input().split(' ')))

def algGCF(a,b):
  if a % b == 0:
    return b
  else:
    return algGCF(b,a%b)
GCF = abs(X-L[0])
for i in range(1,N):
  GCF = algGCF(GCF,X-L[i])
print(GCF)  

Fixed code:
N,X = map(int,input().split(' '))
L = list(map(int,input().split(' ')))

def algGCF(a,b):
  if a % b == 0:
    return b
  else:
    return algGCF(b,a%b)
GCF = abs(X-L[0])
for i in range(1,N):
  GCF = algGCF(GCF,abs(X-L[i]))
print(GCF)
Buggy code:
n, place = [int(x) for x in input().split(' ')]
city_address = sorted([abs(int(x) - place) for x in input().split(' ')], reverse=True)
print(city_address)
def gcd(x, y):
    if y == 0:
        return x
    else:
        return gcd(y, x % y)
 
answer = city_address[0]
for address in city_address:
	answer = gcd(answer, address)
 
print(answer)

Fixed code:
n, place = [int(x) for x in input().split(' ')]
city_address = sorted([abs(int(x) - place) for x in input().split(' ')], reverse=True)
def gcd(x, y):
    if y == 0:
        return x
    else:
        return gcd(y, x % y)

answer = city_address[0]
for address in city_address:
	answer = gcd(answer, address)

print(answer)
Buggy code:
N,X = map(int,input().split())
positions_from_X = [abs(int(x)-X) for x in input().split()]

min_distance = min(positions_from_X)

n = min_distance

for d in sorted([i for i in range(1,n+1) if n%i==0], reverse=True):
    flg = d
    for p in positions_from_X:
        if p%d !=0:
            flg=0
            break
    if flg:
        break

print(flg)

Fixed code:
N,X = map(int,input().split())
positions_from_X = [abs(int(x)-X) for x in input().split()]

n = min(positions_from_X)

if N==1:
    flg = n
else:
    for d in sorted([i for i in range(1,n+1) if n%i==0], reverse=True):
        flg = d
        for p in positions_from_X:
            if p%d !=0:
                flg=0
                break
        if flg:
            break

print(flg)
Buggy code:
def gcd(A, B):
    while B != 0:
        A, B = B, A%B
    return A
N, X = map(int, input().split())
x = [abs(int(i) - X) for i in input().split()] 
y = x[0]
for i in range(N):
    if x[i] % y == 0:
        continue
    y = gcd(y, x[i])
print(min(gcd_x))

Fixed code:
def gcd(A, B):
    while B != 0:
        A, B = B, A%B
    return A
N, X = map(int, input().split())
x = [abs(int(i) - X) for i in input().split()] 
y = x[0]
for i in range(N):
    if x[i] % y == 0:
        continue
    y = gcd(y, x[i])
print(y)
Buggy code:
def gcd(a,b):
    while b:
        a,b = b ,a % b

    return a

N,X = map(int,input().split())
cities = [int(x) - X for x in input().split()]

#print(cities)

if N == 1:
    print(abs(cities[0] - X))
else:
    ans = gcd(cities[0],cities[1])

    for i in range(1,len(cities) - 1):
        ans = gcd(ans, cities[i+1])
        #print(ans)

    print(abs(ans))

Fixed code:
def gcd(a,b):
    while b:
        a,b = b ,a % b

    return a

N,X = map(int,input().split())
cities = [int(x) - X for x in input().split()]

#print(cities)

if N == 1:
    print(abs(cities[0]))
else:
    ans = gcd(cities[0],cities[1])

    for i in range(1,len(cities) - 1):
        ans = gcd(ans, cities[i+1])
        #print(ans)

    print(abs(ans))
Buggy code:
N, X = map(int, input().split())
x_list=list(int(x)-X for x in input().split())

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

ans=0
for x in x_list:
  ans=gcd(ans, x)
print(ans)




Fixed code:
N, X = map(int, input().split())
x_list=list(int(x)-X for x in input().split())

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

ans=0
for x in x_list:
  ans=gcd(ans, x)
print(abs(ans))
Buggy code:
import math

N, X = map(int, input().split())
x= list(map(int, input().split()))

absx = [abs(X - xx) for xx in x]
absx.sort()

divx0 = []

for i in range(math.ceil(math.sqrt(absx[0])), 0, -1):
    if absx[0] % i == 0:
        divx0.append(i)

t = []
for x in divx0:
    t.append(x)
    t.append(absx[0] // x)

divx0 = t

for dx0 in divx0:
    isok = True
    for xx in absx:
        if xx % dx0 != 0:
            isok = False
            break

    if isok:
        print(dx0)
        exit()

Fixed code:
import math

N, X = map(int, input().split())
x= list(map(int, input().split()))

absx = [abs(X - xx) for xx in x]
absx.sort()

divx0 = []

for i in range(math.ceil(math.sqrt(absx[0])), 0, -1):
    if absx[0] % i == 0:
        divx0.append(i)

t = []
for x in divx0:
    t.append(x)
    t.append(absx[0] // x)

divx0 = t
divx0.sort(reverse=True)

for dx0 in divx0:
    isok = True
    for xx in absx:
        if xx % dx0 != 0:
            isok = False
            break

    if isok:
        print(dx0)
        exit()
Buggy code:
n,x=map(int,input().split())
a=list(map(int,input().split()))
b=[]
if n==1 and x==a[0]:
    print(max(x,10**9-x))
    exit()
for i in range(n):
    b.append(abs(a[i]-x))
import math
for i in range(n):
    c=0
    c=math.gcd(c,b[i])
    if c==1:
        break
print(c)

Fixed code:
n,x=map(int,input().split())
a=list(map(int,input().split()))
b=[]
if n==1 and x==a[0]:
    print(max(x,10**9-x))
    exit()
for i in range(n):
    b.append(abs(a[i]-x))
import math
c=0
for i in range(n):
    c=math.gcd(c,b[i])
    if c==1:
        break
print(c)
Buggy code:
n, x = map(int, input().split())
l = list(map(int, input().split()))

def gcd(x, y):
    while (y != 0):
        x, y = y, x%y

    return x

diff = []

for j in l:
    diff.append(abs(j - x))

ans = diff[0]

for d in range(d[1:]):
    ans = gcd(ans, d)

print(ans)



Fixed code:
n, x = map(int, input().split())
l = list(map(int, input().split()))

def gcd(x, y):
    while (y != 0):
        x, y = y, x%y

    return x

diff = []

for j in l:
    diff.append(abs(j - x))

ans = diff[0]

for d in diff[1:]:
    ans = gcd(ans, d)

print(ans)