Buggy python submission (verdict: Runtime Error):
import itertools
import math 

n,s = [int(input()) for _ in range(2)]

def n_base_sum(n,b):
    if(int(n/b)):
        return n_base_sum(int(n/b),b)+n%b
    else:
        return n%b

def search_p(n,s):
    for p in range(math.ceil(math.sqrt(n))+1,0,-1):
        b = n //p
        q = n % b
        if p+q ==s:
            return b
    return -1

ans =-1
flag = False
answers = []
if s == n:
    ans = n+1
    flag =True
    answers.append(ans)
for b in  range(2,math.ceil(math.sqrt(n))+1):
    if s== n_base_sum(n,b):
        ans = b
        flag = True
        answers.append(ans)
        break
ans = search_p(n,s)
if ans != -1:
    flag =True
    answers.append(ans)


if not flag:
    print(-1)
else:
    print(int(min(answers)))


Fixed submission:
import itertools
import math 
 
n,s = [int(input()) for _ in range(2)]
 
def n_base_sum(n,b):
    if(math.floor(n/b)):
        return n_base_sum(math.floor(n/b),b)+n%b
    else:
        return n%b
 
def search_p(n,s):
    for p in range(math.floor(math.sqrt(n))+1,0,-1):
        b = (n-s)//p + 1
        if b >1 :
            q = n % b
            if p+q ==s and q < b and n == p*b+q and p<b:
                return b
        
    return -1
 
ans =-1
flag = False
answers = []
if s == n:
    ans = n+1
    flag =True
    answers.append(ans)
for b in  range(2,math.ceil(math.sqrt(n))+1):
    if s== n_base_sum(n,b):
        ans = b
        flag = True
        answers.append(ans)
        break
ans = search_p(n,s)
if ans != -1:
    flag =True
    answers.append(ans)
 
if not flag:
    print(-1)
else:
    print(int(min(answers)))

Buggy python submission (verdict: Runtime Error):
import itertools
import math 

n,s = [int(input()) for _ in range(2)]

def n_base_sum(n,b):
    if(int(n/b)):
        return n_base_sum(int(n/b),b)+n%b
    else:
        return n%b

def search_p(n,s):
    for p in range(math.ceil(math.sqrt(n))+1,0,-1):
        b = (n-s)//p + 1
        q = n % b
        if p+q ==s:
            return b
    return -1

ans =-1
flag = False
answers = []
if s == n:
    ans = n+1
    flag =True
    answers.append(ans)
for b in  range(2,math.ceil(math.sqrt(n))+1):
    if s== n_base_sum(n,b):
        ans = b
        flag = True
        answers.append(ans)
        break
ans = search_p(n,s)
if ans != -1:
    flag =True
    answers.append(ans)


if not flag:
    print(-1)
else:
    print(int(min(answers)))






Fixed submission:
import itertools
import math 
 
n,s = [int(input()) for _ in range(2)]
 
def n_base_sum(n,b):
    if(math.floor(n/b)):
        return n_base_sum(math.floor(n/b),b)+n%b
    else:
        return n%b
 
def search_p(n,s):
    for p in range(math.floor(math.sqrt(n))+1,0,-1):
        b = (n-s)//p + 1
        if b >1 :
            q = n % b
            if p+q ==s and q < b and n == p*b+q and p<b:
                return b
        
    return -1
 
ans =-1
flag = False
answers = []
if s == n:
    ans = n+1
    flag =True
    answers.append(ans)
for b in  range(2,math.ceil(math.sqrt(n))+1):
    if s== n_base_sum(n,b):
        ans = b
        flag = True
        answers.append(ans)
        break
ans = search_p(n,s)
if ans != -1:
    flag =True
    answers.append(ans)
 
if not flag:
    print(-1)
else:
    print(int(min(answers)))

Buggy python submission (verdict: Runtime Error):
import itertools
import math 

n,s = [int(input()) for _ in range(2)]

def calc_s(b,n):
    i = 0
    s = 0
    while(1):
        s+= n %b
        n = math.floor(n/b)
        i+=1
        if n ==0:
            break
    return s

def search_p(n,s):
    for p in range(1,math.ceil(math.sqrt(n))+1):
        b = n//p
        q = n - b*p
        if p+q ==s:
            return b
    return -1

if s == n:
    ans = n+1
elif s < math.sqrt(n):
    flag = False
    for b in  range(2,math.ceil(math.sqrt(n))+1):
        if s== calc_s(b,n):
            ans = b
            flag = True
            break
    if flag == False:
        ans = search_p(n,s)
print(ans)






Fixed submission:
import itertools
import math 
 
n,s = [int(input()) for _ in range(2)]
 
def n_base_sum(n,b):
    if(math.floor(n/b)):
        return n_base_sum(math.floor(n/b),b)+n%b
    else:
        return n%b
 
def search_p(n,s):
    for p in range(math.floor(math.sqrt(n))+1,0,-1):
        b = (n-s)//p + 1
        if b >1 :
            q = n % b
            if p+q ==s and q < b and n == p*b+q and p<b:
                return b
        
    return -1
 
ans =-1
flag = False
answers = []
if s == n:
    ans = n+1
    flag =True
    answers.append(ans)
for b in  range(2,math.ceil(math.sqrt(n))+1):
    if s== n_base_sum(n,b):
        ans = b
        flag = True
        answers.append(ans)
        break
ans = search_p(n,s)
if ans != -1:
    flag =True
    answers.append(ans)
 
if not flag:
    print(-1)
else:
    print(int(min(answers)))