Problem: You are given integers N and M.  Consider a sequence a of length N consisting of positive integers such that a_1 + a_2 + ... + a_N = M. Find the maximum possible value of the greatest common divisor of a_1, a_2, ..., a_N.

Submission attempts (in order):
# -*- coding: utf-8 -*-
import itertools
from collections import Counter

N, M = map(int, input().split())

def primes(n):
    primfac = []
    d = 2
    while d*d <= n:
        while (n % d) == 0:
            primfac.append(d)  # supposing you want multiple factors repeated
            n //= d
        d += 1
    if n > 1:
       primfac.append(n)
    return primfac


mod = M % N
div = M // N
if mod == 0:
    print(M//N)
    exit()

f = primes(M)


if len(f) <= 1:
    print(1)
    exit()

cnt = Counter(f)
ans_list = []

tmp_list = []
for k,v in cnt.items():
  tmp_list.append([i for i in range(v+1)])

# prod = itertools.product(*tmp_list)
# print(tmp_list)
# print(list(prod))
# print(prod)
for p in itertools.product(*tmp_list):
    # print(cnt.keys(), p)
    tmp = 1
    for k,i in zip(cnt.keys(),p):
        # print(k,i)
        tmp = tmp * (k ** i)

    if tmp >= N:
        ans_list.append(M//tmp)



# -*- coding: utf-8 -*-
import itertools

N, M = map(int, input().split())

def primes(n):
    primfac = []
    d = 2
    while d*d <= n:
        while (n % d) == 0:
            primfac.append(d)  # supposing you want multiple factors repeated
            n //= d
        d += 1
    if n > 1:
       primfac.append(n)
    return primfac


mod = M % N
div = M // N
if mod == 0:
    print(M//N)
    exit()

f = primes(M)


if len(f) <= 1:
    print(1)
    exit()

ans_list = []
for i in range(1,len(f)):
    set1 = set([tuple(sorted(l)) forl in list(itertools.combinations(f, i))])
    for com in set1:
        tmp = 1
        for c in com:
            tmp *= c
        if tmp >= N:
            ans_list.append(M//tmp)

if len(ans_list) == 0:
    print(1)
else:
    print(max(ans_list))


# -*- coding: utf-8 -*-
import itertools
from collections import Counter

N, M = map(int, input().split())

def primes(n):
    primfac = []
    d = 2
    while d*d <= n:
        while (n % d) == 0:
            primfac.append(d)  # supposing you want multiple factors repeated
            n //= d
        d += 1
    if n > 1:
       primfac.append(n)
    return primfac


mod = M % N
div = M // N
if mod == 0:
    print(M//N)
    exit()

f = primes(M)


if len(f) <= 1:
    print(1)
    exit()

cnt = Counter(f)
ans_list = []

tmp_list = []
for k,v in cnt.items():
  tmp_list.append([i for i in range(v+1)])

# prod = itertools.product(*tmp_list)
# print(tmp_list)
# print(list(prod))
# print(prod)
for p in itertools.product(*tmp_list):
    # print(cnt.keys(), p)
    tmp = 1
    for k,i in zip(cnt.keys(),p):
        # print(k,i)
        tmp = tmp * (k ** i)

        if tmp >= N:
            ans_list.append(M//tmp)


# -*- coding: utf-8 -*-
import itertools
from collections import Counter

N, M = map(int, input().split())

def primes(n):
    primfac = []
    d = 2
    while d*d <= n:
        while (n % d) == 0:
            primfac.append(d)  # supposing you want multiple factors repeated
            n //= d
        d += 1
    if n > 1:
       primfac.append(n)
    return primfac


mod = M % N
div = M // N
if mod == 0:
    print(M//N)
    exit()

f = primes(M)


if len(f) <= 1:
    print(1)
    exit()

cnt = Counter(f)
ans_list = []

tmp_list = []
for k,v in cnt.items():
  tmp_list.append([i for i in range(v+1)])

for p in itertools.product(tmp_list):
    tmp = 1
    for k,i in zip(cnt.keys(),*p):
        tmp = tmp * (k ** i)

        if tmp >= N:
            ans_list.append(M//tmp)


# -*- coding: utf-8 -*-
import itertools
from collections import Counter

N, M = map(int, input().split())

def primes(n):
    primfac = []
    d = 2
    while d*d <= n:
        while (n % d) == 0:
            primfac.append(d)  # supposing you want multiple factors repeated
            n //= d
        d += 1
    if n > 1:
       primfac.append(n)
    return primfac


mod = M % N
div = M // N
if mod == 0:
    print(M//N)
    exit()

f = primes(M)


if len(f) <= 1:
    print(1)
    exit()

cnt = Counter(f)
ans_list = []

tmp_list = []
for k,v in cnt.items():
  tmp_list.append([i for i in range(v+1)])

for p in itertools.product(tmp_list):
    tmp = 1
    for k,i in zip(cnt.keys(),*p):
        tmp = tmp * (k ** i)

        if tmp >= N and tmp > 1:
            ans_list.append(M//tmp)



# -*- coding: utf-8 -*-
import itertools
from collections import Counter

N, M = map(int, input().split())

def primes(n):
    primfac = []
    d = 2
    while d*d <= n:
        while (n % d) == 0:
            primfac.append(d)  # supposing you want multiple factors repeated
            n //= d
        d += 1
    if n > 1:
       primfac.append(n)
    return primfac


mod = M % N
div = M // N
if mod == 0:
    print(M//N)
    exit()

f = primes(M)


if len(f) == 1:
    print(1)
    exit()

cnt = Counter(f)
ans_list = []

tmp_list = []
for k,v in cnt.items():
  tmp_list.append([i for i in range(v+1)])

print(cnt)
print(list(itertools.product(*tmp_list)))
for p in itertools.product(*tmp_list):
    tmp = 1
    for k,i in zip(cnt.keys(),p):
        tmp = tmp * (k ** i)

    if tmp > N:
        ans_list.append(M//tmp)

if len(ans_list) == 0:
    print(1)
else:
    print(max(ans_list))


# -*- coding: utf-8 -*-
import itertools
from collections import Counter

N, M = map(int, input().split())

def primes(n):
    primfac = []
    d = 2
    while d*d <= n:
        while (n % d) == 0:
            primfac.append(d)  # supposing you want multiple factors repeated
            n //= d
        d += 1
    if n > 1:
       primfac.append(n)
    return primfac


mod = M % N
div = M // N
if mod == 0:
    print(M//N)
    exit()

f = primes(M)


if len(f) == 1:
    print(1)
    exit()

cnt = Counter(f)
ans_list = []

tmp_list = []
for k,v in cnt.items():
  tmp_list.append([i for i in range(v+1)])

# print(cnt)
# print(list(itertools.product(*tmp_list)))
for p in itertools.product(*tmp_list):
    tmp = 1
    for k,i in zip(cnt.keys(),p):
        tmp = tmp * (k ** i)

    if tmp > N:
        ans_list.append(M//tmp)

if len(ans_list) == 0:
    print(1)
else:
    print(max(ans_list))


Verdicts: Wrong Answer

Runtime Error

Wrong Answer

Wrong Answer

Wrong Answer

Wrong Answer

Accepted