Problem:
Score : 400 points

Problem Statement

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.

Constraints

All values in input are integers.

1 \leq N \leq 10^5

N \leq M \leq 10^9

Input

Input is given from Standard Input in the following format:

N M

Output

Print the maximum possible value of the greatest common divisor of a sequence a_1, a_2, ..., a_N that satisfies the condition.

Sample Input 1

3 14

Sample Output 1

2

Consider the sequence (a_1, a_2, a_3) = (2, 4, 8). Their greatest common divisor is 2, and this is the maximum value.

Sample Input 2

10 123

Sample Output 2

3

Sample Input 3

100000 1000000000

Sample Output 3

10000

Solution in Ruby (2.3.3) (judge verdict: Wrong Answer)

n, m = gets.split.map(&:to_i)

if m % n == 0
    puts m / n
    exit
end

maxval = 1 + Math.sqrt(m).to_i
is_prime = [true] * maxval
is_prime[0] = false
is_prime[1] = false
is_prime.each_with_index{|isp, num|
    if isp
        (0..maxval).step(num).drop(2).each{|i|
            is_prime[i] = false
        }
    end
}
primes = is_prime.each_with_index.map{|isp, num|
    if isp
        num
    else
        nil
    end
}.select{|n| n != nil}

primes.each{|p|
    if p >= n && m % p == 0
        puts m / p
        exit
    end
}
primes.reverse_each{|p|
    if m / p >= n && m % p == 0
        puts p
        exit
    end
}

puts 1