Divisors

2000ms

262144K

Description:

Bizon the Champion isn't just friendly, he also is a rigorous coder.

Let's define function f(a), where a is a sequence of integers. Function f(a) returns the following sequence: first all divisors of a₁ go in the increasing order, then all divisors of a₂ go in the increasing order, and so on till the last element of sequence a. For example, f([2, 9, 1]) = [1, 2, 1, 3, 9, 1].

Let's determine the sequence X_i, for integer i (i ≥ 0): X₀ = [X] ([X] is a sequence consisting of a single number X), X_i = f(X_i - 1) (i > 0). For example, at X = 6 we get X₀ = [6], X₁ = [1, 2, 3, 6], X₂ = [1, 1, 2, 1, 3, 1, 2, 3, 6].

Given the numbers X and k, find the sequence X_k. As the answer can be rather large, find only the first 10⁵ elements of this sequence.

Input:

A single line contains two space-separated integers — X (1 ≤ X ≤ 10¹²) and k (0 ≤ k ≤ 10¹⁸).

Output:

Print the elements of the sequence X_k in a single line, separated by a space. If the number of elements exceeds 10⁵, then print only the first 10⁵ elements.

Sample Input:

6 1

Sample Output:

1 2 3 6

Sample Input:

4 2

Sample Output:

1 1 2 1 2 4

Sample Input:

10 3

Sample Output:

1 1 1 2 1 1 5 1 1 2 1 5 1 2 5 10

Informação

Provedor Codeforces

Código CF448E