Fibonomial

The Fibonacci sequence $f_n$ is defined as follows.

$f_0 = 0, \quad f_1 = 1, \quad f_n = f_{n-1} + f_{n-2} \;\; (n \ge 2)$

The Fibonomial $F_n$ ($n \ge 1$) is defined as $F_n = f_1 \times f_2 \times \cdots \times f_n$, the product of $f_1$ through $f_n$.

For each integer $k$ with $2 \le k \le p$, write a program that reports how many times $F_n$ has to be divided by $k$ before $F_n$ is no longer divisible by $k$.

The first line holds two integers $n$ and $p$, separated by one space. ($1 \le n \le 10^9$, $2 \le p \le 10^3$)

Print the answers on $p - 1$ lines. Line $i$ ($1 \le i \le p - 1$) holds how many times $F_n$ has to be divided by $i + 1$ before $F_n$ is no longer divisible by $i + 1$.

$F_{12} = 1570247078400 = 2^9 \times 3^4 \times 5^2 \times 7 \times 11 \times 13 \times 17 \times 89$, so $F_{12}$ can be divided by $2$ nine times and by $4$ four times.