CF1097D.Makoto and a Blackboard

Makoto has a big blackboard with a positive integer $n$ written on it. He will perform the following action exactly $k$ times:

Suppose the number currently written on the blackboard is $v$ . He will randomly pick one of the divisors of $v$ (possibly $1$ and $v$ ) and replace $v$ with this divisor. As Makoto uses his famous random number generator (RNG) and as he always uses $58$ as his generator seed, each divisor is guaranteed to be chosen with equal probability.

He now wonders what is the expected value of the number written on the blackboard after $k$ steps.

It can be shown that this value can be represented as $\frac{P}{Q}$ where $P$ and $Q$ are coprime integers and $Q \not\equiv 0 \pmod{10^9+7}$ . Print the value of $P \cdot Q^{-1}$ modulo $10^9+7$ .

The only line of the input contains two integers $n$ and $k$ ( $1 \leq n \leq 10^{15}$ , $1 \leq k \leq 10^4$ ).

Print a single integer — the expected value of the number on the blackboard after $k$ steps as $P \cdot Q^{-1} \pmod{10^9+7}$ for $P$ , $Q$ defined above.

In the first example, after one step, the number written on the blackboard is $1$ , $2$ , $3$ or $6$ — each occurring with equal probability. Hence, the answer is $\frac{1+2+3+6}{4}=3$ .

In the second example, the answer is equal to $1 \cdot \frac{9}{16}+2 \cdot \frac{3}{16}+3 \cdot \frac{3}{16}+6 \cdot \frac{1}{16}=\frac{15}{8}$ .