Number Discovery

Ujan needs some rest from cleaning, so he started playing with infinite sequences. He has two integers $$$n$$$ and $$$k$$$. He creates an infinite sequence $$$s$$$ by repeating the following steps.

1. Find $$$k$$$ smallest distinct positive integers that are not in $$$s$$$. Let's call them $$$u_{1}, u_{2}, \ldots, u_{k}$$$ from the smallest to the largest.
2. Append $$$u_{1}, u_{2}, \ldots, u_{k}$$$ and $$$\sum_{i=1}^{k} u_{i}$$$ to $$$s$$$ in this order.
3. Go back to the first step.

Ujan will stop procrastinating when he writes the number $$$n$$$ in the sequence $$$s$$$. Help him find the index of $$$n$$$ in $$$s$$$. In other words, find the integer $$$x$$$ such that $$$s_{x} = n$$$. It's possible to prove that all positive integers are included in $$$s$$$ only once.