Counting Good Numbers

You are given two positive integers $N$ and $K$. A positive integer $X$ is called a **Good Number** if $X$ can be written as $i_1\ |\ i_2\ |\ \cdots\ |\ i_M$ $^\dagger$, where $K \le i_1 < i_2 < \cdots < i_M < N + K$ and $1 \le M \le N$. Now your task is to answer $Q$ queries of the following type: - $L, R$ : count the number of **Good Numbers** between $l$ and $r$ inclusive. $^\dagger$ Given