Doll Claw Machine

Each time the machine runs, it dispenses a doll with probability $p = \frac{a}{b}$. However, if no doll came out in the previous $c - 1$ runs, a doll is dispensed with certainty regardless of $p$.

Given $p$, $c$, and $n$, find for every natural number $k \le n$ the expected number of dolls obtained after exactly $k$ runs.

The input consists of $T$ test cases. The first line contains the integer $T$. $(1 \le T \le 1\,000\,000)$

Each test case is one line containing the integers $p'$, $c$, and $n$, separated by spaces. $p'$ is the probability that a doll comes out. $(0 \le p' \le 10^9+6;\ 1 \le c, n \le 10^6)$ Here $p' \equiv a \times b^{-1} \pmod{10^9 + 7}$. $(b \not\equiv 0 \pmod{10^9+7})$

The sum of $n$ over all test cases is at most $10^6$.

For each test case, print $n$ lines. On line $k$, print the expected number of dolls obtained after exactly $k$ runs, modulo $10^9+7$. Precisely, if the answer can be written as $\frac{x}{y}$ for natural numbers $x$ and $y$, print $x \times y^{-1} \pmod{10^9+7}$.