Power of Power Partition Function

Let $m$ be a fixed integer such that $m \ge 2$. For a positive integer $n$, let $b\_{m}(n)$ denote the number of ways of writing $n$ as a sum of powers of $m$ using non-negative exponents with repetitions allowed and the order of the summands not being taken into account. We also set $b\_{m}(0) = 1$ (there is one empty sum).

For example, the first $10$ terms of $\\{b\_{2}(n)\\}$ are $\\{1, 1, 2, 2, 4, 4, 6, 6, 10, 10\\}$, and the first $10$ terms of $\\{b\_{3}(n)\\}$ are $\\{1, 1, 1, 2, 2, 2, 3, 3, 3, 5\\}$.

Let $c\_{m}^{k}(n)$ be the $k$-th convolution power of $b\_{m}(n)$, which is defined as follows: $c\_{m}^{k}(n)=\begin{cases} b\_{m}(n), & k = 1 \\\ \sum\limits\_{i=0}^{n} b\_{m}(i) \cdot c\_{m}^{k-1}(n-i), & k \ge 2 \end{cases}$ 

Given $n$, $m$ and $k$, Bobo would like to find the value of $f(n) = \left( \sum\limits\_{i=0}^{n}c^{k}\_{m}(i) \right) \bmod (10^9 + 7)\text{.}$

The first line contains three integers $n$, $m$ and $k$ ($0 \leq n \leq 10^{18}$, $2 \leq m \leq 10^{18}$, $1 \leq k \leq 10$).

Output an integer denoting the value of $f(n)$.