Problem H: Count Words
Problem
  There are $M$ types of characters. Create a string of length $N$ using these characters. How many strings have at least $K$ different types of characters used in them? Find the answer modulo $998244353$.
  Here two strings of length $N$ are considered different if there exists an $i$ $(1 \leq i \leq N)$ such that $S_i \neq T_i$ where $S = S_1S_2 \ldots S_N$ and $T = T_1T_2 \ldots T_N$.
Input
The input is given in the following format:
$M$ $N$ $K$
  $M, N,$ and $K$ are given on a single line separated by a single space.
Constraints
The input satisfies the following constraints:
$1 \leq M \leq 10^{18} $
$1 \leq N \leq 10^{18} $
$1 \leq K \leq 1000 $
All input values are integers.
Output
  Print the number of strings of length $N$ using $M$ characters such that at least $K$ different types of characters are used. The answer should be printed modulo $998244353$.
Sample Input 1
2 10 1
Sample Output 1
1024
Sample Input 2
1 1 2
Sample Output 2
0
Sample Input 3
5 10 3
Sample Output 3
9755400
Sample Input 4
7 8 3
Sample Output 4
5759460
Sample Input 5
1000000000000000000 1000000000000000000 1000
Sample Output 5
133611974
