You are an expert competitive programmer. You will be given a problem statement, test case constraints and example test inputs and outputs. Please reason step by step about the solution (that must respect memory and time limits), then provide a complete implementation in python3.

Your solution must read input from standard input (cin), write output to standard output (cout).
Do not include any debug prints or additional output.

Put your final solution within a single code block:
```python
<your code here>
```

Execution time limit: 6.0 seconds
Memory limit: 512.0 MB

# Problem
You are given three integers $$$n$$$, $$$k$$$ and $$$f$$$.

Consider all binary strings (i. e. all strings consisting of characters $$$0$$$ and/or $$$1$$$) of length from $$$1$$$ to $$$n$$$. For every such string $$$s$$$, you need to choose an integer $$$c_s$$$ from $$$0$$$ to $$$k$$$.

A multiset of binary strings of length exactly $$$n$$$ is considered beautiful if for every binary string $$$s$$$ with length from $$$1$$$ to $$$n$$$, the number of strings in the multiset such that $$$s$$$ is their prefix is not exceeding $$$c_s$$$.

For example, let $$$n = 2$$$, $$$c_{0} = 3$$$, $$$c_{00} = 1$$$, $$$c_{01} = 2$$$, $$$c_{1} = 1$$$, $$$c_{10} = 2$$$, and $$$c_{11} = 3$$$. The multiset of strings $$$\{11, 01, 00, 01\}$$$ is beautiful, since:

- for the string $$$0$$$, there are $$$3$$$ strings in the multiset such that $$$0$$$ is their prefix, and $$$3 \le c_0$$$;
- for the string $$$00$$$, there is one string in the multiset such that $$$00$$$ is its prefix, and $$$1 \le c_{00}$$$;
- for the string $$$01$$$, there are $$$2$$$ strings in the multiset such that $$$01$$$ is their prefix, and $$$2 \le c_{01}$$$;
- for the string $$$1$$$, there is one string in the multiset such that $$$1$$$ is its prefix, and $$$1 \le c_1$$$;
- for the string $$$10$$$, there are $$$0$$$ strings in the multiset such that $$$10$$$ is their prefix, and $$$0 \le c_{10}$$$;
- for the string $$$11$$$, there is one string in the multiset such that $$$11$$$ is its prefix, and $$$1 \le c_{11}$$$.

Now, for the problem itself. You have to calculate the number of ways to choose the integer $$$c_s$$$ for every binary string $$$s$$$ of length from $$$1$$$ to $$$n$$$ in such a way that the maximum possible size of a beautiful multiset is exactly $$$f$$$.

## Input Format
The only line of input contains three integers $$$n$$$, $$$k$$$ and $$$f$$$ ($$$1 \le n \le 15$$$; $$$1 \le k, f \le 2 \cdot 10^5$$$).

## Output Format
Print one integer — the number of ways to choose the integer $$$c_s$$$ for every binary string $$$s$$$ of length from $$$1$$$ to $$$n$$$ in such a way that the maximum possible size of a beautiful multiset is exactly $$$f$$$. Since it can be huge, print it modulo $$$998244353$$$.

## Examples
```input
1 42 2
```
```output
3
```
-----
```input
2 37 13
```
```output
36871576
```
-----
```input
4 1252 325
```
```output
861735572
```
-----
```input
6 153 23699
```
```output
0
```
-----
```input
15 200000 198756
```
```output
612404746
```

## Note
In the first example, the three ways to choose the integers $$$c_s$$$ are:

- $$$c_0 = 0$$$, $$$c_1 = 2$$$, then the maximum beautiful multiset is $$$\{1, 1\}$$$;
- $$$c_0 = 1$$$, $$$c_1 = 1$$$, then the maximum beautiful multiset is $$$\{0, 1\}$$$;
- $$$c_0 = 2$$$, $$$c_1 = 0$$$, then the maximum beautiful multiset is $$$\{0, 0\}$$$.

Now solve the problem and return the code.