### Problem Statement

Print the number of integer sequences of length $N$, $A = (A_1, A_2, \ldots, A_N)$, that satisfy both of the following conditions, modulo $998244353$.

-   $0 \leq A_1 \leq A_2 \leq \cdots \leq A_N \leq M$
-   $A_1 \oplus A_2 \oplus \cdots \oplus A_N = X$

Here, $\oplus$ denotes bitwise XOR.

What is bitwise XOR?

The bitwise XOR of non-negative integers $A$ and $B$, $A \oplus B$, is defined as follows.

-   When $A \oplus B$ is written in binary, the $k$-th lowest bit ($k \geq 0$) is $1$ if exactly one of the $k$\-th lowest bits of $A$ and $B$ is $1$, and $0$ otherwise.

For instance, $3 \oplus 5 = 6$ (in binary: $011 \oplus 101 = 110$).

### Input

The input is given from Standard Input in the following format:

```
$N$ $M$ $X$
```

### Output

Print the answer.

### Constraints

-   $1 \leq N \leq 200$
-   $0 \leq M \lt 2^{30}$
-   $0 \leq X \lt 2^{30}$
-   All values in the input are integers.

5

Here are the five sequences of length N that satisfy both conditions in the statement: (0,0,2),(0,1,3),(1,1,2),(2,2,2),(2,3,3).