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: $011 \oplus 101 = 110$).

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.

Input

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

N M X

Output

Print the answer.