A15632 | Koxia and Sequence

Mari has three integers $n$ , $x$ , and $y$ .

Call an array $a$ of $n$ non-negative integers good if it satisfies the following conditions:

- $a_1+a_2+\ldots+a_n=x$ , and
- $a_1 \, | \, a_2 \, | \, \ldots \, | \, a_n=y$ , where $|$ denotes the [bitwise OR operation](https://en.wikipedia.org/wiki/Bitwise_operation#OR).

The score of a good array is the value of $a_1 \oplus a_2 \oplus \ldots \oplus a_n$ , where $\oplus$ denotes the [bitwise XOR operation](https://en.wikipedia.org/wiki/Bitwise_operation#XOR).

Koxia wants you to find the total bitwise XOR of the scores of all good arrays. If there are no good arrays, output $0$ instead.

The first line of input contains three integers $n$ , $x$ and $y$ ( $1 \leq n < 2^{40}$ , $0 \leq x < 2^{60}$ , $0 \leq y < 2^{20}$ ).

Output a single integer — the total bitwise XOR of the scores of all good arrays.