The Number of Sequences

Consider a sequence of $N$ numbers that satisfies all four conditions below.

1. Every number in the sequence is an integer between $0$ and $2^{31} - 1$, inclusive.
2. The bitwise OR of every number in the sequence is $X$.
3. The bitwise AND of every number in the sequence is $Y$.
4. The bitwise XOR of every number in the sequence is $Z$.

Taekhee owned every sequence that satisfies these conditions, but he lost some of them while moving. Once he knows $X$, $Y$, and $Z$, he can build all of them again.

Taekhee remembers two facts. The sequence length is $N$, and exactly $C$ sequences satisfy all four conditions.

Find the values of $X$, $Y$, and $Z$. Two sequences whose numbers appear in a different order count as different sequences.

The first line contains the sequence length $N$ and the number of sequences $C$ that satisfy the conditions, separated by a space. ($1 \le N \le 10^5$, $0 \le C \le 10^{18}$)

On the first line print integers $X$, $Y$, and $Z$ between $0$ and $2^{31} - 1$, separated by spaces, for which exactly $C$ sequences satisfy the conditions.

If several triples $(X, Y, Z)$ satisfy the conditions, print the lexicographically smallest one. Take the smallest $X$, among those the smallest $Y$, and among those the smallest $Z$.

If no such $X$, $Y$, $Z$ exist, print $-1$ and nothing else.