XOR Sequence Construction

Given three integers (n), (m), and (k), construct a sequence (a_1,a_2,\dots,a_n) of non-negative integers satisfying:

1. For every (1 \le i \le n), (0 \le a_i \le m).
2. (a_1 \oplus a_2 \oplus \dots \oplus a_n = k), where (\oplus) denotes the bitwise XOR operation.

If no such sequence exists, output -1.

inputFormat

Input consists of three integers (n), (m), and (k) provided on a single line.

outputFormat

If a valid sequence exists, output the (n) numbers (a_1,a_2,\dots,a_n) separated by spaces. Otherwise, output -1.

sample

1 5 3

3