Lantern Chain Code Recovery

Along a straight corridor there are n lanterns in a row, each configured with a secret numeric glow-code. A sensor mounted between each pair of adjacent lanterns can only measure the bitwise XOR of the two codes it sits between, never either code directly, producing a log with n - 1 entries. Separately, before the sensors were installed, a technician wrote down the exact glow-code of the very first lantern. Using the sensor log and that one recorded value, recover the glow-code of every lantern in order.

Input format

• Line 1: an integer m, the number of sensor-log entries (m = n - 1, where n is the number of lanterns).
• Line 2: m integers, the sensor log, where the i-th value (1-indexed) equals the bitwise XOR of the glow-codes of lantern i and lantern i+1.
• Line 3: an integer first, the recorded glow-code of the first lantern.

Output format

Print n integers separated by single spaces on one line: the recovered glow-code of every lantern, from the first to the last.

Constraints

• 1 <= m <= 9999 (so 2 <= n <= 10000)
• 0 <= each sensor-log value <= 10^5
• 0 <= first <= 10^5

4
1 2 3 1
1

1 0 2 1 0

1
7
5

5 2