Decoding Task

In the near future, research and publication in cryptography become strictly regulated for national security reasons. As a result, organizations develop their own proprietary cryptographic systems to protect sensitive information.

The ACM Corporation uses a special encryption system called the Intercontinental Cryptographic Protection Code (ICPC) to secure its communications over intercontinental lines, which are easier to intercept than its internal lines. The ICPC is considered highly secure; it uses a long, randomly-generated key that is changed every week and is shared securely among all relevant systems.

As part of internal system audits, the corporation regularly verifies the robustness and correct operation of its cryptographic system. One such audit involves analyzing pairs of encrypted messages. Newsletters are automatically generated and distributed to various departments weekly, immediately after the key update. Occasionally, due to differences in document templates or automated processes, an extra space character (with decimal value $32$) may be inserted at the beginning of the message for some recipients, while others receive the original form. By comparing two encrypted versions—one with the space and one without—analysts can recover the portion of the key used.

You are given two messages encrypted by ICPC: the first of length $N$ bytes, the second of length N+1 bytes. The second message corresponds to the same plain-text as the first, but with an extra space character at the beginning. Both are encrypted using the same key, and encryption is performed by applying a bitwise exclusive OR (XOR) between each byte of the message and the corresponding key byte:

where K_i is the $i$-th byte of the key and C_i is the $i$-th byte of the plain-text.

Your task is to reconstruct the first N+1 bytes of the encryption key using the provided encrypted messages.