Determine Hidden Sequence and Permutation

ID: 19928

Type: Default

1000ms

256MiB

We randomly generated three numbers (R_0, R_1, R_2) and used the recurrence

(R_n = R_{n-2} \oplus R_{n-1}), where (\oplus) denotes the bitwise XOR operation.

Additionally, there is a bijective function (M) such that for any (x \neq y), (M(x) \neq M(y)).

After multiple queries, your goal is to determine (R_0, R_1, R_2, M(0), M(1), \ldots, M(255)).

Interaction: Your program should read from standard input and write to standard output. In each query, you output an integer (A). If this is your (N)th query, you will receive the value

(M(A \oplus R_{N-1})).

When you have determined all values, output a line containing the string SOLUTION followed by 259 lines containing (R_0, R_1, R_2, M(0), M(1), \ldots, M(255)).

Remember to flush the output after printing each line!

inputFormat

The input consists of 259 lines. The first three lines give (R_0, R_1, R_2) respectively, followed by 256 lines representing (M(0), M(1), \ldots, M(255)).

outputFormat

Output should begin with the line SOLUTION followed by 259 lines containing (R_0, R_1, R_2, M(0), M(1), \ldots, M(255)).

sample

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#P6720. Determine Hidden Sequence and Permutation

Determine Hidden Sequence and Permutation