P4335 - Beautiful Sequence

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We call a sequence

of length

n

beautiful when all the following conditions are true:

$A_{1} \leq A_{2} \leq \dots \leq A_{n}$
For each ( $1 \leq i \leq n$ ), $0 \leq A_{i} < 2^{30}$ .
For each , $A_{i} \oplus A_{i + 1} = B_{i}$ , where $B$ is a given sequence, and represents bitwise XOR.

You need to find the

k

-th smallest lexicographically legal beautiful sequence

第一行两个整数 n,k.(

1 \leq k \leq 2^{30}

)
第二行n-1个整数

(

0 \leq B_{i} < 2^{30}

)

If the number of beautiful sequences is less than

k

, output one line containing an integer

.
Otherwise, output one line containing

n

integers

separated by spaces --- the

-th smallest lexicographically legal beautiful sequence.

3 3
1 2

8 9 11

二进制分块

4335: Beautiful Sequence