Nasser and the Target OR#12351
Nasser gives you an array of length and an integer .
In one operation, you can choose:
A subarray a[l,...,r] (1 \le l \le r \le n)
A specific bit position (0 \le p < 30)
Flip the -th bit in some (possibly all) elements of the chosen subarray
Your task is to find the minimum number of operations needed such that there exists at least one subarray a[l,...,r] : (1 \le l \le r \le n) whose OR equals .
A subarray is defined as a contiguous segment of the array.
Formally, for an array of length , a subarray is any sequence of the form a_l, a_{l+1}, \ldots, a_r where 1 \le l \le r \le n.
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The bitwise OR of a sequence of numbers is calculated by applying the OR operation to all its elements. For instance, the bitwise OR of is 1 | 2 = 3.
Since Nasser is not confident with bitwise operations, he asked you to help him solve this problem efficiently.
The first line contains a single integer (1 \le t \le 10^4) — the number of test cases.
The first line of each test case contains two integers (1 \le n \le 4 \cdot 10^5, 0 \le k < 2^{30}) — the size of the array and the target value.
The second line contains integers a_1, a_2, \ldots, a_n (0 \le a_1,a_2,\ldots,a_n < 2^{30}) — the elements of the array.
It is guaranteed that the sum of all over all test cases does not exceed 4 \cdot 10^5.
For each test case, output two lines:
First line: a single integer — the minimum number of operations.
Second line: space-separated integers p_1, p_2, \ldots, p_m (0 \le p_i < 30) — the bit positions to flip .
If there are multiple optimal sequences of bit positions, you may output any of them.
Example 1
Subtask ( points) : (n=1,0 \le k \le 1000)
Subtask ( points) : (1 \le \sum n \le 100,0 \le k \le 10^{6})
Subtask ( points) : (1 \le \sum n \le 5000,0 \le k \le 10^{9})
Subtask ( points) : No additional constraints.