Person in charge

• 035966_L3

Problem Description

struct S
{
    bool c[5012];
    int dc[5012][2];
    int ts = 1;
    int x;
    void init(int h)
    {
        memset(c, 0, sizeof c);
        memset(dc, 0, sizeof dc);
        c[1] = 0;
        ts = 1;
        x = h;
    }
    void add(int num)
    {
        int now = 1;
        for (int i = 1, j = x; j >= 0; i++, j--)
        {
            bool cc = num & (1 << j);
            int xx = ts + 1;
            if (dc[now][cc]) xx = dc[now][cc];
            if (xx > ts)
            {
                ts++;
                dc[now][cc] = ts;
                c[ts] = cc;
            }
            now = xx;
        }
    }
};

The above code implements a 01 Trie.

This 01 Trie can store any integer in the range $[0,2^x)$ via the add function. After insertion, the value of variable ts reflects the actual space used by this 01 Trie.

Your task is to insert $y$ integers from $[0,2^x)$ into such a 01 Trie to maximize its actual space usage.

Input Format

Multiple test cases.

The first line contains a positive integer $T$, indicating the number of test cases.

Each of the next $T$ lines contains two positive integers $x$ and $y$.

Output Format

For each test case, output one line containing $y$ integers from $[0,2^x)$, representing the integers you insert.

Sample

6
1 1
1 2
2 1
2 2
2 3
2 4

1
0 1
0
1 2
3 0 1
2 3 0 1

Sample Explanation

The ts values for the 6 test cases are $2,3,3,5,6,7$ respectively.

Note: The solution is not unique.

Constraints

$1 \le T \le 2046, 1 \le x \le 10, 1 \le y \le 2^x.$