Aujasvit just came up with a new game to play with his friends. N people stand in a circle, each assigned an index from 1 to N in clockwise order. Then the following operation is done N-1 times.

The person with the lowest index holds a coin.
Then, the coin then moves to the next person clockwise M-1 times.
Then, the person who is holding the coin is removed from the circle.

The last person remaining after N-1 operations is the winner.

Aujasvit has already decided on the integer M to be used in the game. Before inviting people to play his game, Aujasvit wants to know the winner if the game has 1 player, 2 players, 3 players, ..., X players. That is, you need to output the winner when N = 1, N = 2, ..., N = X.

------ Input Format ------

• The first line of each input contains T - the number of test cases. The test cases then follow.
• The only line of each test case contains two space-separated integers M and X.

------ Output Format ------

For each testcase, output $X integers A_{1}, A_{2}, \dots, A_{X}$, where A_{i} is the index of the winner if i people are playing this game.

------ Constraints ------

$1 ≤ T ≤ 1000$
$1 ≤ M ≤ 10^{9}$
$1 ≤ X ≤ 10000$
- Sum of $X$ over all testcases is not more than $5 \cdot 10^{5}$

----- Sample Input 1 ------
1
2 3

----- Sample Output 1 ------
1 1 1
----- explanation 1 ------
- Test case $1$:
- When there is only $1$ player, they are the winner. Therefore player $1$ wins.
- When there are $2$ players, player $2$ is removed in the first round. Therefore player $1$ wins.
- When there are $3$ players, player $2$ is removed in the first round, and player $3$ is removed in the second round. Therefore player $1$ wins.

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