Constructive Fun

Input

The first line contains a single integer $t$ $(1 \leq t \leq 1 0^{4})$ (1 \le t \le 10^4) – the number of test cases.

The only line of each test case contains two integers $n$ , $k$ $(1 \leq n \leq 1 0^{6}; 0 \leq k \leq 1 0^{6})$ (1 \le n \le 10^6 ; 0 \le k \le 10^6) – the length of array $a$ and the required value.

Additional constraints :

It's guaranteed that the sum of $n$ doesn't exceed $1 0^{6}$ 10^6 across all test cases.
It's guaranteed that the sum of $k$ doesn't exceed $6 \cdot 1 0^{6}$ 6 \cdot 10^6 across all test cases.

Output

For each test case, output any valid array $(a_{1}, a_{2}, ..., a_{n})$ (a_1,a_2,...,a_n) where $(1 \leq a_{1}, a_{2}, ..., a_{n} \leq 1 0^{9})$ (1 \le a_1,a_2,...,a_n \le 10^{9})

It's guaranteed that there exists at least one valid array across all tests.

Examples

Example 1

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Note

In the first test case, $a = [10, 11, 12]$ a=[10,11,12] is valid because :

For the first index $∣11 - 10∣ + ∣12 - 10∣ = 1 + 2 = 3$ |11-10|+|12-10|=1+2=3.
For the second index $∣12 - 11∣ = 1$ |12-11|=1.

Total of $4$ .

For the second test case , $a = [1, 10, 4, 2]$ a=[1,10,4,2] is valid because :

For the first index $∣10 - 1∣ + ∣4 - 1∣ + ∣2 - 1∣ = 9 + 3 + 1 = 13$ |10-1|+|4-1|+|2-1|=9+3+1=13.
For the second index $∣4 - 10∣ + ∣2 - 10∣ = 6 + 8 = 14$ |4-10|+|2-10|=6+8=14.
For the third and fourth indices $∣4 - 2∣ = 2$ |4-2|=2.

Total of $29$ .

For the third test case , $a = [1, 3, 8, 2, 1, 10, 11]$ a=[1 ,3 ,8 ,2 ,1 ,10, 11] is valid because :

For the first index $∣3 - 1∣ + ∣8 - 1∣ + ∣2 - 1∣ + ∣1 - 1∣ + ∣10 - 1∣ + ∣11 - 1∣ = 29$ |3-1|+|8-1|+|2-1|+|1-1|+|10-1|+|11-1|=29.
For the second index $∣8 - 3∣ + ∣2 - 3∣ + ∣1 - 3∣ + ∣10 - 3∣ + ∣11 - 3∣ = 23$ |8-3|+|2-3|+|1-3|+|10-3|+|11-3|=23.
For the third index $∣2 - 8∣ + ∣1 - 8∣ + ∣10 - 8∣ + ∣11 - 8∣ = 18$ |2-8|+|1-8|+|10-8|+|11-8|=18.
For the fourth index $∣1 - 2∣ + ∣10 - 2∣ + ∣11 - 2∣ = 18$ |1-2|+|10-2|+|11-2|=18.
For the fifth index $∣10 - 1∣ + ∣11 - 1∣ = 19$ |10-1|+|11-1|=19.
For the sixth index $∣11 - 10∣ = 1$ |11-10|=1.

Total of $108$ .

For the fourth test case , $a = [2, 4, 8, 7, 1]$ a=[2,4,8,7,1] is valid because :

For the first index $∣4 - 2∣ + ∣8 - 2∣ + ∣7 - 2∣ + ∣1 - 2∣ = 14$ |4-2|+|8-2|+|7-2|+|1-2|=14.
For the second index $∣8 - 4∣ + ∣8 - 7∣ + ∣8 - 1∣ = 10$ |8-4|+|8-7|+|8-1|=10.
For the third index $∣7 - 8∣ + ∣1 - 8∣ = 8$ |7-8|+|1-8|=8.
For the fourth index $∣1 - 7∣ = 6$ |1-7|=6.

Total of $38$ .

Scoring

Subtask $1$ ( $5$ points) : $(k = 0)$ (k=0).
Subtask $2$ ( $15$ points) : It's guaranteed that there exists an array that satisfies the conditions with $(a_{i} \in {1, 2})$ (a_i \in \{1,2\}) and $(1 \leq n \leq 20)$ (1 \le n \le 20).
Subtask $3$ ( $20$ points) : $(1 \leq k \leq 10)$ (1 \le k \le 10).
Subtask $4$ ( $30$ points) : $(1 \leq k \leq 100)$ (1 \le k \le 100).
Subtask $5$ ( $40$ points) : $(1 \leq k \leq 1000)$ (1 \le k \le 1000).
Subtask $6$ ( $50$ points) : $(1 \leq k \leq 1 0^{4})$ (1 \le k \le 10^4).
Subtask $7$ ( $60$ points) : $(1 \leq \sum n \cdot k \leq 1 0^{6})$ (1 \le \sum n\cdot k \le 10^6).
Subtask $8$ ( $80$ points) : No additional Constraints.