In order to establish dominance amongst his friends, Chef has decided that he will only walk in large steps of length exactly $K$ feet. However, this has presented many problems in Chef’s life because there are certain distances that he cannot traverse. Eg. If his step length is $5$ feet, he cannot travel a distance of $12$ feet. Chef has a strict travel plan that he follows on most days, but now he is worried that some of those distances may become impossible to travel. Given $N$ distances, tell Chef which ones he cannot travel.

-----Input:-----
- The first line will contain a single integer $T$, the number of test cases.
- The first line of each test case will contain two space separated integers - $N$, the number of distances, and $K$, Chef’s step length.
- The second line of each test case will contain $N$ space separated integers, the $i^{th}$ of which represents $D_i$, the distance of the $i^{th}$ path.

-----Output:-----
For each testcase, output a string consisting of $N$ characters. The $i^{th}$ character should be $1$ if the distance is traversable, and $0$ if not.

-----Constraints-----
- $1 \leq T \leq 1000$
- $1 \leq N \leq 1000$
- $1 \leq K \leq 10^9$
- $1 \leq D_i \leq 10^9$

-----Subtasks-----
- 100 points : No additional constraints.

-----Sample Input:-----
1
5 3
12 13 18 20 27216

-----Sample Output:-----
10101

-----Explanation:-----
The first distance can be traversed in $4$ steps.

The second distance cannot be traversed.

The third distance can be traversed in $6$ steps.

The fourth distance cannot be traversed.

The fifth distance can be traversed in $9072$ steps.

见题面

见题面