- Prepare
- Mathematics
- Number Theory
- Constructing a Number

# Constructing a Number

# Constructing a Number

Manipulating numbers is at the core of a programmer's job. To test how well you know their properties, you are asked to solve the following problem.

You are given non-negative integers , , ..., . You want to know whether it's possible to construct a new integer using all the digits of these numbers such that it would be divisible by . You can reorder the digits as you want. The resulting number can contain leading zeros.

For example, consider the numbers from which you have to construct a new integer as described above. Numerous arrangements of digits are possible; but we have illustrated one below.

Complete the function `canConstruct`

which takes an integer array as input and return "`Yes`

" or "`No`

" based on whether or not the required integer can be formed.

**Input Format**

The first line contains a single integer denoting the number of queries. The following lines describe the queries.

Each query is described in two lines. The first of these lines contains a single integer . The second contains space-separated integers , , ..., .

**Constraints**

**Subtasks**

For 33.33% of the total score:

**Output Format**

For each query, print a single line containing "`Yes`

" if it's possible to construct such integer and "`No`

" otherwise.

**Sample Input 0**

```
3
1
9
3
40 50 90
2
1 4
```

**Sample Output 0**

```
Yes
Yes
No
```

**Explanation 0**

In the first example, is divisible by , so the answer is "`Yes`

".

In the second example you can construct the number which is divisible by , so the answer is "`Yes`

". Note that there may be other numbers you can construct, some of which are shown in the challenge statement.

In the third example, the only possible numbers are and , but both of them are not divisible by , so the answer is "`No`

".