#### Periodic Palindrome Construction

Chef recently learned about concept of periodicity of strings. A string is said to have a period **P**, if **P** divides **N** and for each i, the i-th of character of the string is same as **i-P**^{th}character (provided it exists), e.g. “abab” has a period **P = 2**, It also has a period of **P = 4**, but it doesn’t have a period of 1 or 3.

Chef wants to construct a string of length **N** that is a palindrome and has a period **P**. It’s guaranteed that **N** is divisible by **P**. This string can only contain character ‘a’ or ‘b’. Chef doesn’t like the strings that contain all a’s or all b’s.

Given the values of **N, P**, can you construct one such palindromic string that Chef likes? If it’s impossible to do so, output “impossible” (without quotes)

### Input

The first line of the input contains an integer **T** denoting the number of test cases.

The only line of each test case contains two space separated integers **N, P**.

### Output

For each test case, output a single line containing the answer of the problem, i.e. the valid string if it exists otherwise “impossible” (without quotes). If there are more than possible answers, you can output any.

### Constraints

**1 ≤ T ≤ 20****1 ≤ P, N ≤ 10**^{5}

### Subtasks

**Subtask #1**(25 points) :**P = N****Subtask #2**(75 points) : No additional constraints

### Example

Input5 3 1 2 2 3 3 4 4 6 3Outputimpossible impossible aba abba abaaba

### Explanation

**Example 1**: The only strings possible are either aaa or bbb, which Chef doesn’t like. So, the answer is impossible.

**Example 2**: There are four possible strings, aa, ab, ba, bb. Only aa and bb are palindromic, but Chef doesn’t like these strings. Hence, the answer is impossible.

**Example 4**: The string abba is a palindrome and has a period of 4.

**Example 5**: The string abaaba is a palindrome and has a period of length 3.

### Solution

Working on the solution.