Lexicographically Smallest Prime Sequence

You are given several test cases. In each test case, you are given two integers N and M. Your task is to construct a sequence of length N which contains exactly M prime numbers. The sequence should be formed by taking the first M prime numbers followed by N-M copies of the number 1. If it is impossible to create such a sequence (i.e. when M > N), output SEQUENCE IMPOSSIBLE.

Note: The sequence is to be printed as a space-separated string on a single line for each test case.

Examples:

Input:
3
2 1
4 2
5 6
Output:
2 1
2 3 1 1
SEQUENCE IMPOSSIBLE

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Another example:

Input:
3
10 0
10 1
10 10
Output:
1 1 1 1 1 1 1 1 1 1
2 1 1 1 1 1 1 1 1 1
2 3 5 7 11 13 17 19 23 29

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inputFormat

The first line of input contains a single integer T representing the number of test cases. Each of the following T lines contains two space-separated integers N and M, where N is the length of the sequence and M is the required number of prime numbers in the sequence.

outputFormat

For each test case, output a single line containing the lexicographically smallest sequence that satisfies the condition. If no valid sequence exists, output SEQUENCE IMPOSSIBLE.

## sample

3
2 1
4 2
5 6

2 1
2 3 1 1
SEQUENCE IMPOSSIBLE

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