# Perfect Permutation solution codechef- An index ii in a permutation PP of length NN is said to be good if: PiPi is divisible by ii You are given 22 integers NN and KK. You need to construct a permutation PP of length NN such that exactly KK indices in that permutation are good. If no such permutation exists, output −1−1. If multiple such permutations exist, output any.

## Perfect Permutation solution codechef

An index ii in a permutation PP of length NN is said to be good if:

• PiPi is divisible by ii

You are given 22 integers NN and KK. You need to construct a permutation PP of length NN such that exactly KK indices in that permutation are good.

If no such permutation exists, output 1−1.

If multiple such permutations exist, output any.

### Input Format

• The first line contains a single integer TT – the number of test cases. Then the test cases follow.
• The first and only line of each test case contains two integers NN and KK – the length of the permutation to be constructed and the number of good indices.

### Output Format

For each test case, output any permutation satisfying the given condition.

### Constraints

• 1T10001≤T≤1000
• 1N1051≤N≤105
• 1KN1≤K≤N
• Sum of NN over all testcases does not exceed 21052⋅105

### Sample Input 1

2
1 1
6 2


### Sample Output 1

1
4 5 6 1 2 3


### Explanation

Test case-1: In [1][1]P1=1P1=1 is divisible by 11. Therefore it is a valid permutation having 11 good index.

Test case-2: In [4,5,6,1,2,3][4,5,6,1,2,3]P1=4P1=4 is divisible by 11 and P3=6P3=6 is divisible by 33. Therefore it is a valid permutation having 22 good indices.