Perfect Permutation

 An index 

i$i$ in a permutation P$P$ of length N$N$ is said to be good if:

• Pi$P_i$ is divisible by i$i$

You are given 2$2$ integers N$N$ and K$K$. You need to construct a permutation P$P$ of length N$N$ such that exactly K$K$ 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 T$T$ - the number of test cases. Then the test cases follow.
• The first and only line of each test case contains two integers N$N$ and K$K$ - 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

• 1≤T≤1000$1\le T\le 1000$
• 1≤N≤105$1\le N\le {10}^5$
• 1≤K≤N$1\le K\le N$
• Sum of N$N$ over all testcases does not exceed 2⋅105$2\cdot {10}^5$

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=1$P_1=1$ is divisible by 1$1$. Therefore it is a valid permutation having 1$1$ good index.

Test case-2: In [4,5,6,1,2,3]$[4,5,6,1,2,3]$, P1=4$P_1=4$ is divisible by 1$1$ and P3=6$P_3=6$ is divisible by 3$3$. Therefore it is a valid permutation having 2$2$ good indices.

• Tweet
• Share
• Share
• Share
• Share

Related Post