Increasing and Decreasing

Problem Description

Notice：Don't output extra spaces at the end of one line. Given $n, x, y$, please construct a permutation of length $n$, satisfying that:

• The length of LIS(Longest Increasing Subsequence) is equal to $x$.
• The length of LDS(Longest Decreasing Subsequence) is equal to $y$. If there are multiple possible permutations satisfying all the conditions, print the lexicographically minimum one.

Input

The first line contains an integer $T(1 \leq T \leq 100)$, indicating the number of test cases. Each test case contains one line, which contains three integers $n, x, y(1 \leq n \leq 10^5, 1 \leq x, y \leq n)$.

Output

For each test case, the first line contains YES'' or NO'', indicating if the answer exists. If the answer exists, output another line which contains $n$ integers, indicating the permutation.

Sample Input

4
10 1 10
10 10 1
10 5 5
10 8 8

Sample Output

YES
10 9 8 7 6 5 4 3 2 1
YES
1 2 3 4 5 6 7 8 9 10
YES
1 2 3 5 4 10 9 8 7 6
NO

Source

2020 Multi-University Training Contest 7