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.