2020杭电多校第七场1009（Increasing and Decreasing）

题目链接：http://acm.hdu.edu.cn/showproblem.php?pid=6852

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≤T≤100), indicating the number of test cases.
Each test case contains one line, which contains three integers n,x,y(1≤n≤1e5,1≤x,y≤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

 

题意：给出字典序最小的，长度为n的，最长上升子序列为x，最长下降子序列为y的序列

题解：n必须大于x*y+1并且n要小于x+y-1，之后将序列分成a块，设第i块长度为xi，则x1+x2+...+xa=n且xa=b，1<=xi<=b，并逐个枚举