CF1015D.Walking Between Houses

There are $n$ houses in a row. They are numbered from $1$ to $n$ in order from left to right. Initially you are in the house $1$.

You have to perform $k$ moves to other house. In one move you go from your current house to some other house. You can't stay where you are (i.e., in each move the new house differs from the current house). If you go from the house $x$ to the house $y$, the total distance you walked increases by $|x-y|$ units of distance, where $|a|$ is the absolute value of $a$. It is possible to visit the same house multiple times (but you can't visit the same house in sequence).

Your goal is to walk exactly $s$ units of distance in total.

If it is impossible, print "NO". Otherwise print "YES" and any of the ways to do that. Remember that you should do exactly $k$ moves.

一行中有 $n$ 座房子，从左到右依次编号为 $1$ 到 $n$。初始时你位于第 $1$ 号房子。

你需要恰好执行 $k$ 次移动，每次移动都必须前往另一座房子（即不能停留在当前房子，每次移动后所在房子编号必须与移动前不同）。若你从房子 $x$ 移动到房子 $y$，则总行走距离增加 $|x-y|$ 个单位长度，其中 $|a|$ 表示 $a$ 的绝对值。允许重复访问同一座房子（但不允许连续两次停留在同一座房子）。

你的目标是使总行走距离恰好为 $s$ 个单位长度。

若无法实现，输出 "NO"；否则输出 "YES"，并给出任意一种满足条件的移动方案。注意：你必须恰好执行 $k$ 次移动。

The first line of the input contains three integers $n$, $k$, $s$ ($2 \le n \le 10^9$, $1 \le k \le 2 \cdot 10^5$, $1 \le s \le 10^{18}$) — the number of houses, the number of moves and the total distance you want to walk.

输入的第一行包含三个整数 $n$、$k$、$s$（$2 \le n \le 10^9$，$1 \le k \le 2 \cdot 10^5$，$1 \le s \le 10^{18}$）——分别表示房屋数量、移动次数以及你希望行走的总距离。

If you cannot perform $k$ moves with total walking distance equal to $s$, print "NO".

Otherwise print "YES" on the first line and then print exactly $k$ integers $h_i$ ($1 \le h_i \le n$) on the second line, where $h_i$ is the house you visit on the $i$-th move.

For each $j$ from $1$ to $k-1$ the following condition should be satisfied: $h_j \ne h_{j + 1}$. Also $h_1 \ne 1$ should be satisfied.

如果无法通过 $k$ 次移动使得总行走距离恰好等于 $s$，则输出 "NO"。

否则，在第一行输出 "YES"，并在第二行输出恰好 $k$ 个整数 $h_i$（$1 \le h_i \le n$），其中 $h_i$ 表示第 $i$ 次移动所访问的房子编号。

对于每个从 $1$ 到 $k-1$ 的 $j$，需满足条件：$h_j \ne h_{j + 1}$。此外，还需满足 $h_1 \ne 1$。