CF1157D.N Problems During K Days

Polycarp has to solve exactly $n$ problems to improve his programming skill before an important programming competition. But this competition will be held very soon, most precisely, it will start in $k$ days. It means that Polycarp has exactly $k$ days for training!

Polycarp doesn't want to procrastinate, so he wants to solve at least one problem during each of $k$ days. He also doesn't want to overwork, so if he solves $x$ problems during some day, he should solve no more than $2x$ problems during the next day. And, at last, he wants to improve his skill, so if he solves $x$ problems during some day, he should solve at least $x+1$ problem during the next day.

More formally: let $[a_1, a_2, \dots, a_k]$ be the array of numbers of problems solved by Polycarp. The $i$-th element of this array is the number of problems Polycarp solves during the $i$-th day of his training. Then the following conditions must be satisfied:

• sum of all $a_i$ for $i$ from $1$ to $k$ should be $n$;
• $a_i$ should be greater than zero for each $i$ from $1$ to $k$;
• the condition $a_i \lt a_{i + 1} \le 2 a_i$ should be satisfied for each $i$ from $1$ to $k-1$.

Your problem is to find any array $a$ of length $k$ satisfying the conditions above or say that it is impossible to do it.

Polycarp 需要在一场重要的编程竞赛前恰好解决 $n$ 道题目，以提升自己的编程能力。而这场竞赛很快就要举行，确切地说，将在 $k$ 天后开始。这意味着 Polycarp 恰好有 $k$ 天时间进行训练！

Polycarp 不想拖延，因此他希望在 $k$ 天中的每一天至少解决一道题。他也不想过度劳累，因此若某天他解决了 $x$ 道题，则下一天解决的题目数量不能超过 $2x$ 道。最后，为了切实提升能力，若某天他解决了 $x$ 道题，则下一天解决的题目数量至少应为 $x+1$ 道。

更形式化地：设 $[a_1, a_2, \dots, a_k]$ 为 Polycarp 每天所解题数构成的数组，其中第 $i$ 个元素 $a_i$ 表示他在训练第 $i$ 天所解决的题目数量。则该数组必须满足以下条件：

• 所有 $a_i$（其中 $i$ 从 $1$ 到 $k$）之和应等于 $n$；
• 对每个 $i$（从 $1$ 到 $k$），$a_i > 0$；
• 对每个 $i$（从 $1$ 到 $k-1$），需满足条件 $a_i < a_{i + 1} \le 2 a_i$。

你的任务是：找出任意一个长度为 $k$ 的满足上述条件的数组 $a$；若不存在这样的数组，则判定其不可能。

The first line of the input contains two integers $n$ and $k$ ($1 \le n \le 10^9, 1 \le k \le 10^5$) — the number of problems Polycarp wants to solve and the number of days Polycarp wants to train.

输入的第一行包含两个整数 $n$ 和 $k$（$1 \le n \le 10^9$，$1 \le k \le 10^5$）—— 分别表示 Polycarp 想要解决的问题数量以及他想要训练的天数。

If it is impossible to find any array $a$ of length $k$ satisfying Polycarp's rules of training, print "NO" in the first line.

Otherwise print "YES" in the first line, then print $k$ integers $a_1, a_2, \dots, a_k$ in the second line, where $a_i$ should be the number of problems Polycarp should solve during the $i$-th day. If there are multiple answers, you can print any.

如果无法找到满足 Polycarp 训练规则的长度为 $k$ 的数组 $a$，则在第一行输出 "NO"。

否则，在第一行输出 "YES"，在第二行输出 $k$ 个整数 $a_1, a_2, \dots, a_k$，其中 $a_i$ 表示 Polycarp 在第 $i$ 天应解决的问题数量。若存在多个答案，输出任意一个即可。