CF1305E.Kuroni and the Score Distribution

Kuroni is the coordinator of the next Mathforces round written by the "Proof by AC" team. All the preparation has been done, and he is discussing with the team about the score distribution for the round.

The round consists of $n$ problems, numbered from $1$ to $n$. The problems are ordered in increasing order of difficulty, no two problems have the same difficulty. A score distribution for the round can be denoted by an array $a_1, a_2, \dots, a_n$, where $a_i$ is the score of $i$-th problem.

Kuroni thinks that the score distribution should satisfy the following requirements:

• The score of each problem should be a positive integer not exceeding $10^9$.
• A harder problem should grant a strictly higher score than an easier problem. In other words, $1 \leq a_1 \lt a_2 \lt \dots \lt a_n \leq 10^9$.
• The balance of the score distribution, defined as the number of triples $(i, j, k)$ such that $1 \leq i \lt j \lt k \leq n$ and $a_i + a_j = a_k$, should be exactly $m$.

Help the team find a score distribution that satisfies Kuroni's requirement. In case such a score distribution does not exist, output $-1$.

Kuroni 是由 “Proof by AC” 团队编写的下一届 Mathforces 比赛的负责人。所有准备工作均已就绪，他正与团队讨论本次比赛的分值分布方案。

本场竞赛共包含 $n$ 道题目，编号为 $1$ 到 $n$。题目按难度递增顺序排列，任意两道题的难度均不相同。一轮比赛的分值分布可用一个数组 $a_1, a_2, \dots, a_n$ 表示，其中 $a_i$ 表示第 $i$ 道题的分值。

Kuroni 认为分值分布应满足以下要求：

• 每道题的分值必须是不超过 $10^9$ 的正整数；
• 更难的题目分值必须严格高于更简单的题目，即满足 $1 \leq a_1 \lt a_2 \lt \dots \lt a_n \leq 10^9$；
• 分值分布的平衡度（balance）定义为满足 $1 \leq i \lt j \lt k \leq n$ 且 $a_i + a_j = a_k$ 的三元组 $(i, j, k)$ 的个数，该平衡度必须恰好等于 $m$。

请帮助该团队找出一个满足 Kuroni 要求的分值分布。若不存在这样的分值分布，则输出 $-1$。

The first and single line contains two integers $n$ and $m$ ($1 \le n \le 5000$, $0 \leq m \leq 10^9$) — the number of problems and the required balance.

第一行且唯一一行包含两个整数 $n$ 和 $m$（$1 \le n \le 5000$，$0 \leq m \leq 10^9$）—— 分别表示题目数量和所需的平衡值。

If there is no solution, print a single integer $-1$.

Otherwise, print a line containing $n$ integers $a_1, a_2, \dots, a_n$, representing a score distribution that satisfies all the requirements. If there are multiple answers, print any of them.

如果无解，输出一个整数 $-1$。

否则，输出一行包含 $n$ 个整数 $a_1, a_2, \dots, a_n$ 的序列，表示一个满足所有要求的得分分布。如果有多个答案，输出任意一个即可。

In the first example, there are $3$ triples $(i, j, k)$ that contribute to the balance of the score distribution.

• $(1, 2, 3)$
• $(1, 3, 4)$
• $(2, 4, 5)$

在第一个例子中，有 $3$ 个三元组 $(i, j, k)$ 对分数分布的平衡性有贡献。

• $(1, 2, 3)$
• $(1, 3, 4)$
• $(2, 4, 5)$