AT_abc473_d.Coefficient Stair

Output all length-$N$ sequences $A=(A _ 1,A _ 2,\ldots,A _ N)$ consisting of non-negative integers that satisfy $\displaystyle\sum _ {i=1} ^ Ni\times A _ i=K$, in lexicographic order from smallest to largest.

Here, you will only receive inputs such that the number of sequences satisfying the condition is at most $3\times10 ^ 5$.

What is lexicographic order for sequences?

A sequence $S = (S_1,S_2,\ldots,S_{|S|})$ is said to be lexicographically smaller than a sequence $T = (T_1,T_2,\ldots,T_{|T|})$ if either 1. or 2. below holds. Here, $|S|$ and $|T|$ denote the lengths of $S$ and $T$, respectively.

1. $|S| \lt |T|$ and $(S_1,S_2,\ldots,S_{|S|}) = (T_1,T_2,\ldots,T_{|S|})$.
2. There exists an integer $1 \leq i \leq \min\lbrace |S|, |T| \rbrace$ such that both of the following hold.
   • $(S_1,S_2,\ldots,S_{i-1}) = (T_1,T_2,\ldots,T_{i-1})$
   • $S_i$ is (numerically) smaller than $T_i$.

输出所有长度为 $N$ 的非负整数序列 $A=(A _ 1,A _ 2,\ldots,A _ N)$，满足 $\displaystyle\sum _ {i=1} ^ Ni\times A _ i=K$，并按字典序从小到大排列。

本题保证输入数据满足：满足条件的序列总数不超过 $3\times10 ^ 5$。

什么是序列的字典序？

序列 $S = (S_1,S_2,\ldots,S_{|S|})$ 被称为字典序小于序列 $T = (T_1,T_2,\ldots,T_{|T|})$，当且仅当以下条件 1 或 2 成立。其中，$|S|$ 和 $|T|$ 分别表示序列 $S$ 和 $T$ 的长度。

1. $|S| \lt |T|$，且 $(S_1,S_2,\ldots,S_{|S|}) = (T_1,T_2,\ldots,T_{|S|})$。
2. 存在整数 $1 \leq i \leq \min\lbrace |S|, |T| \rbrace$，使得以下两个条件同时成立：
   • $(S_1,S_2,\ldots,S_{i-1}) = (T_1,T_2,\ldots,T_{i-1})$；
   • $S_i$（数值上）小于 $T_i$。

The input is given from Standard Input in the following format:

$N$ $K$

输入从标准输入中以如下格式给出：

$N$ $K$

Let $q$ be the number of sequences of non-negative integers satisfying the condition; output them over $q$ lines. Each line should contain the elements of a sequence of non-negative integers satisfying the condition, in order, separated by spaces. For every sequence, all sequences outputted before it must be lexicographically smaller than it.

设 $q$ 为满足该条件的非负整数序列的个数；将这些序列按行输出，共 $q$ 行。每行应按顺序包含一个满足条件的非负整数序列的各元素，元素之间用空格分隔。对于任意一个序列，所有在它之前输出的序列都必须字典序小于它。

Sample 1 Explanation:
For example, for the sequence $(0,1,2)$ we have $0\times1+1\times2+2\times3=0+2+6=8$, so it satisfies the condition. There is no sequence satisfying the condition that is lexicographically smaller than this one, so output 0 1 2 on the first line.

Including $(0,1,2)$, ten sequences satisfy the condition. Output these in lexicographic order from smallest to largest.

Constraints

• $1\le N\le 10$
• $1\le K\le 2\times10 ^ 5$
• The number of sequences satisfying the condition is at most $3\times10 ^ 5$.
• All input values are integers.

样例 1 解释：
例如，对于序列 $(0,1,2)$，有 $0\times1+1\times2+2\times3=0+2+6=8$，因此它满足条件。不存在字典序比该序列更小且满足条件的序列，故第一行输出 0 1 2。

包括 $(0,1,2)$ 在内，共有十个序列满足条件。请将这些序列按字典序从小到大输出。

限制条件

• $1\le N\le 10$
• $1\le K\le 2\times10 ^ 5$
• 满足条件的序列个数至多为 $3\times10 ^ 5$。
• 所有输入值均为整数。