Problem Statement

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. $|S| \lt |T|$ and $(S_1,S_2,\ldots,S_{|S|}) = (T_1,T_2,\ldots,T_{|S|})$. 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 $T_i$.

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.

Input

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

N K

Output

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 outputed before it must be lexicographically smaller than it.