Numbers $*k*$-bonacci ($*k*$ is integer, $*k* > 1$) are a generalization of Fibonacci numbers and are determined as follows:

• $*F*(*k*, *n*) = 0$, for integer $*n*$, $1 ≤ *n* < *k*$;
• $*F*(*k*, *k*) = 1$;
• $*F*(*k*, *n*) = *F*(*k*, *n* - 1) + *F*(*k*, *n* - 2) + ... + *F*(*k*, *n* - *k*)$, for integer $*n*$, $*n* > *k*$.

Note that we determine the $*k*$-bonacci numbers, $*F*(*k*, *n*)$, only for integer values of $*n*$ and $*k*$.

You've got a number $*s*$, represent it as a sum of several (at least two) distinct $*k*$-bonacci numbers.

Input

The first line contains two integers $*s*$ and $*k*$ $(1 ≤ *s*, *k* ≤ 10^{9}; *k* > 1)$.

Output

In the first line print an integer $*m*$ $(*m* ≥ 2)$ that shows how many numbers are in the found representation. In the second line print $*m*$ distinct integers $*a*_{1}, *a*_{2}, ..., *a*_{*m*}$. Each printed integer should be a $*k*$-bonacci number. The sum of printed integers must equal $*s*$.

It is guaranteed that the answer exists. If there are several possible answers, print any of them.