U Cluj

Task

After RANDy sold U Cluj for their terrible performance last season, he is now wondering what to invest the money into. After hearing about the prestigious fireman olympiad, he had a marvelous idea: a fireman department business.

You are very eager to become a fireman, so you go to an interview and got the following question: "You are given an integer $N$ and an integer $P$. For every $K$ from $1$ to $P$, compute the number of ways you can write $N$ as a sum of $K$ numbers which can be written as $2^x - 1$ for some integer $x \geq 1$, modulo $10^9 + 7$".

RANDy promises you that if you solve this problem, he will give you his best hose and put it on your shoulder, thus making you the most prolific fireman the world has ever seen, and you can be sure you'll get the gold medal at the fireman olympics!

Input data

The first line of the input contains two integers, $N$ and $P$.

Output data

The first line of the output contains $P$ integers, separated by spaces. The $K^{th}$ integer represents the number of ways you can write $N$ as a sum of $K$ numbers which can be written as $2^x - 1$ for some integer $x \geq 1$, modulo $10^9 + 7$.

Constraints and clarifications

• $1 \leq N \leq 10^{18}$.
• $1 \leq P \leq 500$.

Example 1

stdin

4 2

stdout

0 1

Explanation

For $K = 1$, there exists no solution.
For $K = 2$, $4 = 3 + 1$.

Example 2

stdin

14 4

stdout

0 1 0 1

Explanation

For $K = 1$, there exists no solution.
For $K = 2$, $14 = 7 + 7$.
For $K = 3$, there exists no solution.
For $K = 4$, $14 = 7 + 3 + 3 + 1$.

Example 3

stdin

9 3

stdout

0 0 2

Explanation

For $K = 1$, there exists no solution.
For $K = 2$, there exists no solution.
For $K = 3$, $9 = 3 + 3 + 3$ and $9 = 7 + 1 + 1$.