The Last of Us

Your friend Herok loves Math so much. He is going to write some numbers on some paper. As he is your best friend you know how he writes the numbers one after another. For the first number, he writes a random integer $p$, between 1 and $n$ inclusive. After that for the next numbers, he will choose a number $q(1 \leq q \leq n)$ such that either $q$ is divisible by the last number he wrote or the last number wrote is divisible by $q$. For example, let $n=10$ and the last number he wrote was $4$, the possible values of $q$ for the next number are $1, 2, 4, 8$. Among all the possible options of $q$ he chooses randomly. He has written $k$ numbers on some secret paper. You are wondering about what’s the last number he wrote on the paper.

Given the values of $n$ and $k$, for each integer from $1$ to $n$, you have to print the probability that he wrote that number as the last number. Print the probability modulo $10^9+7$.

Input

The input consists of 2 space-separated integers $n, k (1 \leq n,k \leq 5000)$ described above.

Output

Print $n$ space-separated integers in a line, for each integer from $1$ to $n$, the probability that Herok wrote that number as the last number. Print the probability modulo $10^9+7$.

Samples

Input	Output
2 3	500000004 500000004

Input	Output
1 3	1