Neko and function
Time Limit: 15000/10000 MS (Java/Others) Memory Limit: 524288/524288 K (Java/Others)Total Submission(s): 45 Accepted Submission(s): 2
Problem Description
Neko learnt a new function $f(n,k)$ today.
$f(n,k)$ is the number of way to select $k$ numbers $a_{i},(a_{i} > 1)$ and $\prod_{i=1}^{k} a_{i} = n$
Neko thinks this function is too easy, so she want to know $\sum_{i = 1} ^ {n} f(i,k)$
Calculate the sum after mod $10^9+7$.
Note that if $n = 6$, $6 = 2 \times 3$ and $n = 3 \times 2$ are different way.
$f(n,k)$ is the number of way to select $k$ numbers $a_{i},(a_{i} > 1)$ and $\prod_{i=1}^{k} a_{i} = n$
Neko thinks this function is too easy, so she want to know $\sum_{i = 1} ^ {n} f(i,k)$
Calculate the sum after mod $10^9+7$.
Note that if $n = 6$, $6 = 2 \times 3$ and $n = 3 \times 2$ are different way.
Input
Input one line contains two integers $n, k(1 \leq n \leq 2^{30}, 1 \leq k \leq 30)$.
Output
Output the number of way for selecting nodes.
Sample Input
10 2
Sample Output
8