The $h$-index of an author is the largest $h$ where he has at least $h$ papers with citations not less than $h$.
Bobo has no papers and he is going to publish some subsequently.
If he works on a paper for $x$ hours, the paper will get $(a \cdot x)$ citations, where $a$ is a known constant.
It's clear that $x$ should be a positive integer.
There is also a trick -- one can cite his own papers published earlier.
Given Bobo has $n$ working hours, find the maximum $h$-index of him.
The input consists of several test cases and is terminated by end-of-file.
Each test case contains two integers $n$ and $a$.
For each test case, print an integer which denotes the maximum $h$-index.
## Constraint
* $1 \leq n \leq 10^9$
* $0 \leq a \leq n$
* The number of test cases does not exceed $10^4$.
3 0
3 1
1000000000 1000000000