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 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.

输入描述:

The input consists of several test cases and is terminated by end-of-file.
Each test case contains two integers n and a.
* 
* 
* The number of test cases does not exceed .

输出描述:

For each test case, print an integer which denotes the maximum h-index.

3 0
3 1
1000000000 1000000000

1
2
1000000000

备注:

For the first sample, Bobo can work 3 papers for 1 hour each.
With the trick mentioned, he will get papers with citations 2, 1, 0. Thus, his h-index is 1.
For the second sample, Bobo can work 2 papers for 1 and 2 hours respectively. He will get papers with citations 1 + 1, 2 + 0. Thus, his h-index is 2.