B. Higher h-index

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·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.

Input

The input consists of several test cases and is terminated by end-of-ﬁle.
Each test case contains two integers n and a.

Output

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

Constraint

• 1≤ n ≤109
• 0≤ a ≤ n
• The number of test cases does not exceed 104.

Sample Input

3 0
3 1
1000000000 1000000000

Sample Output

1
2
1000000000

Note

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.

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