SPOJ Problem Set (classical) 7186. Counting Pascal Problem code: COUNTPAS

Pascal’s triangle is a common figure in combinatorics. It is a triangle formed by rows of integers.
The top row contains a single 1. Each new row has one element more than the previous one
and is formed as follows: the leftmost and rightmost values are 1, while each of the other values
is the sum of the two values above it. Here we depict the first 7 rows of the triangle.

						1
					1		1
				1		2		1
			1		3		3		1
		1		4		6		4		1
	1		5		10		10		5		1
1		6		15		20		15		6		1

Pascal’s triangle is infinite, of course, and contains the value 1 an unbounded number of times.
However, any other value appears a finite number of times in the triangle. In this problem you
are given an integer K ≥ 2. Your task is to calculate the number of values in the triangle that
are different from 1 and less than or equal to K.

Input

The input contains several test cases. Each test case is described in a single line that contains
an integer K (2 ≤ K ≤ 10⁹ ). The last line of the input contains a single −1 and should not be
processed as a test case.

Output

For each test case output a single line with an integer indicating the number of values in Pascal’s
triangle that are different from 1 and less than or equal to K.

Example

Input:
2
6
-1

Output:
1
10

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Added by:	Pablo Ariel Heiber
Date:	2010-08-19
Time limit:	6s
Source limit:	50000B
Languages:	All except: PERL 6
Resource:	FCEyN UBA ICPC Selection 2008