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RATF - Roads Around The Farm

Aram Shatakhtsyan, 2007

Farmer John's cows have taken an interest in exploring the territory around the farm. Initially, all N (1 <= N <= 1,000,000,000) cows commence traveling down a road in one big group. Upon encountering a fork in the road, the group sometimes chooses to break into two smaller (nonempty) groups with each group continuing down one of the roads. When one of those groups arrives at another fork, it might split again, and so on.

The cows have crafted a peculiar way of splitting: if they can split into two groups such that the sizes of the groups differ by exactly K (1 <= K <= 1000), then they will split in that way; otherwise, they stop exploring and just start grazing peacefully.

Assuming that there will always be new forks in the road, compute the final number of groups of peacefully grazing cows.

Input

  • Line 1: Two space-separated integers: N and K

Output

  • Line 1: A single integer representing the number of groups of grazing cows

Example

Input:
6 2

There are 6 cows and the difference in group sizes is 2.

Output:
3

There are 3 final groups (with 2, 1, and 3 cows in them).

   6
  / \
 2   4
    / \
   1   3

Adicionado por:Wanderley Guimarăes
Data:2008-06-06
Tempo limite:0.100s
Tamanho do fonte:50000B
Memory limit:1536MB
Cluster: Cube (Intel G860)
Linguagem permitida:ADA95 DOC ASM32 BASH BF C CSHARP CPP C99 CLPS LISP sbcl LISP clisp D FORTRAN HASK ICON ICK JAVA LUA NEM NICE OCAML PAS-GPC PAS-FPC PDF PERL PHP PIKE PS PRLG-swi PYTHON RUBY SCM guile SCM qobi ST TEXT WHITESPACE
Origem:USACO Open 2008 - Silver

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