CodeForces 275C k-Multiple Free Set

C. k-Multiple Free Set

time limit per test

2 seconds

memory limit per test

256 megabytes

input

standard input

output

standard output

A k-multiple free set is a set of integers where there is no pair of integers where one is equal to another integer multiplied by k. That is, there are no two integers x and y (x < y) from the set, such that y = x·k.

You're given a set of n distinct positive integers. Your task is to find the size of it's largest k-multiple free subset.

Input

The first line of the input contains two integers n and k (1 ≤ n ≤ 10⁵, 1 ≤ k ≤ 10⁹). The next line contains a list of n distinct positive integers a₁, a₂, ..., a_n (1 ≤ a_i ≤ 10⁹).

All the numbers in the lines are separated by single spaces.

Output

On the only line of the output print the size of the largest k-multiple free subset of {a₁, a₂, ..., a_n}.

Sample test(s)

input

6 22 3 6 5 4 10

output

3

Note

In the sample input one of the possible maximum 2-multiple free subsets is {4, 5, 6}.

二分查找

（写得有点丑！）

#include<stdio.h>#include<algorithm>using namespace std;long long a[100010],vis[100010];long long ans,n,k;void search(long long x){  long long l=1,r=n;  while(l<r)  {    if(a[l]==x)    {      if(!vis[l])      {        vis[l]=1;        ans--;        break;      }    }    if(a[r]==x)    {      if(!vis[r])      {        vis[r]=1;        ans--;        break;      }    }    long long mid=(l+r)/2;    if(a[mid]>x)    {      r=mid;    }    else if(a[mid]<x)    {      l=mid;    }    else if(a[mid]==x)    {      if(!vis[mid])      {        vis[mid]=1;        ans--;        break;      }    }    if(l+1==r)break;  }}int main(){  scanf("%I64d%I64d",&n,&k);  for(long long i=1;i<=n;i++)  {    scanf("%I64d",&a[i]);  }  if(k==1&&n>1)  {    printf("%I64d\n",n);    return 0;  }  sort(a+1,a+n+1);  for(long long i=1;i<=n;i++)vis[i]=0;  ans=n;  for(long long i=1;i<=n;i++)  {    if(!vis[i])search(a[i]*k);  }  printf("%I64d\n",ans);  return 0;}