codeforces 274A. k-Multiple Free Set【二分】

A. 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, ..., an (1 ≤ ai ≤ 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, ..., an}.

Examples

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}.

#include<iostream>#include<cstdio>#include<cstdlib>#include<cstring>#include<algorithm>#include<cmath>#include<queue>#include<list>#include<vector>using namespace std;const int maxn=100010;bool vis[maxn];long long num[maxn];int main(){    int n;    long long k;    scanf("%d%lld",&n,&k);    for(int i=1;i<=n;++i){        scanf("%lld",&num[i]);    }    sort(num+1,num+n+1);    memset(vis,false,sizeof(vis));    int ans=n;    for(int i=1;i<=n;++i){        if(vis[i])continue;        int left=i+1,right=n;        long long temp = num[i]*k;        while(left<=right){            int mid=(left+right)>>1;            if(num[mid]==temp){                vis[mid]=true;ans--;break;            }            else if(num[mid]>temp){                right=mid-1;            }            else{                left=mid+1;            }        }    }    printf("%d\n",ans);    return 0;}