hdu1796容斥原理

题目大意：给定n和一个大小为m的集合，集合元素为非负整数。为1…n内能被集合里任意一个数整除的数字个数。n<=2^31,m<=10

import java.io.BufferedInputStream;
import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStream;
import java.io.InputStreamReader;
import java.io.OutputStreamWriter;
import java.io.PrintWriter;
import java.io.StreamTokenizer;
import java.math.BigInteger;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.Collection;
import java.util.Collections;
import java.util.Comparator;
import java.util.HashMap;
import java.util.HashSet;
import java.util.Iterator;
import java.util.LinkedList;
import java.util.NavigableSet;
import java.util.PriorityQueue;
import java.util.Queue;
import java.util.Scanner;
import java.util.Set;
import java.util.SortedSet;
import java.util.Stack;
import java.util.StringTokenizer;
import java.util.TreeSet;

public class Main {

    public static void main(String[] args) throws IOException{
           StreamTokenizer cin = new StreamTokenizer(new BufferedInputStream(System.in)); 
           InputReader in = new InputReader(System.in)  ;
           PrintWriter out = new PrintWriter(System.out) ;

           while(cin.nextToken() != cin.TT_EOF){
                long n = (long) cin.nval ; 
                n-- ;
                cin.nextToken() ; int  m = (int) cin.nval ;
                new Task().solve(n , m , cin, out); 
           }

           out.flush() ; 


    }


}

class  Task{

       long gcd(long x , long y){
            return y == 0 ? x : gcd(y , x % y) ;
       }

       long lcm(long x , long y){
            return x / gcd(x , y) * y ;
       }

       public void solve(long n , int m ,StreamTokenizer cin , PrintWriter out) throws IOException{
              ArrayList<Long> num = new ArrayList<Long>()  ;
              for(int i = 0 ; i < m ; i++){
                  cin.nextToken(); long c = (long)cin.nval ;
                  if(c != 0) num.add(c) ;
              }


              m = num.size() ;
              int limit = 1<<m ;
              long sum = 0 ;

              for(int i = 1 ; i < limit ; i++){
                   int k = 0 ;
                   long val = 1 ;
                   for(int j = 0 ; j < m ; j++){
                        if((i & (1<<j)) > 0){
                             k++ ;
                             val = lcm(val , num.get(j)) ;
                        }          
                   }

                   if((k&1) > 0) sum += n / val ;
                   else sum -= n / val ;
              }

              out.println(sum);// out.flush(); 
       }

}

class   InputReader{
        public BufferedReader  reader;
        public StringTokenizer  tokenizer;

        public InputReader(InputStream stream){
                    reader = new BufferedReader(new InputStreamReader(stream), 32768) ;
                    tokenizer = null ;
        }

        public String next(){
                    while(tokenizer == null || ! tokenizer.hasMoreTokens()){
                        try{
                                tokenizer = new StringTokenizer(reader.readLine());
                        }catch (IOException e) {
                                throw new RuntimeException(e);
                        }
                    }
                    return tokenizer.nextToken();  
        }

        public int  nextInt(){
                    return Integer.parseInt(next());
        }

        public long nextLong(){
                    return Long.parseLong(next());
        }

        public double nextDouble(){
                    return  Double.parseDouble(next());
        }

}