(AcWing) a number that can be divisible evenly

Given an integer n and m different prime numbers p1,p2,...,pm.

Please find out how many integers from 1∼n are divisible by at least one of p1,p2,…,pm.

input format

The first line contains the integers n and m.

The second row contains m prime numbers.

output format

Output an integer representing the number of integers that satisfy the condition.

data range

1≤m≤16,
1≤n,pi≤10^9,

Input sample:

10 2
2 3

Sample output:

7

#include<iostream>
#include<algorithm>
using namespace std;
typedef long long LL;
const int N = 20;
int p[N];
int n,m;
int main()
{
    cin>>n>>m;
    for(int i=0;i<m;i++) cin>>p[i];
    
    int res = 0;
    
    for(int i=1;i<(1<<m);i++){ //(1>>m)相当于2^m
        int t = 1,s = 0;       //t表示当前选取的集合的乘积，s表示已经选取的集合
        for(int j=0;j<m;j++){  //j<m表示的是最大被选取的集合数为m
            if(i>>j&1){        //例如5：101，表示集合1和集合3已被选取
                if((LL)t*p[j]>n){
                    t = -1;
                    break;
                }
                t*=p[j];//更新集合的乘积
                s++;    //更新被选取的集合
            }
        }
        
        if(t!=-1){//韦恩图的奇加偶减的规律
            if(s%2) res+=(n/t);
            else res-=(n/t);
        }
    }
    
    cout<<res<<endl;
    return 0;
}