poj2773 Happy 2006

標籤：poj

Happy 2006

Time Limit: 3000MS		Memory Limit: 65536K
Total Submissions: 9987		Accepted: 3434

Description

Two positive integers are said to be relatively prime to each other if the Great Common Divisor (GCD) is 1. For instance, 1, 3, 5, 7, 9...are all relatively prime to 2006. 

Now your job is easy: for the given integer m, find the K-th element which is relatively prime to m when these elements are sorted in ascending order. 

Input

The input contains multiple test cases. For each test case, it contains two integers m (1 <= m <= 1000000), K (1 <= K <= 100000000).

Output

Output the K-th element in a single line.

Sample Input

2006 12006 22006 3

Sample Output

135

解題思路：二分枚舉1-2^64之間的數x，找到1-x與m互質的個數s，這裡利用容斥原理，如果s與k相等，那麼該x即為結果；

參考代碼：

#include <iostream>#include <vector>#include <math.h>using namespace std;typedef long long ll;const int MAX = 1000010;int p[MAX],count;void fun(ll n){ll i;count=0;for (i=2;i*i<=n;i++){if (n%i==0){p[count++]=i;while (n%i==0)n/=i;}}if (n>1)p[count++]=n;}ll solve(ll n,ll r){ll sum=0;for (int i=1;i<(1<<count);i++){ll mult=1,bits=0;for (int j=0;j<count;j++){if (i&(1<<j)){bits++;mult*=p[j];}}ll cur=r/mult;if (bits%2==1)sum+=cur;elsesum-=cur;}return r - sum;}int main(){ll n,m,mid,num;while (cin>>n>>m){fun(n);ll r=0xffffffff,l=1;while (r-l>0){mid=(r+l)/2;num=solve(n,mid);if (num>=m)r=mid;elsel=mid+1;}cout<<l<<endl;}return 0;}

poj2773 Happy 2006