Happy 2006

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M - Happy 2006

Time Limit:3000MS Memory Limit:65536KB 64bit IO Format:%I64d & %I64u

Submit Status

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

只能说很水的一道题，当时考虑的时候忘记考虑超过2006的情况，一直以为后面的会比前面的小，

考虑到这个情况也应该注意不要超时，如果gcd（a,i）==1那么gcd（a*t+i,i）==1。这样会

大大节约时间，看到一个题目，首先想到的与之相关的算法。而不是耍聪明，自以为.

这个题目就是容斥原理的运用。

#include<stdio.h>__int64 s[1001000];long f(long  a,long  b){    if(b==0)    return a;    return  f(b,a%b);}int main(){   __int64 m,n;    __int64 i;    while(~scanf("%I64d%I64d",&m,&n))    {       __int64 t=0;        for(i=1;i<=m;i++)        {            if(f(m,i)==1)            s[t++]=i;        }        __int64 sum=n/t*m+s[n%t-1];        __int64 tun=(n/t-1)*m+s[t-1];        if(n%t)        printf("%I64d\n",sum);        else        printf("%I64d\n",tun);    }    return 0;}

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