Happy 2006 Euclidean theorem

Happy 2006

Time Limit: 3000MS		Memory Limit: 65536K
Total Submissions: 11956		Accepted: 4224

Description

The positive integers is said to being relatively prime to all other if the great Common Divisor (GCD) is 1. For instance, 1, 3, 5, 7, 9...are-relatively prime to 2006.

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

Input

The input contains multiple test cases. For each test case, it contains 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

Source

Periodic!

#include <iostream>#include<cstdio>#include<algorithm>#include<cstring>using namespaceStd;typedefLong LongLL;#defineMAXN 1000002/*required to find the number gcd (A, b) = gcd (b*t+a,b) with M coprime's K-Large*/LL A[MAXN]; ll GCD (ll A,ll b) {if(b==0)        returnA; returnGCD (b,a%b);}intMain () {LL m,k;  while(SCANF ("%lld%lld", &m,&k)! =EOF) {LL P=0;  for(intI=1; i<=m;i++)        {            if(GCD (i,m) = =1) a[++P] =i; }        if(k%p==0) printf ("%lld\n", (k/p-1) *m+a[p]); Elseprintf ("%lld\n", (k/p) *m+a[k%p]); }}

Happy 2006 Euclidean theorem