PRoblem Description Given a positive integer N, your task is to calculate the sum of the positive integers less than N which are not coprime to N. A is said to be coprime to B if A, B share no common positive divisors except 1.

Input For each test case, there is a line containing a positive integer N(1 ≤ N ≤ 1000000000). A line containing a single 0 follows the last test case.

Output For each test case, you should print the sum module 1000000007 in a line.

Sample Input 3 4 0

Sample Output 0 2

解題報告

∑gcd(i,n)=1i<ni=n?φ(n)/2 $$/sum_{gcd(i,n)=1}^{i<n}i=n/cdot φ(n)/2$$