Practice on Toph

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Life of Phi II

Limits 1s, 512 MB

You will be given two integers n and m where GCD(n, m) = 1. You have to tell that how many numbers are there from 1 to m×n that is co-prime to:

  1. n but not with m,
  2. m but not with n, and
  3. both m and n.

Input

The only line of input contains two integers n and m (1 ≤ n, m ≤ 106). It is guaranteed that n and m are relatively prime.

Output

Output three numbers as mentioned above.

Samples

InputOutput
2 3
1 2 2
InputOutput
5 7
4 6 24

Please note that for relatively prime numbers n and m, Phi(n×m) = Phi(n)×Phi(m).

Discussion