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Time limit 3000/4000/4000/4000 ms. Memory limit 65000/65000/65000/65000 Kb.
: , .

You are given an infinite sequence of integers:
A0 = 0
Ai = ( Ai-1 + q ) mod p, for i > 0

Where p is a prime number, a mod p is reminder of division a by p.

Your task is to count how many integers in the range [0..p-1] are not included in this sequence. Notice that p can be very large.

Input
The first line contains one prime integer p.
The second line contains one integer q. (0 ≤ qp ≤ 10100).

Output
Output a single number the answer for the problem.

Input 1 Output 1
5
1
0

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