Problem: The campus has m rooms numbered from 0 to m - 1. Also the x-mouse lives in the campus. The x-mouse is not just a mouse: each second x-mouse moves from room i to the room i ⋅ x mod{m} (in fact, it teleports from one room to another since it doesn't visit any intermediate room). Starting position of the x-mouse is unknown.

You are responsible to catch the x-mouse in the campus, so you are guessing about minimum possible number of traps (one trap in one room) you need to place. You are sure that if the x-mouse enters a trapped room, it immediately gets caught.

And the only observation you made is GCD (x, m) = 1.

Input

The only line contains two integers m and x (2 ≤ m ≤ 10^{14}, 1 ≤ x < m, GCD (x, m) = 1) — the number of rooms and the parameter of x-mouse. 

Output

Print the only integer — minimum number of traps you need to install to catch the x-mouse.

Examples

Input

4 3


Output

3


Input

5 2


Output

2

Note

In the first example you can, for example, put traps in rooms 0, 2, 3. If the x-mouse starts in one of this rooms it will be caught immediately. If x-mouse starts in the 1-st rooms then it will move to the room 3, where it will be caught.

In the second example you can put one trap in room 0 and one trap in any other room since x-mouse will visit all rooms 1..m-1 if it will start in any of these rooms.

Solution (in CPP):

Solution:
#include <bits/stdc++.h>
using namespace std;
const int N = 2e6 + 5;
long long mul_mod(long long a, long long b, long long mod) {
  long long q = (long double)a * (long double)b / (long double)mod;
  return (a * b - q * mod + 5 * mod) % mod;
}
long long bin_pow(long long a, long long n, long long m) {
  long long res = 1;
  a %= m;
  while (n) {
    if (n & 1) res = mul_mod(res, a, m);
    a = mul_mod(a, a, m);
    n >>= 1;
  }
  return res;
}
long long m, x;
vector<pair<long long, int> > divisiorM;
vector<pair<long long, int> > divisiorEylerM;
long long eylerFunction(long long val) {
  for (auto it : divisiorM) {
    if (val % it.first == 0) {
      val -= val / it.first;
    }
  }
  return val;
}
vector<pair<long long, int> > divisiors(long long val) {
  vector<pair<long long, int> > divisior;
  for (long long i = 2; i * i <= val; ++i) {
    if (val % i == 0) {
      int cnt = 0;
      while (val % i == 0) {
        val /= i;
      }
      cnt++;
      divisior.push_back({i, cnt});
    }
  }
  if (val > 1) divisior.push_back({val, 1});
  return divisior;
}
long long eylerM;
long long fndMinimumDegree(long long val) {
  long long d = eylerM;
  for (auto it : divisiorEylerM) {
    auto div = it.first;
    while (d % div == 0 && (bin_pow(x, d / div, val) - 1) % val == 0) {
      d /= div;
    }
  }
  return d;
}
long long fndAns(long long n) {
  long long ans = eylerFunction(m / n);
  ans /= fndMinimumDegree(m / n);
  return ans;
}
int main() {
  ios_base::sync_with_stdio(false);
  cin >> m >> x;
  divisiorM = divisiors(m);
  eylerM = eylerFunction(m);
  divisiorEylerM = divisiors(eylerM);
  long long ans = 0;
  for (long long i = 1; i * i <= m; ++i) {
    if (m % i == 0) {
      ans += fndAns(i);
      if (i * i != m) ans += fndAns(m / i);
    }
  }
  cout << ans << endl;
  return 0;
}