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 = 1e5 + 100;
vector<long long> gfactor(long long n) {
  vector<long long> ret;
  for (long long x = 2; x * x <= n; x++) {
    if (n % x == 0) {
      while (n % x == 0) n /= x;
      ret.emplace_back(x);
    }
  }
  if (n != 1) ret.emplace_back(n);
  return ret;
}
vector<pair<long long, long long> > factor(long long n,
                                           const vector<long long> &p) {
  vector<pair<long long, long long> > ret(1, pair<long long, long long>(1, 1));
  for (auto &e : p) {
    int t = 1;
    while (n % e == 0) n /= e, t++;
    int sz = ret.size(), nsz = sz * t;
    ret.resize(nsz);
    for (int i = sz; i < nsz; i++) {
      ret[i].first = ret[i - sz].first * e;
      if (i < sz * 2)
        ret[i].second = ret[i - sz].second * (e - 1);
      else
        ret[i].second = ret[i - sz].second * e;
    }
  }
  sort((ret).begin(), (ret).end());
  return ret;
}
long long power_mod(long long a, long long b, long long m) {
  long long ret = 1;
  for (; b; b >>= 1, a = (__int128)a * a % m)
    if (b & 1) ret = (__int128)ret * a % m;
  return ret;
}
long long cnt = 0;
vector<long long> p1, p2;
long long ord(long long a, long long phi, long long m,
              const vector<long long> &p) {
  auto _phi = factor(phi, p);
  cnt += _phi.size();
  long long ret = phi;
  for (auto &e : _phi) {
    if (power_mod(a, e.first, m) == 1) {
      ret = e.first;
      break;
    }
  }
  return ret;
}
int main() {
  ios::sync_with_stdio(false);
  cin.tie(0), cout.tie(0);
  long long m, x;
  cin >> m >> x;
  p1 = gfactor(m);
  for (auto &p : p1) {
    if (m / p % p == 0) p2.push_back(p);
    if (~p & 1) continue;
    auto t = gfactor((p - 1) / 2);
    p2.insert(p2.end(), (t).begin(), (t).end());
  }
  sort((p2).begin(), (p2).end());
  p2.erase(unique((p2).begin(), (p2).end()), p2.end());
  auto fm = factor(m, p1);
  fm.erase(fm.begin());
  long long res = 1;
  for (auto &e : fm) {
    long long tm, tphi;
    tie(tm, tphi) = e;
    long long d = ord(x, tphi, tm, p2);
    res += tphi / d;
  }
  cout << res << '\n';
  return 0;
}