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;
unsigned long long m, n;
vector<unsigned long long> prime;
unsigned long long p[100];
void factorize(unsigned long long x) {
  unsigned long long cnt = 0;
  if (x % 2 == 0) {
    prime.push_back(2);
    cnt++;
    while (x % 2 == 0) {
      p[cnt]++;
      x /= 2;
    }
  }
  for (unsigned long long i = 3; i <= sqrt(x) + 0.5; i += 2)
    if (x % i == 0) {
      prime.push_back(i);
      cnt++;
      while (x % i == 0) {
        p[cnt]++;
        x /= i;
      }
    }
  if (x > 1) {
    prime.push_back(x);
    p[++cnt]++;
  }
}
void fac(unsigned long long x) {
  prime.clear();
  if (x % 2 == 0) {
    prime.push_back(2);
    while (x % 2 == 0) {
      x /= 2;
    }
  }
  for (unsigned long long i = 3; i <= sqrt(x) + 0.5; i += 2)
    if (x % i == 0) {
      prime.push_back(i);
      while (x % i == 0) {
        x /= i;
      }
    }
  if (x > 1) {
    prime.push_back(x);
  }
}
vector<unsigned long long> divisor;
vector<unsigned long long> pn;
unsigned long long fast_exp(unsigned long long a, unsigned long long b) {
  unsigned long long ans = 1;
  while (b != 0) {
    if (b & 1) ans *= a;
    b = b / 2;
    a = a * a;
  }
  return ans;
}
unsigned long long all() {
  unsigned long long ans = 1;
  for (unsigned long long i = 0; i < prime.size(); i++) {
    ans *= fast_exp(prime[i], pn[i]);
  }
  return ans;
}
unordered_map<unsigned long long, unsigned long long> phis;
unsigned long long phi(unsigned long long x) {
  unsigned long long ans = x;
  for (unsigned long long i = 0; i < pn.size(); i++)
    if (pn[i] >= 1) {
      ans = ans / prime[i] * (prime[i] - 1);
    }
  return ans;
}
void dfs(unsigned long long d) {
  if (pn.size() == prime.size()) {
    unsigned long long ans = all();
    divisor.push_back(ans);
    phis[ans] = phi(ans);
    return;
  }
  for (unsigned long long i = 0; i < p[d] + 1; i++) {
    pn.push_back(i);
    dfs(d + 1);
    pn.pop_back();
  }
}
inline unsigned long long mul(unsigned long long x, unsigned long long y,
                              unsigned long long P) {
  x %= P;
  y %= P;
  unsigned long long ans = 0;
  for (; y; y /= 10000) {
    if (y % 10000 != 0) ans = (ans + x * (y % 10000)) % P;
    x = (x * 10000) % P;
  }
  return ans;
}
unsigned long long pw(unsigned long long a, unsigned long long b,
                      unsigned long long p) {
  unsigned long long ans = 1;
  for (; b; b >>= 1, a = mul(a, a, p))
    if (b & 1) ans = mul(ans, a, p);
  return ans;
}
void ord(unsigned long long x, unsigned long long& k, unsigned long long mod,
         unsigned long long phid) {
  k = 1;
  if (mod == 1) return;
  unsigned long long tmp = x % mod;
  x %= mod;
  fac(phid);
  for (auto p : prime) {
    while (phid % p == 0 && pw(x, phid / p, mod) == 1) phid /= p;
  }
  k = phid;
}
int main() {
  cin >> m >> n;
  factorize(m);
  dfs(1);
  unsigned long long ans = 0;
  for (auto d : divisor) {
    unsigned long long k;
    unsigned long long tmp = phis[d];
    ord(n, k, d, tmp);
    ans += tmp / k;
  }
  cout << ans << endl;
}