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;
long long P, X, m, p[1005], q[1005], ans, l;
long long phi(long long x) {
  long long ret = x;
  for (int i = 1; i <= m; i++)
    if (x % p[i] == 0) ret /= p[i], ret *= p[i] - 1;
  return ret;
}
inline long long MUL(long long x, long long y, long long P) {
  return ((x * y - (long long)(((long double)x * y + 0.5) / P) * P) % P + P) %
         P;
}
long long Pow(long long a, long long b, long long P) {
  long long ret = 1;
  for (; b; b >>= 1, a = MUL(a, a, P))
    if (b & 1) ret = MUL(ret, a, P);
  return ret;
}
void work(long long g) {
  long long mod = P / g;
  long long num = phi(mod);
  long long x = X % mod;
  long long k = num;
  for (int i = 1; i <= l; i++)
    while (k % q[i] == 0 && Pow(x, k / q[i], mod) == 1) k /= q[i];
  ans += num / k;
}
void Divide(long long n) {
  for (int i = 2; 1ll * i * i <= n; i++)
    if (n % i == 0) {
      q[++l] = i;
      while (n % i == 0) n /= i;
    }
  if (n > 1) q[++l] = n;
}
int main() {
  cin >> P >> X;
  long long n = P;
  for (int i = 2; 1ll * i * i <= n; i++)
    if (n % i == 0) {
      p[++m] = i;
      while (n % i == 0) n /= i;
    }
  if (n > 1) p[++m] = n;
  for (int i = 1; i <= m; i++) {
    q[++l] = p[i];
    Divide(p[i] - 1);
  }
  sort(q + 1, q + l + 1);
  l = unique(q + 1, q + l + 1) - (q + 1);
  for (int g = 1; 1ll * g * g <= P; g++)
    if (P % g == 0) {
      work(g);
      if (g != 1 && 1ll * g * g < P) work(P / g);
    }
  cout << ans + 1 << endl;
}