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;
template <typename T, typename U>
inline void smin(T &a, const U &b) {
  if (a > b) a = b;
}
template <typename T, typename U>
inline void smax(T &a, const U &b) {
  if (a < b) a = b;
}
template <class T>
inline void gn(T &first) {
  char c, sg = 0;
  while (c = getchar(), (c > '9' || c < '0') && c != '-')
    ;
  for ((c == '-' ? sg = 1, c = getchar() : 0), first = 0; c >= '0' && c <= '9';
       c = getchar())
    first = (first << 1) + (first << 3) + c - '0';
  if (sg) first = -first;
}
template <class T1, class T2>
inline void gn(T1 &x1, T2 &x2) {
  gn(x1), gn(x2);
}
template <class T1, class T2, class T3>
inline void gn(T1 &x1, T2 &x2, T3 &x3) {
  gn(x1, x2), gn(x3);
}
template <class T1, class T2, class T3, class T4>
inline void gn(T1 &x1, T2 &x2, T3 &x3, T4 &x4) {
  gn(x1, x2, x3), gn(x4);
}
template <class T1, class T2, class T3, class T4, class T5>
inline void gn(T1 &x1, T2 &x2, T3 &x3, T4 &x4, T5 &x5) {
  gn(x1, x2, x3, x4), gn(x5);
}
template <class T>
inline void print(T first) {
  if (first < 0) {
    putchar('-');
    return print(-first);
  }
  if (first < 10) {
    putchar('0' + first);
    return;
  }
  print(first / 10);
  putchar(first % 10 + '0');
}
template <class T>
inline void println(T first) {
  print(first);
  putchar('\n');
}
template <class T>
inline void printsp(T first) {
  print(first);
  putchar(' ');
}
template <class T1, class T2>
inline void print(T1 x1, T2 x2) {
  printsp(x1), println(x2);
}
template <class T1, class T2, class T3>
inline void print(T1 x1, T2 x2, T3 x3) {
  printsp(x1), printsp(x2), println(x3);
}
template <class T1, class T2, class T3, class T4>
inline void print(T1 x1, T2 x2, T3 x3, T4 x4) {
  printsp(x1), printsp(x2), printsp(x3), println(x4);
}
template <class T1, class T2, class T3, class T4, class T5>
inline void print(T1 x1, T2 x2, T3 x3, T4 x4, T5 x5) {
  printsp(x1), printsp(x2), printsp(x3), printsp(x4), println(x5);
}
long long multi(long long a, long long b, long long c) {
  return ((a * b - (long long)(a / (long double)c * b + 1e-5) * c + c) % c +
          c) %
         c;
}
long long power(long long a, long long b, long long m, long long ans = 1) {
  for (; b; b >>= 1, a = multi(a, a, m))
    if (b & 1) ans = multi(ans, a, m);
  return ans;
}
vector<long long> res;
long long pi;
void find_prime(long long first) {
  res.clear();
  for (int i = 2; (long long)i * i <= first; i++)
    if (first % i == 0) {
      res.push_back(i);
      while (first % i == 0) first /= i;
    }
  if (first > 1) res.push_back(first);
}
long long calc(long long val, long long first) {
  first %= val;
  if (val == 1) return 1;
  find_prime(val);
  long long pi = val;
  for (int i = 0; i < res.size(); i++) {
    pi -= pi / res[i];
  }
  long long ans = 1;
  find_prime(pi);
  if (power(first, pi, val) != 1) {
    assert(0);
  }
  while (1) {
    int flag = 1;
    for (int i = 0; i < res.size(); i++)
      if (pi % res[i] == 0) {
        long long second = pi / res[i];
        if (power(first, second, val) == 1) {
          pi /= res[i];
          ans *= res[i];
          flag = 0;
          break;
        }
      }
    if (flag) break;
  }
  return ans;
}
int main() {
  long long m, first;
  gn(m, first);
  long long ans = 0;
  for (int i = 1; (long long)i * i <= m; i++)
    if (m % i == 0) {
      ans += calc(m / i, first);
      if (m / i != i) ans += calc(i, first);
    }
  println(ans);
}