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>
const int con = 998244353;
long long m, x;
long long ans;
long long seq[100];
long long ordseq[10000];
int tot, otot;
std::map<long long, int> fact;
long long mult(long long u, long long v, long long modv) {
  long long re = 0;
  while (v) {
    if (v & 1) {
      re = re + u;
      if (re >= modv) re -= modv;
    }
    u = u + u;
    if (u >= modv) u -= modv;
    v /= 2;
  }
  return re;
}
long long power(long long u, long long v, long long modv) {
  long long re = 1;
  u = u % modv;
  while (v) {
    if (v & 1) re = mult(re, u, modv);
    u = mult(u, u, modv);
    v /= 2;
  }
  return re;
}
long long Compute(long long y) {
  long long ord = y;
  long long re = 1;
  long long temp;
  for (int i = 0; i < tot; ++i)
    if (y % seq[i] == 0) ord = ord / seq[i] * (seq[i] - 1);
  for (int i = 0; i < otot; ++i) {
    while (ord % ordseq[i] == 0) {
      temp = power(x, ord / ordseq[i], y);
      if (temp != 1) break;
      ord /= ordseq[i];
      re *= ordseq[i];
    }
  }
  return re;
}
int main() {
  scanf("%I64d %I64d", &m, &x);
  fact.clear();
  long long temp;
  temp = m;
  for (long long i = 2; i <= m; ++i) {
    if (i * i > m) break;
    if (temp % i == 0) {
      fact[i] = 1;
      while (temp % i == 0) temp /= i;
    }
  }
  if (temp > 1) fact[temp] = 1;
  for (auto iter = fact.begin(); iter != fact.end(); ++iter)
    seq[tot++] = iter->first;
  for (int i = 0; i < tot; ++i) {
    temp = seq[i] - 1;
    for (long long j = 2; j <= seq[i]; ++j) {
      if (j * j > seq[i] - 1) break;
      if (temp % j == 0) {
        fact[j] = 1;
        while (temp % j == 0) temp /= j;
      }
    }
    if (temp > 1) fact[temp] = 1;
  }
  for (auto iter = fact.begin(); iter != fact.end(); ++iter)
    ordseq[otot++] = iter->first;
  for (long long i = 1; i <= m; ++i) {
    if (i * i > m) break;
    if (m % i == 0) {
      ans += Compute(i);
      if (i * i != m) ans += Compute(m / i);
    }
  }
  printf("%I64d\n", ans);
  return 0;
}