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 E = 65535;
long long M, m, X, a[23405], b[23405], p[23405], ans, j, t;
long long A[60][23405], P[60][23405], T[60];
long long mut(long long x, long long y) {
  long long rt = 0, tt = x;
  while (y) {
    rt = (rt + tt * (y & 0xffff)) % M;
    tt = (tt << 16) % M;
    y >>= 16;
  }
  return rt;
}
long long pow_(long long x, long long y) {
  long long rt = 1;
  while (y) {
    if (y & 1) rt = mut(rt, x);
    x = mut(x, x);
    y >>= 1;
  }
  return rt;
}
void dfs(int x) {
  if (x == t) {
    long long w = 1, res = 1;
    M = 1;
    for (int i = 0; i < t; i++)
      for (int j = 0; j < b[i]; j++) {
        if (j)
          w *= p[i];
        else
          w *= (p[i] - 1);
        M *= p[i];
      }
    for (int i = 0; i < t; i++)
      for (int j = 0; j < b[i] - 1; j++)
        if (pow_(X, w / p[i]) == 1) w /= p[i], res *= p[i];
    for (int i = 0; i < t; i++)
      if (b[i]) {
        for (int I = 0; I < T[i]; I++)
          for (int j = 0; j < A[i][I]; j++)
            if (pow_(X, w / P[i][I]) == 1) w /= P[i][I], res *= P[i][I];
      }
    ans += res;
  } else {
    for (int i = 0; i <= a[x]; i++) b[x] = i, dfs(x + 1);
  }
}
int main() {
  cin >> m >> X;
  if (X == 1) {
    cout << m << endl;
    return 0;
  }
  j = 2;
  t = -1;
  while (j * j <= m) {
    if (m % j == 0) {
      t++;
      p[t] = j;
      while (m % j == 0) a[t]++, m /= j;
    }
    j++;
  }
  if (m > 1) t++, p[t] = m, a[t] = 1;
  t++;
  for (int i = 0; i < t; i++) {
    m = p[i] - 1;
    j = 2;
    T[i] = -1;
    while (j * j <= m) {
      if (m % j == 0) {
        T[i]++;
        P[i][T[i]] = j;
        A[i][T[i]] = 0;
        while (m % j == 0) A[i][T[i]]++, m /= j;
      }
      j++;
    }
    if (m > 1) T[i]++, P[i][T[i]] = m, A[i][T[i]] = 1;
    T[i]++;
  }
  dfs(0);
  cout << ans << endl;
}