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 N = 1e6;
long long prfac[2][N], fac[N];
int tot, cnt;
long long mul(long long x, long long y, long long mod) {
  long long res = (x * y - (long long)((double)x * y / mod + 0.1) * mod) % mod;
  if (res < 0) res += mod;
  return res;
}
long long mod_pow(long long x, long long n, long long mod) {
  x %= mod;
  long long res = 1;
  while (n > 0) {
    if (n & 1) res = mul(res, x, mod);
    x = mul(x, x, mod);
    n >>= 1;
  }
  return res;
}
long long Euler(long long x) {
  for (int i = 1; i <= tot; i++) {
    if (x % prfac[0][i] == 0) x = x / prfac[0][i] * (prfac[0][i] - 1);
  }
  return x;
}
int main() {
  long long m, x, temp, eu, ans;
  int rec;
  cin >> m >> x;
  cnt = 0;
  for (long long i = 1; i * i <= m; i++) {
    if (m % i == 0) {
      fac[++cnt] = i;
      if (i * i != m) fac[++cnt] = m / i;
    }
  }
  sort(fac + 1, fac + cnt + 1);
  tot = 0;
  temp = m;
  for (long long i = 2; i * i <= m; i++) {
    if (temp % i == 0) prfac[0][++tot] = i;
    while (temp % i == 0) temp /= i;
  }
  if (temp > 1) prfac[0][++tot] = temp;
  sort(prfac[0] + 1, prfac[0] + tot + 1);
  eu = Euler(m);
  rec = 0;
  temp = eu;
  for (long long i = 2; i * i <= eu; i++) {
    if (temp % i == 0) prfac[1][++rec] = i;
    while (temp % i == 0) temp /= i;
  }
  if (temp > 1) prfac[1][++rec] = temp;
  sort(prfac[1] + 1, prfac[1] + rec + 1);
  ans = 0;
  for (int i = 1; i <= cnt; i++) {
    eu = Euler(fac[i]);
    temp = eu;
    for (int j = 1; j <= rec; j++) {
      if (temp == 1) break;
      while (temp % prfac[1][j] == 0 &&
             mod_pow(x, temp / prfac[1][j], fac[i]) == 1)
        temp /= prfac[1][j];
    }
    ans += eu / temp;
  }
  printf("%I64d\n", ans);
  return 0;
}