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 maxN = 1e5 + 5999, MOD = 998244353, lg = 19;
const long long LIM = 2e18;
long long bat, ans = 0, et, prdivs[100], prsz[100], prdivF[100][100], prc = 0;
long long origFac[100], origFacC = 0;
long long mulm(long long a, long long b, long long MOD) {
  long long ret = 0;
  while (b) {
    ret = (ret + b % bat * a) % MOD;
    b /= bat, a = a * bat % MOD;
  }
  return ret;
}
long long fastPow(long long a, long long b, long long MOD) {
  long long ret = 1;
  a %= MOD;
  while (b) {
    if (b & 1) ret = mulm(ret, a, MOD);
    b >>= 1, a = mulm(a, a, MOD);
  }
  return ret % MOD;
}
long long m, x;
void consid(long long divi) {
  if (divi == 1) return void(ans++);
  bat = max(2LL, LIM / divi);
  long long ringsz = 1, net = divi;
  for (int i = 0; i < origFacC; i++)
    if (net % origFac[i] == 0) net = net - net / origFac[i];
  for (int i = 0; i < prc; i++) {
    int l = -1, m, r = prsz[i];
    while (l + 1 < r) {
      m = (l + r) >> 1;
      if (fastPow(x, prdivF[i][m], divi) == 1)
        r = m;
      else
        l = m;
    }
    ringsz *= et / prdivF[i][prsz[i] - r];
  }
  ans += net / ringsz;
}
map<long long, int> getpr(long long x) {
  map<long long, int> ret;
  for (long long i = 2; i * i <= x; i++)
    while (x % i == 0) x /= i, ret[i]++;
  if (x > 1) ret[x]++;
  return ret;
}
set<long long> divs;
int main() {
  ios::sync_with_stdio(false);
  cin.tie(0), cout.tie(0);
  cin >> m >> x;
  map<long long, int> ordiv = getpr(m);
  for (auto it = ordiv.begin(); it != ordiv.end(); it++, origFacC++)
    origFac[origFacC] = it->first;
  et = m;
  for (auto it = ordiv.begin(); it != ordiv.end(); it++)
    et = et - et / it->first;
  map<long long, int> prdv = getpr(et);
  for (auto it = prdv.begin(); it != prdv.end(); it++, prc++) {
    prdivs[prc] = it->first;
    prdivF[prc][it->second] = et;
    prsz[prc] = it->second;
    for (int j = it->second - 1; j >= 0; j--)
      prdivF[prc][j] = prdivF[prc][j + 1] / it->first;
  }
  for (long long i = 1; i * i <= m; i++)
    if (m % i == 0) divs.insert(i), divs.insert(m / i);
  for (auto it = divs.begin(); it != divs.end(); it++) consid(*it);
  cout << ans << '\n';
}