Vasya is studying number theory. He has denoted a function f(a, b) such that:

  * f(a, 0) = 0; 
  * f(a, b) = 1 + f(a, b - gcd(a, b)), where gcd(a, b) is the greatest common divisor of a and b. 



Vasya has two numbers x and y, and he wants to calculate f(x, y). He tried to do it by himself, but found out that calculating this function the way he wants to do that might take very long time. So he decided to ask you to implement a program that will calculate this function swiftly.

Input

The first line contains two integer numbers x and y (1 ≤ x, y ≤ 1012).

Output

Print f(x, y).

Examples

Input

3 5


Output

3


Input

6 3


Output

1
import java.io.OutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.StringTokenizer;
import java.io.BufferedReader;
import java.io.InputStreamReader;
import java.io.InputStream;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 */
public class Main {
    public static void main(String[] args) {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        Scanner in = new Scanner(inputStream);
        PrintWriter out = new PrintWriter(outputStream);
        TaskE solver = new TaskE();
        solver.solve(1, in, out);
        out.close();
    }

    static class TaskE {
        long solve(long a, long b) {
            if (b == 0) return 0;
            long g = gcd(a, b);
            long bestNeeded = Long.MAX_VALUE, num = g;
            for (long d = 1; d * d <= a; d++) {
                if (a % d == 0 && d % g == 0 && d > g) {
                    long needed = (b - (b / d) * d) / g;
                    if (needed < bestNeeded) {
                        bestNeeded = needed;
                        num = d;
                    }
                }
                if (a % d == 0) {
                    long d2 = a / d;
                    if (d2 > g && d2 % g == 0) {
                        long needed = (b - (b / d2) * d2) / g;
                        if (needed < bestNeeded) {
                            bestNeeded = needed;
                            num = d2;
                        }
                    }
                }
            }
            if (num == g) return b / g;
            else {
                return bestNeeded + solve(a, b - g * bestNeeded);
            }
        }

        public void solve(int testNumber, Scanner sc, PrintWriter out) {
            out.println(solve(sc.nextLong(), sc.nextLong()));
        }

        static long gcd(long a, long b) {
            return b == 0 ? a : gcd(b, a % b);
        }

    }

    static class Scanner {
        StringTokenizer st;
        BufferedReader br;

        public Scanner(InputStream s) {
            br = new BufferedReader(new InputStreamReader(s));
        }

        public String next() {
            while (st == null || !st.hasMoreTokens()) {
                try {
                    st = new StringTokenizer(br.readLine());
                } catch (Exception e) {
                }
                ;
            }
            return st.nextToken();
        }

        public long nextLong() {
            return Long.parseLong(next());
        }

    }
}

