Memory is now interested in the de-evolution of objects, specifically triangles. He starts with an equilateral triangle of side length x, and he wishes to perform operations to obtain an equilateral triangle of side length y.

In a single second, he can modify the length of a single side of the current triangle such that it remains a non-degenerate triangle (triangle of positive area). At any moment of time, the length of each side should be integer.

What is the minimum number of seconds required for Memory to obtain the equilateral triangle of side length y?

Input

The first and only line contains two integers x and y (3 ≤ y < x ≤ 100 000) — the starting and ending equilateral triangle side lengths respectively.

Output

Print a single integer — the minimum number of seconds required for Memory to obtain the equilateral triangle of side length y if he starts with the equilateral triangle of side length x.

Examples

Input

6 3


Output

4


Input

8 5


Output

3


Input

22 4


Output

6

Note

In the first sample test, Memory starts with an equilateral triangle of side length 6 and wants one of side length 3. Denote a triangle with sides a, b, and c as (a, b, c). Then, Memory can do <image>.

In the second sample test, Memory can do <image>.

In the third sample test, Memory can do: <image>

<image>.
import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStream;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.math.BigInteger;
import java.util.Arrays;
import java.util.StringTokenizer;

public class CF712C {

	public static void main(String args[]){
		InputReader in = new InputReader(System.in);
		//OutputStream outputStream = System.out;
		PrintWriter out = new PrintWriter(System.out);
		int o,f;
		o=in.nextInt();
		f=in.nextInt();
		int ar[]=new int[3];
		ar[0]=f;
		ar[1]=f;
		ar[2]=f;
		int ans=0;
		while(ar[0]!=o){
			ar[0]=Math.min((ar[1]+ar[2]-1), o);
			Arrays.sort(ar);
			ans++;
		}
		out.println(ans);
		out.close();
		
}
static class Pair implements Comparable<Pair> {
	int u;
	int v;
	BigInteger bi;
	public Pair(int u, int v) {
		this.u = u;
		this.v = v;
	}

	public int hashCode() {
		int hu = (int) (u ^ (u >>> 32));
		int hv = (int) (v ^ (v >>> 32));
		return 31 * hu + hv;
	}

	public boolean equals(Object o) {
		Pair other = (Pair) o;
		return u == other.u && v == other.v;
	}

	public int compareTo(Pair other) {
		return Long.compare(u, other.u) != 0 ? Long.compare(u, other.u) : Long.compare(v, other.v);
	}

	public String toString() {
		return "[u=" + u + ", v=" + v + "]";
	}
}
public static void debug(Object... o) {
	System.out.println(Arrays.deepToString(o));
}
static long modulo(long a,long b,long c) {
	long x=1;
	long y=a;
	while(b > 0){
		if(b%2 == 1){
			x=(x*y)%c;
		}
		y = (y*y)%c; // squaring the base
		b /= 2;
	}
	return  x%c;
}
static long gcd(long x, long y)
{
	if(x==0)
		return y;
	if(y==0)
		return x;
	long r=0, a, b;
	a = (x > y) ? x : y; // a is greater number
	b = (x < y) ? x : y; // b is smaller number
	r = b;
	while(a % b != 0)
	{
		r = a % b;
		a = b;
		b = r;
	}
	return r;
}
static class InputReader {
	public BufferedReader reader;
	public StringTokenizer tokenizer;

	public InputReader(InputStream inputstream) {
		reader = new BufferedReader(new InputStreamReader(inputstream));
		tokenizer = null;
	}

	public String nextLine(){
		String fullLine=null;
		while (tokenizer == null || !tokenizer.hasMoreTokens()) {
			try {
				fullLine=reader.readLine();
			} catch (IOException e) {
				throw new RuntimeException(e);
			}
			return fullLine;
		}
		return fullLine;
	}
	public String next() {
		while (tokenizer == null || !tokenizer.hasMoreTokens()) {
			try {
				tokenizer = new StringTokenizer(reader.readLine());
			} catch (IOException e) {
				throw new RuntimeException(e);
			}
		}
		return tokenizer.nextToken();
	}
	public long nextLong() {
		return Long.parseLong(next());
	}
	public int nextInt() {
		return Integer.parseInt(next());
	}
}

}
