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.util.*;
import java.io.*;
import java.math.BigDecimal;
import java.math.BigInteger;
import java.math.MathContext;

import static java.lang.Math.*;
import static java.util.Arrays.*;
import static java.util.Collections.*;



/*``````````````````````````````````````````````````````````````````````````````````````````````````````````````````````````````````````````````````````````````````````*/
/*^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ CONTROLLER CLASS   ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^*/
/*``````````````````````````````````````````````````````````````````````````````````````````````````````````````````````````````````````````````````````````````````````*/


public class Main {
	public static void main(String[] args) throws Exception {
		InputReader in = new InputReader(System.in);
		PrintWriter out = new PrintWriter(System.out);
		TaskA solver = new TaskA();
		solver.solve(1, in, out);
		out.close();
	}

static class TaskA {
	int[] dx  = {1 , 0, -1, 0 , -1 ,-1 , 1 , 1},
		  dy = {0 , 1 ,0 ,-1 ,-1 ,1 - 1, 1} ;
	//int[] union;
/*``````````````````````````````````````````````````````````````````````````````````````````````````````````````````````````````````````````````````````````````````````*/
/*^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ OTHER USEFULL METHODS ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^*/
/*``````````````````````````````````````````````````````````````````````````````````````````````````````````````````````````````````````````````````````````````````````*/
		// GCD && LCM
		long gcd(long a, long b) {
			return b == 0 ? a : gcd(b, a % b);
		}

		long lcm(long a, long b) {
			return a * (b / gcd(a, b));
		}

		// REverse a String
		String rev(String s) {
			return new StringBuilder(s).reverse().toString();
		}
/*``````````````````````````````````````````````````````````````````````````````````````````````````````````````````````````````````````````````````````````````````````*/
/*^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ SOLUTION  IS RIGHT HERE^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^*/
/*``````````````````````````````````````````````````````````````````````````````````````````````````````````````````````````````````````````````````````````````````````*/
	    
		public void solve(int testNumber, InputReader in, PrintWriter out) throws IOException {
			// BufferedReader br = new BufferedReader(new
			// InputStreamReader(System.in));
			// Scanner sc = new Scanner(System.in);
			//final long mod = (long)1e9+7;
			int x = in.nextInt() , y = in.nextInt();
			int[] a = {y , y, y};
			int cnt = 0;
			while(a[0] != x || a[1] != x || a[2] != x){
				a[cnt%3 ] = min(abs(a[(cnt+1)%3] + a[(cnt+2)%3])-1 , x);
				//out.println(a[0]+" "+a[1]+" "+a[2]);
				cnt++;
			}
			out.println(cnt);
		}
	}

/*``````````````````````````````````````````````````````````````````````````````````````````````````````````````````````````````````````````````````````````````````````*/
/*^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ OTHER USEFULL CLASSES ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^*/
/*``````````````````````````````````````````````````````````````````````````````````````````````````````````````````````````````````````````````````````````````````````*/

 /*``````````````````````````````````````````````````````````````````````````````````````````````````````````````````````````````````````````````````````````````````````*/
 /*^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ INPUT READER CLASS ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^*/
 /*``````````````````````````````````````````````````````````````````````````````````````````````````````````````````````````````````````````````````````````````````````*/
	


    static class InputReader {
		private byte[] buf = new byte[8000];
		private int index;
		private int total;
		private InputStream in;
		//BufferedReader br = new BufferedReader(new InputStreamReader(System.in));

		public InputReader(InputStream stream) {
			in = stream;
		}

		public int scan() {
			if (total == -1)
				throw new InputMismatchException();
			if (index >= total) {
				index = 0;
				try {
					total = in.read(buf);
				} catch (IOException e) {
					throw new InputMismatchException();
				}
				if (total <= 0)
					return -1;
			}
			return buf[index++];
		}

		public long scanlong() {
			long integer = 0;
			int n = scan();
			while (isWhiteSpace(n))
				n = scan();
			int neg = 1;
			if (n == '-') {
				neg = -1;
				n = scan();
			}
			while (!isWhiteSpace(n)) {
				if (n >= '0' && n <= '9') {
					integer *= 10;
					integer += n - '0';
					n = scan();
				} else
					throw new InputMismatchException();
			}
			return neg * integer;
		}

		private int scanInt() {
			int integer = 0;
			int n = scan();
			while (isWhiteSpace(n))
				n = scan();
			int neg = 1;
			if (n == '-') {
				neg = -1;
				n = scan();
			}
			while (!isWhiteSpace(n)) {
				if (n >= '0' && n <= '9') {
					integer *= 10;
					integer += n - '0';
					n = scan();
				} else
					throw new InputMismatchException();
			}
			return neg * integer;
		}

		public double scandouble() {
			double doubll = 0;
			int n = scan();
			int neg = 1;
			while (isWhiteSpace(n))
				n = scan();
			if (n == '-') {
				neg = -1;
				n = scan();
			}
			while (!isWhiteSpace(n) && n != '.') {
				if (n >= '0' && n <= '9') {
					doubll *= 10;
					doubll += n - '0';
					n = scan();
				}
			}
			if (n == '.') {
				n = scan();
				double temp = 1;
				while (!isWhiteSpace(n)) {
					if (n >= '0' && n <= '9') {
						temp /= 10;
						doubll += (n - '0') * temp;
						n = scan();
					}
				}
			}
			return neg * doubll;
		}

		private float scanfloat() {
			float doubll = 0;
			int n = scan();
			int neg = 1;
			while (isWhiteSpace(n))
				n = scan();
			if (n == '-') {
				neg = -1;
				n = scan();
			}
			while (!isWhiteSpace(n) && n != '.') {
				if (n >= '0' && n <= '9') {
					doubll *= 10;
					doubll += n - '0';
					n = scan();
				}
			}
			if (n == '.') {
				n = scan();
				double temp = 1;
				while (!isWhiteSpace(n)) {
					if (n >= '0' && n <= '9') {
						temp /= 10;
						doubll += (n - '0') * temp;
						n = scan();
					}
				}
			}
			return neg * doubll;
		}

		public String scanstring() {
			StringBuilder sb = new StringBuilder();
			int n = scan();
			while (isWhiteSpace(n))
				n = scan();
			while (!isWhiteSpace(n)) {
				sb.append((char) n);
				n = scan();
			}
			return sb.toString();
		}

		public String scan_nextLine() {
			int n = scan();
			while (isWhiteSpace(n))
				n = scan();
			StringBuilder res = new StringBuilder();
			do {
				res.appendCodePoint(n);
				n = scan();
			} while (!isEndOfLine(n));
			return res.toString();
		}

		public boolean isWhiteSpace(int n) {
			if (n == ' ' || n == '\n' || n == '\r' || n == '\t' || n == -1)
				return true;
			return false;
		}

		private boolean isEndOfLine(int c) {
			return c == '\n' || c == '\r' || c == -1;
		}
		/// Input module

		public int nextInt() {
			return scanInt();
		}

		public long nextLong() {
			return scanlong();
		}

		public double nextDouble() {
			return scandouble();
		}

		public float nextFloat() {
			return scanfloat();
		}

		public String next() {
			return scanstring();
		}

		public String nextLine() throws IOException {
			return scan_nextLine();
		}

		public int[] readIntArray(int size) {
			int[] array = new int[size];
			for (int i = 0; i < size; i++) {
				array[i] = nextInt();
			}
			return array;
		}
	}
 
}