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.*;
	
			public class codeforces
			{	
				public static void main(String[] args)
				{
					InputReader in = new InputReader(System.in);
					PrintWriter pw = new PrintWriter(System.out);
					
					int x = in.nextInt();
					int y = in.nextInt();
					int a = y, b = y, c = y, max, min, ans = 0;
					
					while(a != x || b != x || c != x)
					{
						min = Math.min(a, Math.min(b, c));
						max = Math.max(a, Math.max(b, c));
						
						b = a+b+c - (max+min);
						a = min;
						c = max;
						
						a = Math.min(b+c-1, x);
						ans++;
						//pw.println(a+" "+b+" "+c);
					}
					
					pw.print(ans);
					
					pw.flush();
					pw.close();
				}
				
				public static HashMap<Long, Integer> primeFactorization(long n)
				{
					HashMap<Long, Integer> map = new HashMap<>();
					
					for(long i=2;i*i<=n;i++)
					{
						while(n%i==0)
						{
							if(!map.containsKey(i))
								map.put(i, 1);
							else
								map.put(i, map.get(i)+1);
							
							n/=i;
						}
					}
					if(n!=1)
					{
						if(!map.containsKey(n))
							map.put(n, 1);
						else
							map.put(n, map.get(n)+1);
					}
					
					return map;
				}
				public static int BinarySearch_l(long[] a, long k)
				{
					int n = a.length;
					int i = 0, j = n-1;
					int mid = 0;
					
					if(k - a[n-1] > 0)
						return n;
					else
					{
						while(j - i > 0)
						{
							mid = (i+j)/2;
							
							if(k - a[mid] > 0)
								i = mid + 1;
							else
								j = mid;
						}
					}
					
					return i;
				}
				
				public static int BinarySearch_r(long[] a, long k)
				{
					int n = a.length;
					int i = 0, j = n-1;
					int mid = 0;
					
					if(k - a[0] < 0)
						return -1;
					else
					{
						while(j - i > 0)
						{
							mid = (int)Math.ceil((double)(i+j)/2);
							
							if(k - a[mid] >= 0)
								i = mid;
							else
								j = mid - 1;
						}
					}
					
					return i;
				}
				public static long fact(long n, long M)
				{
					long ans = 1;
					
					for(long i=n;i>0;i--)
					{
						ans = (ans*i)%M;
					}
					
					return ans;
				}
				
			/*	public static void DFS(int sourse)
				{
					int count = 0;
					visited[sourse] = true;
					
					for(int u : adj[sourse])
					{
						if(!visited[u])
						{
							DFS(u);
						}
					}
					
					
				}*/
				
				public static ArrayList Divisors(int n)
				{
				    ArrayList<Integer> div = new ArrayList<>();
				    
				    for (int i=1; i<=Math.sqrt(n); i++)
				    {
				        if (n%i == 0)
				        {
				        	div.add(i);
				                
				            if(n/i != i)
				            	div.add(n/i);
				        }
				    }
				    return div;
				}
			
				public static long GCD(long a,long b)
				{
					if(b==0)
						return a;
					else
						return GCD(b,a%b);
				}
				
				public static long LCM(long a,long b)
				{
					return (a*b)/GCD(a, b);
				}
				
				static class pair implements Comparable<pair>
				{
					Integer x, y;
					pair(int x,int y)
					{
						this.x=x;
						this.y=y;
					}
					
					public int compareTo(pair o) {
						int result = x.compareTo(o.x);
						if(result==0)
							result = y.compareTo(o.y);
						
						return result;
					}  
					
					public String toString()
					{
						return x+" "+y;
					}
					
					public boolean equals(Object o)
					{
						if (o instanceof pair)
					    {
							pair p = (pair)o;
							return p.x - x == 0 && p.y - y == 0 ;
						}
						return false;
					}
					
					public int hashCode()
					{
						return new Long(x).hashCode()*31 + new Long(y).hashCode();
					}
				}
				
				static class InputReader 
				{
					 
					private final InputStream stream;
					private final byte[] buf = new byte[8192];
					private int curChar, snumChars;
					private SpaceCharFilter filter;
			 
					public InputReader(InputStream stream) 
					{
						this.stream = stream;
					}
			 
					public int snext() 
					{
						if (snumChars == -1)
							throw new InputMismatchException();
						if (curChar >= snumChars) 
						{
							curChar = 0;
							try 
							{
								snumChars = stream.read(buf);
							} 
							catch (IOException e) 
							{
								throw new InputMismatchException();
							}
							if (snumChars <= 0)
								return -1;
						}
						return buf[curChar++];
					}
			 
					public int nextInt() 
				    {
						int c = snext();
						while (isSpaceChar(c)) 
						{
							c = snext();
						}
						int sgn = 1;
						if (c == '-')
					    {
							sgn = -1;
							c = snext();
						}
						int res = 0;
						do 
						{
							if (c < '0' || c > '9')
								throw new InputMismatchException();
							res *= 10;
							res += c - '0';
							c = snext();
						} while (!isSpaceChar(c));
						return res * sgn;
					}
			 
					public long nextLong()
				    {
						int c = snext();
						while (isSpaceChar(c)) 
						{
							c = snext();
						}
						int sgn = 1;
						if (c == '-') 
						{
							sgn = -1;
							c = snext();
						}
						long res = 0;
						do 
						{
							if (c < '0' || c > '9')
								throw new InputMismatchException();
							res *= 10;
							res += c - '0';
							c = snext();
						} while (!isSpaceChar(c));
						return res * sgn;
					}
			 
					public int[] nextIntArray(int n) 
					{
						int a[] = new int[n];
						for (int i = 0; i < n; i++) 
						{
							a[i] = nextInt();
						}
						return a;
					}
			 
					public String readString()
				    {
						int c = snext();
						while (isSpaceChar(c)) 
						{
							c = snext();
						}
						StringBuilder res = new StringBuilder();
						do 
						{
							res.appendCodePoint(c);
							c = snext();
						} while (!isSpaceChar(c));
						return res.toString();
					}
			 
					public String nextLine() 
					{
						int c = snext();
						while (isSpaceChar(c))
							c = snext();
						StringBuilder res = new StringBuilder();
						do 
						{
							res.appendCodePoint(c);
							c = snext();
						} while (!isEndOfLine(c));
						return res.toString();
					}
			 
					public boolean isSpaceChar(int c) 
					{
						if (filter != null)
							return filter.isSpaceChar(c);
						return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
					}
			 
					private boolean isEndOfLine(int c) 
					{
						return c == '\n' || c == '\r' || c == -1;
					}
			 
					public interface SpaceCharFilter
				    {
						public boolean isSpaceChar(int ch);
					}
				}
				
				static class CodeX {
		        public static void sort(long arr[]) {
		            merge_sort(arr, 0, arr.length - 1);
		        }
		
		        private static void merge_sort(long A[], long start, long end) {
		            if (start < end) {
		                long mid = (start + end) / 2;
		                merge_sort(A, start, mid);
		                merge_sort(A, mid + 1, end);
		                merge(A, start, mid, end);
		            }
		
		        }
		
		        private static void merge(long A[], long start,long mid, long end) {
		            long p = start, q = mid + 1;
		            long Arr[] = new long[(int)(end - start + 1)];
		            long k = 0;
		
		            for (int i = (int)start; i <= end; i++) {
		                if (p > mid)
		                    Arr[(int)k++] = A[(int)q++];
		
		                else if (q > end)
		                    Arr[(int)k++] = A[(int)p++];
		
		                else if (A[(int)p] < A[(int)q])
		                    Arr[(int)k++] = A[(int)p++];
		
		                else
		                    Arr[(int)k++] = A[(int)q++];
		            }
		            for (int i = 0; i < k; i++) {
		                A[(int)start++] = Arr[i];
		            }
		
		        }
		
		    }
			}	
			
	
				