Description

Farmer John has been informed of the location of a fugitive cow and wants to catch her immediately. He starts at a pointN(0 ≤N≤ 100,000) on a number line and the cow is at a pointK(0 ≤K≤ 100,000) on the same number line. Farmer John has two modes of transportation: walking and teleporting.

* Walking: FJ can move from any pointXto the pointsX- 1 orX+ 1 in a single minute
* Teleporting: FJ can move from any pointXto the point 2 ×Xin a single minute.

If the cow, unaware of its pursuit, does not move at all, how long does it take for Farmer John to retrieve it?

Input

Output

Sample Input

5 17

Sample Output

4

Hint

Source

 1 #include <cstdio>
 2 #include <cstdlib>
 3 #include <cstring>
 4 #include <queue>
 5 #include <stack>
 6 #include <vector>
 7 #include <iostream>
 8 #include "algorithm"
 9 using namespace std;
10 const int MAX=100005;
11 int n,m,ans;
12 bool co[MAX];
13 struct num{
14     int x,y;
15 };
16 queue <num> q;
17 int main(){
18     freopen ("cow.in","r",stdin);
19     freopen ("cow.out","w",stdout);
20     int i,j;
21     scanf("%d%d",&n,&m);
22     memset(co,true,sizeof(co));
23     num a,b;a.x=n,a.y=0;
24     q.push(a);
25     co[a.x]=false;
26     while (!q.empty()){
27         a=q.front();q.pop();
28         if (a.x*2<MAX && co[a.x*2]){
29             b.x=a.x*2,b.y=a.y+1;
30             q.push(b);
31             co[b.x]=false;
32             if (b.x==m){ans=b.y;break;}
33         }
34         if (a.x+1<MAX && co[a.x+1]){
35             b.x=a.x+1,b.y=a.y+1;
36             q.push(b);
37             co[b.x]=false;
38             if (b.x==m){ans=b.y;break;}
39         }
40         if (a.x-1>=0 && co[a.x-1]){
41             b.x=a.x-1,b.y=a.y+1;
42             q.push(b);
43             co[b.x]=false;
44             if (b.x==m){ans=b.y;break;}
45         }
46     }
47     printf("%d",ans);
48     return 0;
49 }