Description
Vasily has a number a, which he wants to turn into a number b. For this purpose, he can do two types of operations:
- multiply the current number by 2 (that is, replace the number x by 2·x);
- append the digit 1 to the right of current number (that is, replace the number x by 10·x + 1).
You need to help Vasily to transform the number a into the number b using only the operations described above, or find that it is impossible.
Note that in this task you are not required to minimize the number of operations. It suffices to find any way to transform a into b.
Input
The first line contains two positive integers a and b (1 ≤ a < b ≤ 109) — the number which Vasily has and the number he wants to have.
Output
If there is no way to get b from a, print "NO" (without quotes).
Otherwise print three lines. On the first line print "YES" (without quotes). The second line should contain single integer k — the length of the transformation sequence. On the third line print the sequence of transformations x1, x2, ..., xk, where:
- x1 should be equal to a,
- xk should be equal to b,
- xi should be obtained from xi - 1 using any of two described operations (1 < i ≤ k).
If there are multiple answers, print any of them.
Sample Input
2 162
YES 5 2 4 8 81 162
4 42
NO
100 40021
YES 5 100 200 2001 4002 40021
从后往前，暴力进行计算。
#include <iostream>
#include <cstdio>
#include <cstdlib>
#include <cmath>
#include <algorithm>
#include <climits>
#include <cstring>
#include <string>
#include <set>
#include <map>
#include <queue>
#include <stack>
#include <vector>
#include <list>
#define rep(i,m,n) for(i=m;i<=n;i++)
#define rsp(it,s) for(set<int>::iterator it=s.begin();it!=s.end();it++)
const int inf_int = 2e9;
const long long inf_ll = 2e18;
#define inf_add 0x3f3f3f3f
#define mod 1000000007
#define vi vector<int>
#define pb push_back
#define mp make_pair
#define fi first
#define se second
#define pi acos(-1.0)
#define pii pair<int,int>
#define Lson L, mid, rt<<1
#define Rson mid+1, R, rt<<1|1
const int maxn=5e2+10;
using namespace std;
typedef long long ll;
typedef unsigned long long ull;
inline int read(){int ra,fh;char rx;rx=getchar(),ra=0,fh=1;
while((rx<'0'||rx>'9')&&rx!='-')rx=getchar();if(rx=='-')
fh=-1,rx=getchar();while(rx>='0'&&rx<='9')ra*=10,ra+=rx-48,
rx=getchar();return ra*fh;}
//#pragma comment(linker, "/STACK:102400000,102400000")
ll gcd(ll p,ll q){return q==0?p:gcd(q,p%q);}
ll qpow(ll p,ll q){ll f=1;while(q){if(q&1)f=f*p;p=p*p;q>>=1;}return f;}
ll a,b;
ll re[10000005];
int judge(ll n);
int main()
{
int num=0;
cin >> a>> b;
re[num++] = b;
while(b>a)
{
int t = b%10;
if(t==1)
{
b = (b-1)/10;
re[num++] = b;
continue;
}
else if(t%2==1)
{
cout << "NO"<<endl;
return 0;
}
else
{
b /=2;
re[num++] = b;
}
}
if(b<a)
{
cout << "NO"<<endl;
return 0;
}
cout << "YES"<<endl;
cout << num<<endl;
for(int i=num-1;i>=0;i--)
{
cout << re[i] << " ";
}
//cout << a<< " "<<endl;
return 0;
}