Transformation: from A to B

1000ms

262144K

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, ..., x_k, where:

x₁ should be equal to a,
x_k should be equal to b,
x_i should be obtained from x_i - 1 using any of two described operations (1 < i ≤ k).

If there are multiple answers, print any of them.

Sample Input:

2 162

Sample Output:

YES
5
2 4 8 81 162

Sample Input:

4 42

Sample Output:

NO

Sample Input:

100 40021

Sample Output:

YES
5
100 200 2001 4002 40021

Informação

Provedor Codeforces

Código CF727A