Description

In a number game, you start with an initial number S and try to transform the current number into a target number T through a sequence of operations.

There are four operations available in the game. Suppose the current number is x:

Operation	Result	Cost
+3	x + 3	x + 4
-5	x - 5	x + 5
*7	x × 7	x × 2
/2	x / 2	x × 3

The following rules apply:

• The -5 operation can only be used when x >= 5.
• The /2 operation can only be used when x is divisible by 2.
• All numbers must be non-negative integers. Therefore, an operation that results in a number smaller than 0 cannot be used.

Each operation changes the current number and incurs the corresponding cost. The cost is calculated based on the current number x before performing the operation.

For example, when the current number is 10:

• +3: 10 → 13, Cost = 10 + 4 = 14
• -5: 10 → 5, Cost = 10 + 5 = 15
• *7: 10 → 70, Cost = 10 × 2 = 20
• /2: 10 → 5, Cost = 10 × 3 = 30

Your task is to calculate the minimum total cost required to transform the starting number S into the target number T.

Your program MAY use C/C++ standard library headers.

Input

The first line contains two integers S and T where:

• S (0 <= S <= 3000000) represents the starting number.
• T (0 <= T <= 3000000) represents the target number.
• min total cost < 2^64

It is guaranteed that there exists at least one valid sequence of operations that can transform S into T.

Output

Output a single integer representing the minimum total Cost required to transform S into T. Each line of output must be terminated by a newline character ('\n').

Sample Input  Download

Sample Output  Download

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