Multiply by Three at Least Once

Source: Phước Hưng OJ

Version: Phuoc Hung OJ Extended

Problem Statement

Given positive integers $x,T$, each pass replaces $x$ by $3x$ and increments a counter. Perform at least one pass even if $x\ge T$ initially. Stop when the updated $x\ge T$ and output the number of passes.

Input

One line contains positive integers $x,T$ in this order.

Output

Print the number of times multiplication by three was performed.

Subtasks

• Subtask 1 (20%): $1\le x,T\le30$.
• Subtask 2 (30%): $1\le x,T\le10^6$.
• Subtask 3 (50%): $1\le x\le10^6$, $1\le T\le10^9$.

Examples

Example 1

Input

3 20

Output

2

Explanation

Pass 1: 3 becomes 9 (<20). Pass 2: 9 becomes 27 (>=20), so output 2.

Example 2

Input

25 20

Output

1

Explanation

Although 25>=20 initially, one multiplication is mandatory; 75>=20 and the answer is 1.