Bear and Raspberry · Interview Problem

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Codeforces

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Math

Bear and Raspberry

Find how much the first bear must eat to become strictly heavier than the second bear.

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Problem Statement

Problem

Two bears have weights $a$ and $b$ . The first bear wants to be strictly heavier than the second bear. Each year, the first bear gains weight by multiplying its weight by 3, while the second bear gains weight by multiplying its weight by 2.

Your task is to determine the minimum number of years after which the first bear's weight becomes strictly greater than the second bear's weight.

Notes

In each year, both bears grow simultaneously.
You only need to output the smallest non-negative integer $n$ such that $a \cdot 3^n > b \cdot 2^n$ .

Input Format

The first and only line contains two integers $a$ and $b$ .

Output Format

Print one integer: the minimum number of years needed for the first bear to become strictly heavier than the second bear.

Constraints

$1 \le a, b \le 10^9$
The answer fits in a standard integer type.

Examples

Sample cases returned by the problem API.

Example 1

Input

4 7

Output

Explanation

After 1 year: $4\cdot 3=12$ and $7\cdot 2=14$ , so the first bear is still lighter. After 2 years: $12\cdot 3=36$ and $14\cdot 2=28$ , so the first bear becomes heavier.

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