Bear and Big Brother · Interview Problem

Codeforces

Easy

Math

Simulation

Bear and Big Brother

Given two bears with different weights, determine how many years it takes for the first bear to become strictly heavier than the second if both grow at fixed annual rates.

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Codeforces 791A

gfg

Primary

Problem Statement

Problem

Limak and Bob are bears with initial weights $a$ and $b$ kilograms, respectively, where $a < b$ .

Every year:

Limak's weight is multiplied by $3$.
Bob's weight is multiplied by $2$.

Your task is to determine the smallest number of years after which Limak's weight becomes strictly greater than Bob's weight.

Goal

Return that minimum number of years.

Notes

The weights grow exponentially by fixed factors.
You may simulate year by year until Limak overtakes Bob.

Input Format

A single line contains two integers $a$ and $b$ .
It is guaranteed that $a < b$ .

Output Format

Output one integer: the minimum number of years needed for Limak's weight to become strictly greater than Bob's weight.

Constraints

$1 \le a < b \le 10^9$
The answer fits in a 32-bit signed integer.
A simple simulation is sufficient.

Examples

Sample cases returned by the problem API.

Example 1

Input

4 7

Output

Explanation

After 1 year: Limak = 12, Bob = 14. After 2 years: Limak = 36, Bob = 28. Limak becomes strictly heavier in 2 years.

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