Bear and Big Brother

Source: Codeforces

Version: Phuoc Hung OJ Extended

Problem Statement

Initially the younger bear weighs a and the older bear weighs b, with a<=b. Every year the younger weight triples and the older doubles. Find the minimum whole years until the younger bear is strictly heavier.

Input

Two integers a and b.

Output

Print the minimum number of whole years.

Subtasks

• Subtask 1 (20%): 1 <= a=b <= 3.
• Subtask 2 (30%): 1 <= a <= b <= 5.
• Subtask 3 (50%): 1 <= a <= b <= 10.

Examples

Example 1

Input

4 7

Output

2

Explanation

After one year weights are 12 and 14; after two years 36 and 28, so answer 2.

Example 2

Input

4 9

Output

3

Explanation

The sequence is (12,18),(36,36),(108,72); equality in year two is not enough.