I. Ginger's balance
time limit per test
1 second
memory limit per test
256 megabytes
input
standard input
output
standard output

Ginger has a balance. Each plate can only hold $$$n$$$ items(the balance has two plates). Now Ginger has $$$m$$$ items, one of which is a light item, the rest of the items are the same weight, and Ginger wants to know the minimum number of times he weighs to be sure to find the bad item.

Input

The first line contains two integers $$$n$$$ $$$(1 \le n \le 10 ^ 4)$$$, $$$m$$$ $$$(1 \le m \le 10 ^ 6)$$$.

Output

Print the minimum times.

Examples
Input
2 4
Output
2
Input
100 10
Output
3