Multifactorial - 2

In this problem, you are tasked with calculating the m-fold factorial of a number k. Let's review how to compute m-fold factorials, denoted as F. For this, we define t_{i} = k - mi. The following formula applies:

Input

The first line contains two non-negative integers: m and k (1 ≤ m ≤ 100, 1 ≤ k ≤ 50000).

Output

Output a single line with the number of digits in the m-fold factorial of the number k.

Examples