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

The first line contains two non-negative integers: and (1 \leq m \leq 100, 1 \leq k \leq 50000).
Output a single line with the number of digits in the -fold factorial of the number .
Example 1