E. Solve problems every day
time limit per test
1 second
memory limit per test
256 megabytes
input
standard input
output
standard output

Once Maxim thought that it would be great to solve programming problems every day, it would definitely brighten up his life. Then he saw that on a popular website, statistics are kept not only on the number of consecutive days that Maxim solves problems, but also on the number of problems solved per month (it is well known that month $$$k$$$ has $$$k$$$ days).

Now Maxim has set himself a new challenge — to solve problems every day so that the number of problems solved per month is always not less than the number of consecutive days that Maxim solves problems. Moreover, every day he must solve at least one problem.

The number of problems solved per month means the number of problems solved in the last $$$k$$$ days, including the current day. That is, if the day is in the middle of the month, then all problems solved from the middle of last month to the present day are summed up. For example, on May 16, it will be considered that the total number of problems solved for the month is the sum of the problems solved from April 17 to May 16 inclusive.

It is known that he already meets this condition for $$$n$$$ days. It is interesting what is the minimum number of problems that Maxim solved during this period.

Input

The input consists of a single line containing two integers $$$k, n$$$ ($$$1 \le k, n \le 10^6$$$) — the number of days in the month and the duration of the challenge.

Output

Output a single number — the minimum number of problems that Maxim solved during these $$$n$$$ days.

Examples
Input
2 3
Output
4
Input
30 15
Output
15
Input
30 365
Output
2405
Note

Let's consider the first example:

  • On the first day, Maxim solves 1 problem, and the condition is met, because he solved problems for only one day and solved one problem in the last month.
  • On the second day, Maxim solves 1 problem, and the condition is met, because he solved problems for two consecutive days and solved two problems in the last month.
  • On the third day, Maxim solves 2 problems, and the condition is met, because he solved problems for three consecutive days and solved three problems in the last month (that is, the problems solved in the last two days are summed up).