A course consists of numChapters distinct chapters numbered from 0 to numChapters - 1.

The chapters are taught sequentially, one chapter per day. After the last chapter is taught, the course starts again from chapter 0.

Given that a student was absent from day firstDay to day lastDay, both inclusive, determine the number of distinct chapters the student missed.

Input

• numChapters — number of distinct chapters.
• firstDay — first day the student was absent.
• lastDay — last day the student was absent.

The chapter taught on day d is:

(d % numChapters)

Output

Return the number of distinct chapters taught between firstDay and lastDay, inclusive.

Example 1

Input:
numChapters = 4
firstDay = 3
lastDay = 5

Chapters taught:

Day:       0  1  2  3  4  5  6  7
Chapter:   0  1  2  3  0  1  2  3

The student missed:

Day 3 → Chapter 3
Day 4 → Chapter 0
Day 5 → Chapter 1

Distinct chapters missed:

{0, 1, 3}

Therefore:

Answer = 3

Example 2

Input:
numChapters = 4
firstDay = 1
lastDay = 6

Chapters:

1, 2, 3, 0, 1, 2

Distinct chapters:

{0, 1, 2, 3}

Answer = 4

Constraints

1 ≤ numChapters ≤ 10^9
0 ≤ firstDay ≤ lastDay ≤ 10^18

Goal: Find an efficient solution without iterating through every day.