Problem:
Score : 200 points

Problem Statement

Snuke has N integers. Among them, the smallest is A, and the largest is B.
We are interested in the sum of those N integers. How many different possible sums there are?

Constraints

1 ≤ N,A,B ≤ 10^9

A and B are integers.

Input

Input is given from Standard Input in the following format:

N A B

Output

Print the number of the different possible sums.

Sample Input 1

4 4 6

Sample Output 1

5

There are five possible sums: 18=4+4+4+6, 19=4+4+5+6, 20=4+5+5+6, 21=4+5+6+6 and 22=4+6+6+6.

Sample Input 2

5 4 3

Sample Output 2

0

Sample Input 3

1 7 10

Sample Output 3

0

Sample Input 4

1 3 3

Sample Output 4

1

Solution in Ruby (2.3.3) (judge verdict: Runtime Error)

n, a, b = gets.split(" ").map(&:to_i)

if  a != b && n == 1
  puts 0
elsif b - a >= 0
  ary = (a..(a + [n - 1, b - a].min)).to_a.repeated_combination(b-a).to_a
  ary_sum = []
  ary.each {|x|
    ary_sum << x.sum
  }
  p ary_sum.uniq.size
else
  puts 0
end