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 Rust (1.15.1) (judge verdict: Accepted)

#![allow(unused_imports)]

use std::cmp;
use std::cmp::{max, min, Ordering};
use std::collections::{BTreeMap, BTreeSet, BinaryHeap, HashMap, HashSet, VecDeque};
use std::io::stdin;
use std::ops::*;
use std::process::exit;
use std::str::FromStr;

pub const MOD: usize = 1000000007;

fn main() {
    let (n, a, b): (usize, usize, usize) = input_three();
    let mi = a * (n - 1) + b;
    let ma = a + b * (n - 1);
    let ans = if mi > ma {
        0
    } else {
        ma - mi + 1
    };

    println!("{}", ans);
}

pub fn input<T: FromStr>() -> T {
    let mut buf = String::new();
    stdin().read_line(&mut buf).unwrap();
    buf.trim().parse().ok().unwrap()
}

pub fn input_vec<T: FromStr>() -> Vec<T> {
    let mut buf = String::new();
    stdin().read_line(&mut buf).unwrap();
    buf.trim()
        .split_whitespace()
        .map(|x| x.parse().ok().unwrap())
        .collect::<Vec<_>>()
}

pub fn input_lines<T: FromStr>(l: usize) -> Vec<T> {
    let mut res = Vec::new();
    for _i in 0..l {
        res.push(input());
    }
    res
}

pub fn input_lines_two<T: FromStr, U: FromStr>(l: usize) -> Vec<(T, U)> {
    let mut res = Vec::new();
    for _i in 0..l {
        res.push(input_two());
    }
    res
}

pub fn input_lines_three<T: FromStr, U: FromStr, V: FromStr>(l: usize) -> Vec<(T, U, V)> {
    let mut res = Vec::new();
    for _i in 0..l {
        res.push(input_three());
    }
    res
}

pub fn input_two<T: FromStr, U: FromStr>() -> (T, U) {
    let mut buf = String::new();
    stdin().read_line(&mut buf).unwrap();
    let s: Vec<&str> = buf.split_whitespace().collect();
    (
        s[0].parse::<T>().ok().unwrap(),
        s[1].parse::<U>().ok().unwrap(),
    )
}

pub fn input_three<T: FromStr, U: FromStr, V: FromStr>() -> (T, U, V) {
    let mut buf = String::new();
    stdin().read_line(&mut buf).unwrap();
    let s: Vec<&str> = buf.split_whitespace().collect();
    (
        s[0].parse::<T>().ok().unwrap(),
        s[1].parse::<U>().ok().unwrap(),
        s[2].parse::<V>().ok().unwrap(),
    )
}

pub fn input_four<T: FromStr, U: FromStr, V: FromStr, W: FromStr>() -> (T, U, V, W) {
    let mut buf = String::new();
    stdin().read_line(&mut buf).unwrap();
    let s: Vec<&str> = buf.split_whitespace().collect();
    (
        s[0].parse().ok().unwrap(),
        s[1].parse().ok().unwrap(),
        s[2].parse().ok().unwrap(),
        s[3].parse().ok().unwrap(),
    )
}