Problem:
Score : 600 points

Problem Statement

There are N slimes standing on a number line.
The i-th slime from the left is at position x_i.

It is guaruanteed that 1 \leq x_1 < x_2 < \ldots < x_N \leq 10^{9}.

Niwango will perform N-1 operations. The i-th operation consists of the following procedures:

Choose an integer k between 1 and N-i (inclusive) with equal probability.

Move the k-th slime from the left, to the position of the neighboring slime to the right.

Fuse the two slimes at the same position into one slime.

Find the total distance traveled by the slimes multiplied by (N-1)! (we can show that this value is an integer), modulo (10^{9}+7). If a slime is born by a fuse and that slime moves, we count it as just one slime.

Constraints

2 \leq N \leq 10^{5}

1 \leq x_1 < x_2 < \ldots < x_N \leq 10^{9}

x_i is an integer.

Subtasks

400 points will be awarded for passing the test cases satisfying N \leq 2000.

Input

Input is given from Standard Input in the following format:

N
x_1 x_2 \ldots x_N

Output

Print the answer.

Sample Input 1

3
1 2 3

Sample Output 1

5

With probability \frac{1}{2}, the leftmost slime is chosen in the first operation, in which case the total distance traveled is 2.

With probability \frac{1}{2}, the middle slime is chosen in the first operation, in which case the total distance traveled is 3.

The answer is the expected total distance traveled, 2.5, multiplied by 2!, which is 5.

Sample Input 2

12
161735902 211047202 430302156 450968417 628894325 707723857 731963982 822804784 880895728 923078537 971407775 982631932

Sample Output 2

750927044

Find the expected value multiplied by (N-1)!, modulo (10^9+7).

Solution in Rust (1.15.1) (judge verdict: Accepted)

//  ____            _                  _                       _       _
// |  _ \ _   _ ___| |_    ___ _ __   | |_ ___ _ __ ___  _ __ | | __ _| |_ ___
// | |_) | | | / __| __|  / __| '_ \  | __/ _ \ '_ ` _ \| '_ \| |/ _` | __/ _ \
// |  _ <| |_| \__ \ |_  | (__| |_) | | ||  __/ | | | | | |_) | | (_| | ||  __/
// |_| \_\\__,_|___/\__|  \___| .__/___\__\___|_| |_| |_| .__/|_|\__,_|\__\___|
//                            |_| |_____|               |_|

//https://github.com/manta1130/Competitive_Programming_Template_Rust

#[macro_use]
mod input {

    use std;
    use std::io;

    const SPLIT_DELIMITER: char = ' ';

    #[macro_export]
    #[allow(unused_macros)]
    macro_rules! input {
    ( $($x:expr ),*) => {
        {
            let temp_str = input_line_str();
            let mut split_result_iter = temp_str.split_whitespace();
                $(
                let buf_split_result = split_result_iter.next();
                let buf_split_result = buf_split_result.unwrap();
                    ($x) = buf_split_result.parse().unwrap();
                )*
        }
    };
}

    #[allow(dead_code)]
    pub fn input_line_str() -> String {
        let mut s = String::new();
        io::stdin().read_line(&mut s).unwrap();
        s.trim().to_string()
    }

    #[allow(dead_code)]
    pub fn p<T>(t: T)
    where
        T: std::fmt::Display,
    {
        println!("{}", t);
    }

    #[allow(dead_code)]
    pub fn input_vector2d<T>(line: usize) -> Vec<Vec<T>>
    where
        T: std::str::FromStr,
    {
        let mut v: Vec<Vec<T>> = Vec::new();

        for _ in 0..line {
            let vec_line = input_vector();
            v.push(vec_line);
        }
        v
    }

    #[allow(dead_code)]
    pub fn input_vector<T>() -> Vec<T>
    where
        T: std::str::FromStr,
    {
        let mut v: Vec<T> = Vec::new();

        let s = input_line_str();
        let split_result = s.split(SPLIT_DELIMITER);
        for z in split_result {
            let buf = match z.parse() {
                Ok(r) => r,
                Err(_) => panic!("Parse Error"),
            };
            v.push(buf);
        }
        v
    }

    #[allow(dead_code)]
    pub fn input_vector_row<T>(n: usize) -> Vec<T>
    where
        T: std::str::FromStr,
    {
        let mut v = Vec::with_capacity(n);
        for _ in 0..n {
            let buf = match input_line_str().parse() {
                Ok(r) => r,
                Err(_) => panic!("Parse Error"),
            };
            v.push(buf);
        }
        v
    }

    pub trait ToCharVec {
        fn to_charvec(&self) -> Vec<char>;
    }

    impl ToCharVec for String {
        fn to_charvec(&self) -> Vec<char> {
            self.to_string().chars().collect::<Vec<_>>()
        }
    }
}

mod modint {

use std;
use std::fmt;
use std::num::ParseIntError;
use std::ops;
use std::str::FromStr;

type ValueType = usize;

const MODNUM: ValueType = 1_000_000_007;

#[derive(PartialEq, Eq, Debug, Clone)]
pub struct Modint {
    p: ValueType,
    v: ValueType,
}

impl Modint {
    #[allow(dead_code)]
    pub fn new(i: ValueType) -> Modint {
        Modint { p: MODNUM, v: i }
    }
}

impl FromStr for Modint {
    type Err = ParseIntError;

    fn from_str(s: &str) -> Result<Self, Self::Err> {
        let num: ValueType;
        num = s.parse()?;
        Ok(Modint { p: MODNUM, v: num })
    }
}

//print用
impl fmt::Display for Modint {
    fn fmt<'a>(&self, f: &mut fmt::Formatter<'a>) -> fmt::Result {
        write!(f, "{}", self.v)
    }
}

//演算子関係
impl<'a> ops::Add for &'a Modint {
    type Output = Modint;

    #[allow(dead_code)]
    fn add(self, other: &'a Modint) -> Modint {
        if self.p != other.p {
            panic!("Mod Error");
        }
        Modint {
            p: self.p,
            v: (self.v + other.v) % self.p,
        }
    }
}

impl<'a> ops::Sub for &'a Modint {
    type Output = Modint;

    #[allow(dead_code)]
    fn sub(self, other: &'a Modint) -> Modint {
        if self.p != other.p {
            panic!("Mod Error");
        }
        Modint {
            p: self.p,
            v: (self.v + self.p - (other.v % self.p)) % self.p,
        }
    }
}

impl<'a> ops::Mul for &'a Modint {
    type Output = Modint;

    #[allow(dead_code)]
    fn mul(self, other: &'a Modint) -> Modint {
        if self.p != other.p {
            panic!("Mod Error");
        }
        Modint {
            p: self.p,
            v: (self.v * other.v) % self.p,
        }
    }
}

impl<'a> ops::Div for &'a Modint {
    type Output = Modint;

    fn div(self, other: &'a Modint) -> Modint {
        if self.p != other.p {
            panic!("Mod Error");
        }
        let mut obj = self.clone();
        obj.div_uint(other.v);
        obj
    }
}

//ToDo
//AddAssign,SubAssign,MulAssign,DivAssignを実装

impl Modint {
    #[allow(dead_code)]
    pub fn add_uint(&mut self, n: ValueType) -> &Self {
        self.v += n;
        self.v %= self.p;
        self
    }

    #[allow(dead_code)]
    pub fn sub_uint(&mut self, mut n: ValueType) -> &Self {
        n = n % self.p;
        self.v += self.p;
        self.v -= n;
        self.v %= self.p;
        self
    }

    #[allow(dead_code)]
    pub fn mul_uint(&mut self, n: ValueType) -> &Self {
        self.v *= n;
        self.v %= self.p;
        self
    }

    #[allow(dead_code)]
    pub fn div_uint(&mut self, n: ValueType) -> &Self {
        let mut obj = Modint::new(n);
        obj.inv();
        self.v *= obj.v;
        self.v %= self.p;
        self
    }

    #[allow(dead_code)]
    pub fn inv(&mut self) -> &Self {
        let p = self.p;
        self.pow(p as usize - 2);
        self
    }

    #[allow(dead_code)]
    pub fn pow(&mut self, mut n: usize) -> &Self {
        let mut temp = self.v;
        self.v = 1;
        while n > 0 {
            if n & 1 != 0 {
                self.v *= temp;
                self.v %= self.p;
            }
            n >>= 1;
            temp *= temp;
            temp %= self.p;
        }
        self
    }

    #[allow(dead_code)]
    pub fn get_value(&self) -> ValueType {
        self.v
    }
}

pub struct DPFactorial {
    normal: Vec<Modint>,
    inv: Vec<Modint>,
}
impl DPFactorial {
    #[allow(dead_code)]
    pub fn new() -> DPFactorial {
        let mut obj = DPFactorial {
            normal: Vec::new(),
            inv: Vec::new(),
        };
        obj.normal.push(Modint::new(1));
        obj.inv.push(Modint::new(1));
        obj
    }

    #[allow(dead_code)]
    pub fn get_factorial(&mut self, n: usize) -> Modint {
        if n < self.normal.len() {
            return self.normal[n].clone();
        }
        for z in self.normal.len()..n as usize + 1 {
            let buf = Modint::new(z as ValueType);
            let buf = &buf * &self.normal[z - 1];

            self.normal.push(buf);
        }
        return self.normal[n].clone();
    }

    #[allow(dead_code)]
    pub fn get_factorial_inv(&mut self, n: usize) -> Modint {
        if n < self.inv.len() {
            return self.inv[n].clone();
        }
        for z in self.inv.len()..n + 1 {
            let mut buf = Modint::new(z as ValueType);
            buf.inv();
            let buf = &buf * &self.inv[z - 1];
            self.inv.push(buf);
        }
        self.inv[n].clone()
    }

    #[allow(dead_code)]
    pub fn get_combination(&mut self, n: usize, r: usize) -> Modint {
        if n < r {
            return Modint::new(0);
        }
        &(&self.get_factorial(n) * &(self.get_factorial_inv(n - r))) * &(self.get_factorial_inv(r))
    }

    #[allow(dead_code)]
    pub fn get_permutation(&mut self, n: usize, r: usize) -> Modint {
        if n < r {
            return Modint::new(0);
        }
        &self.get_factorial(n) * &(self.get_factorial_inv(n - r))
    }
}
}

use input::*;
use modint::*;

fn main() {
    let n: usize;
    input!(n);
    let x = input_vector::<usize>();
    let mut dpf = DPFactorial::new();
    let mut table = vec![Modint::new(0)];
    for i in 1..n + 1 {
        let mut next;
        {
            let last = table.last().unwrap();
            let mut next_buf = Modint::new(1);
            next_buf = &next_buf / &Modint::new(i);
            let next_buf_int = next_buf.get_value();
            next = last.get_value() + next_buf_int;
        }
        table.push(Modint::new(next));
    }

    let mut ans = Modint::new(0);

    for i in 0..x.len() - 1 {
        ans = &ans + &(&table[i + 1] * &Modint::new(x[i + 1] - x[i]));
    }
    p(&ans * &dpf.get_factorial(n - 1));
}