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 (1.42.0) (judge verdict: Accepted)

pub trait Zero: PartialEq + Sized {
    fn zero() -> Self;
    #[inline]
    fn is_zero(&self) -> bool {
        self == &Self::zero()
    }
}
pub trait One: PartialEq + Sized {
    fn one() -> Self;
    #[inline]
    fn is_one(&self) -> bool {
        self == &Self::one()
    }
}
macro_rules !zero_one_impls {($({$Trait :ident $method :ident $($t :ty ) *,$e :expr } ) *) =>{$($(impl $Trait for $t {#[inline ] fn $method () ->Self {$e } } ) *) *} ;}
zero_one_impls !({Zero zero u8 u16 u32 u64 usize i8 i16 i32 i64 isize u128 i128 ,0 } {Zero zero f32 f64 ,0. } {One one u8 u16 u32 u64 usize i8 i16 i32 i64 isize u128 i128 ,1 } {One one f32 f64 ,1. } ) ;
pub trait IterScan: Sized {
    type Output;
    fn scan<'a, I: Iterator<Item = &'a str>>(iter: &mut I) -> Option<Self::Output>;
}
pub trait MarkedIterScan: Sized {
    type Output;
    fn mscan<'a, I: Iterator<Item = &'a str>>(self, iter: &mut I) -> Option<Self::Output>;
}
#[derive(Clone, Debug)]
pub struct Scanner<'a> {
    iter: std::str::SplitAsciiWhitespace<'a>,
}
mod scanner_impls {
    use super::*;
    impl<'a> Scanner<'a> {
        #[inline]
        pub fn new(s: &'a str) -> Self {
            let iter = s.split_ascii_whitespace();
            Self { iter }
        }
        #[inline]
        pub fn scan<T: IterScan>(&mut self) -> <T as IterScan>::Output {
            <T as IterScan>::scan(&mut self.iter).expect("scan error")
        }
        #[inline]
        pub fn mscan<T: MarkedIterScan>(&mut self, marker: T) -> <T as MarkedIterScan>::Output {
            marker.mscan(&mut self.iter).expect("scan error")
        }
        #[inline]
        pub fn scan_vec<T: IterScan>(&mut self, size: usize) -> Vec<<T as IterScan>::Output> {
            (0..size)
                .map(|_| <T as IterScan>::scan(&mut self.iter).expect("scan error"))
                .collect()
        }
        #[inline]
        pub fn iter<'b, T: IterScan>(&'b mut self) -> ScannerIter<'a, 'b, T> {
            ScannerIter {
                inner: self,
                _marker: std::marker::PhantomData,
            }
        }
    }
    macro_rules !iter_scan_impls {($($t :ty ) *) =>{$(impl IterScan for $t {type Output =Self ;#[inline ] fn scan <'a ,I :Iterator <Item =&'a str >>(iter :&mut I ) ->Option <Self >{iter .next () ?.parse ::<$t >() .ok () } } ) *} ;}
    iter_scan_impls !(char u8 u16 u32 u64 usize i8 i16 i32 i64 isize f32 f64 u128 i128 String ) ;
    macro_rules !iter_scan_tuple_impl {($($T :ident ) *) =>{impl <$($T :IterScan ) ,*>IterScan for ($($T ,) *) {type Output =($(<$T as IterScan >::Output ,) *) ;#[inline ] fn scan <'a ,It :Iterator <Item =&'a str >>(_iter :&mut It ) ->Option <Self ::Output >{Some (($(<$T as IterScan >::scan (_iter ) ?,) *) ) } } } ;}
    iter_scan_tuple_impl!();
    iter_scan_tuple_impl!(A);
    iter_scan_tuple_impl !(A B ) ;
    iter_scan_tuple_impl !(A B C ) ;
    iter_scan_tuple_impl !(A B C D ) ;
    iter_scan_tuple_impl !(A B C D E ) ;
    iter_scan_tuple_impl !(A B C D E F ) ;
    iter_scan_tuple_impl !(A B C D E F G ) ;
    iter_scan_tuple_impl !(A B C D E F G H ) ;
    iter_scan_tuple_impl !(A B C D E F G H I ) ;
    iter_scan_tuple_impl !(A B C D E F G H I J ) ;
    iter_scan_tuple_impl !(A B C D E F G H I J K ) ;
    pub struct ScannerIter<'a, 'b, T> {
        inner: &'b mut Scanner<'a>,
        _marker: std::marker::PhantomData<fn() -> T>,
    }
    impl<'a, 'b, T: IterScan> Iterator for ScannerIter<'a, 'b, T> {
        type Item = <T as IterScan>::Output;
        #[inline]
        fn next(&mut self) -> Option<Self::Item> {
            <T as IterScan>::scan(&mut self.inner.iter)
        }
    }
}
pub mod marker {
    use super::*;
    use std::{iter::FromIterator, marker::PhantomData};
    #[derive(Debug, Copy, Clone)]
    pub struct Usize1;
    impl IterScan for Usize1 {
        type Output = usize;
        #[inline]
        fn scan<'a, I: Iterator<Item = &'a str>>(iter: &mut I) -> Option<Self::Output> {
            Some(<usize as IterScan>::scan(iter)?.checked_sub(1)?)
        }
    }
    #[derive(Debug, Copy, Clone)]
    pub struct Chars;
    impl IterScan for Chars {
        type Output = Vec<char>;
        #[inline]
        fn scan<'a, I: Iterator<Item = &'a str>>(iter: &mut I) -> Option<Self::Output> {
            Some(iter.next()?.chars().collect())
        }
    }
    #[derive(Debug, Copy, Clone)]
    pub struct CharsWithBase(pub char);
    impl MarkedIterScan for CharsWithBase {
        type Output = Vec<usize>;
        #[inline]
        fn mscan<'a, I: Iterator<Item = &'a str>>(self, iter: &mut I) -> Option<Self::Output> {
            Some(
                iter.next()?
                    .chars()
                    .map(|c| (c as u8 - self.0 as u8) as usize)
                    .collect(),
            )
        }
    }
    #[derive(Debug, Copy, Clone)]
    pub struct Collect<T: IterScan, B: FromIterator<<T as IterScan>::Output>> {
        size: usize,
        _marker: PhantomData<fn() -> (T, B)>,
    }
    impl<T: IterScan, B: FromIterator<<T as IterScan>::Output>> Collect<T, B> {
        pub fn new(size: usize) -> Self {
            Self {
                size,
                _marker: PhantomData,
            }
        }
    }
    impl<T: IterScan, B: FromIterator<<T as IterScan>::Output>> MarkedIterScan for Collect<T, B> {
        type Output = B;
        #[inline]
        fn mscan<'a, I: Iterator<Item = &'a str>>(self, iter: &mut I) -> Option<Self::Output> {
            Some(
                (0..self.size)
                    .map(|_| <T as IterScan>::scan(iter).expect("scan error"))
                    .collect::<B>(),
            )
        }
    }
}
#[macro_export]
macro_rules !min {($e :expr ) =>{$e } ;($e :expr ,$($es :expr ) ,+) =>{std ::cmp ::min ($e ,min !($($es ) ,+) ) } ;}
#[macro_export]
macro_rules !chmin {($dst :expr ,$($src :expr ) ,+) =>{{let x =std ::cmp ::min ($dst ,min !($($src ) ,+) ) ;$dst =x ;} } ;}
#[macro_export]
macro_rules !max {($e :expr ) =>{$e } ;($e :expr ,$($es :expr ) ,+) =>{std ::cmp ::max ($e ,max !($($es ) ,+) ) } ;}
#[macro_export]
macro_rules !chmax {($dst :expr ,$($src :expr ) ,+) =>{{let x =std ::cmp ::max ($dst ,max !($($src ) ,+) ) ;$dst =x ;} } ;}
pub trait Modulus {
    fn get_modulus() -> u32;
    #[inline]
    fn modulo(x: u32) -> u32 {
        x % Self::get_modulus()
    }
}
#[allow(unused_macros)]
macro_rules! make_modulus {
    ($t :ident ,$e :expr ) => {
        pub struct $t {}
        impl Modulus for $t {
            #[inline]
            fn get_modulus() -> u32 {
                const MODULUS: u32 = $e;
                MODULUS
            }
        }
    };
}
#[allow(unused_macros)]
macro_rules! make_dynamic_modulus {
    ($t :ident ,$m :ident ,$e :expr ) => {
        pub struct $t {}
        static mut $m: u32 = $e;
        impl Modulus for $t {
            #[inline]
            fn get_modulus() -> u32 {
                unsafe { $m }
            }
        }
    };
}
pub mod modulus {
    use super::*;
    pub struct Modulo1000000007 {}
    impl Modulus for Modulo1000000007 {
        #[inline]
        fn get_modulus() -> u32 {
            const MODULUS: u32 = 1_000_000_007;
            MODULUS
        }
    }
    pub struct Modulo1000000009 {}
    impl Modulus for Modulo1000000009 {
        #[inline]
        fn get_modulus() -> u32 {
            const MODULUS: u32 = 1_000_000_009;
            MODULUS
        }
    }
    pub struct Modulo998244353 {}
    impl Modulus for Modulo998244353 {
        #[inline]
        fn get_modulus() -> u32 {
            const MODULUS: u32 = 998_244_353;
            MODULUS
        }
    }
    pub struct DynModulo {}
    static mut DYN_MODULUS: u32 = 1_000_000_007;
    impl Modulus for DynModulo {
        #[inline]
        fn get_modulus() -> u32 {
            unsafe { DYN_MODULUS }
        }
    }
    pub fn set_dyn_modulus(m: u32) {
        unsafe {
            DYN_MODULUS = m;
        }
    }
}
pub struct MInt<M>
where
    M: Modulus,
{
    x: u32,
    _marker: std::marker::PhantomData<fn() -> M>,
}
mod mint_impls {
    use super::*;
    use std::{
        cmp::Ordering,
        fmt::{self, Debug},
        hash::{Hash, Hasher},
        iter::{Product, Sum},
        marker::PhantomData,
        mem::swap,
        num::ParseIntError,
        ops::{Add, AddAssign, Div, DivAssign, Mul, MulAssign, Neg, Sub, SubAssign},
        str::FromStr,
    };
    impl<M: Modulus> MInt<M> {
        #[inline]
        pub fn new(x: u32) -> Self {
            Self {
                x: M::modulo(x),
                _marker: PhantomData,
            }
        }
        #[inline]
        pub fn new_unchecked(x: u32) -> Self {
            Self {
                x,
                _marker: PhantomData,
            }
        }
        #[inline]
        pub fn inner(self) -> u32 {
            self.x
        }
        #[inline]
        pub fn get_mod() -> u32 {
            M::get_modulus()
        }
        #[inline]
        pub fn pow(mut self, mut y: usize) -> Self {
            let mut x = Self::one();
            while y > 0 {
                if y & 1 == 1 {
                    x *= self;
                }
                self *= self;
                y >>= 1;
            }
            x
        }
        #[inline]
        /// only prime modulus
        pub fn inv(self) -> Self {
            let mut a = self.x;
            let (mut b, mut u, mut s) = (M::get_modulus(), 1, 0);
            let k = a.trailing_zeros();
            a >>= k;
            for _ in 0..k {
                if u & 1 == 1 {
                    u += M::get_modulus();
                }
                u /= 2;
            }
            while a != b {
                if b < a {
                    swap(&mut a, &mut b);
                    swap(&mut u, &mut s);
                }
                b -= a;
                if s < u {
                    s += M::get_modulus();
                }
                s -= u;
                let k = b.trailing_zeros();
                b >>= k;
                for _ in 0..k {
                    if s & 1 == 1 {
                        s += M::get_modulus();
                    }
                    s /= 2;
                }
            }
            Self::new_unchecked(s)
        }
    }
    impl<M: Modulus> Clone for MInt<M> {
        #[inline]
        fn clone(&self) -> Self {
            Self {
                x: Clone::clone(&self.x),
                _marker: PhantomData,
            }
        }
    }
    impl<M: Modulus> Copy for MInt<M> {}
    impl<M: Modulus> Debug for MInt<M> {
        fn fmt(&self, f: &mut std::fmt::Formatter<'_>) -> std::fmt::Result {
            Debug::fmt(&self.x, f)
        }
    }
    impl<M: Modulus> Default for MInt<M> {
        #[inline]
        fn default() -> Self {
            Self::zero()
        }
    }
    impl<M: Modulus> PartialEq for MInt<M> {
        #[inline]
        fn eq(&self, other: &Self) -> bool {
            PartialEq::eq(&self.x, &other.x)
        }
    }
    impl<M: Modulus> PartialOrd for MInt<M> {
        #[inline]
        fn partial_cmp(&self, other: &Self) -> Option<Ordering> {
            PartialOrd::partial_cmp(&self.x, &other.x)
        }
    }
    impl<M: Modulus> Eq for MInt<M> {}
    impl<M: Modulus> Ord for MInt<M> {
        #[inline]
        fn cmp(&self, other: &Self) -> Ordering {
            Ord::cmp(&self.x, &other.x)
        }
    }
    impl<M: Modulus> Hash for MInt<M> {
        #[inline]
        fn hash<H: Hasher>(&self, state: &mut H) {
            Hash::hash(&self.x, state)
        }
    }
    impl<M: Modulus> From<u32> for MInt<M> {
        #[inline]
        fn from(x: u32) -> Self {
            Self::new(x)
        }
    }
    impl<M: Modulus> From<u64> for MInt<M> {
        #[inline]
        fn from(x: u64) -> Self {
            Self::new_unchecked((x % M::get_modulus() as u64) as u32)
        }
    }
    impl<M: Modulus> From<usize> for MInt<M> {
        #[inline]
        fn from(x: usize) -> Self {
            Self::new_unchecked((x % M::get_modulus() as usize) as u32)
        }
    }
    impl<M: Modulus> From<i32> for MInt<M> {
        #[inline]
        fn from(x: i32) -> Self {
            let x = x % M::get_modulus() as i32;
            if x < 0 {
                Self::new_unchecked((x + M::get_modulus() as i32) as u32)
            } else {
                Self::new_unchecked(x as u32)
            }
        }
    }
    impl<M: Modulus> From<i64> for MInt<M> {
        #[inline]
        fn from(x: i64) -> Self {
            let x = x % M::get_modulus() as i64;
            if x < 0 {
                Self::new_unchecked((x + M::get_modulus() as i64) as u32)
            } else {
                Self::new_unchecked(x as u32)
            }
        }
    }
    impl<M: Modulus> From<isize> for MInt<M> {
        #[inline]
        fn from(x: isize) -> Self {
            let x = x % M::get_modulus() as isize;
            if x < 0 {
                Self::new_unchecked((x + M::get_modulus() as isize) as u32)
            } else {
                Self::new_unchecked(x as u32)
            }
        }
    }
    impl<M: Modulus> Add for MInt<M> {
        type Output = Self;
        #[inline]
        fn add(self, rhs: Self) -> Self::Output {
            let mut x = self.x + rhs.x;
            if x >= M::get_modulus() {
                x -= M::get_modulus();
            }
            Self::new_unchecked(x)
        }
    }
    impl<M: Modulus> Sub for MInt<M> {
        type Output = Self;
        #[inline]
        fn sub(self, rhs: Self) -> Self::Output {
            if self.x < rhs.x {
                Self::new_unchecked(self.x + M::get_modulus() - rhs.x)
            } else {
                Self::new_unchecked(self.x - rhs.x)
            }
        }
    }
    impl<M: Modulus> Mul for MInt<M> {
        type Output = Self;
        #[inline]
        fn mul(self, rhs: Self) -> Self::Output {
            Self::new_unchecked((self.x as u64 * rhs.x as u64 % M::get_modulus() as u64) as u32)
        }
    }
    impl<M: Modulus> Div for MInt<M> {
        type Output = Self;
        #[inline]
        fn div(self, rhs: Self) -> Self::Output {
            self * rhs.inv()
        }
    }
    impl<M: Modulus> Neg for MInt<M> {
        type Output = Self;
        #[inline]
        fn neg(self) -> Self::Output {
            if self.x == 0 {
                Self::zero()
            } else {
                Self::new_unchecked(M::get_modulus() - self.x)
            }
        }
    }
    impl<M: Modulus> Sum for MInt<M> {
        #[inline]
        fn sum<I: Iterator<Item = Self>>(iter: I) -> Self {
            iter.fold(Self::zero(), Add::add)
        }
    }
    impl<M: Modulus> Product for MInt<M> {
        #[inline]
        fn product<I: Iterator<Item = Self>>(iter: I) -> Self {
            iter.fold(Self::one(), Mul::mul)
        }
    }
    impl<'a, M: Modulus + 'a> Sum<&'a MInt<M>> for MInt<M> {
        #[inline]
        fn sum<I: Iterator<Item = &'a Self>>(iter: I) -> Self {
            iter.fold(Self::zero(), Add::add)
        }
    }
    impl<'a, M: Modulus + 'a> Product<&'a MInt<M>> for MInt<M> {
        #[inline]
        fn product<I: Iterator<Item = &'a Self>>(iter: I) -> Self {
            iter.fold(Self::one(), Mul::mul)
        }
    }
    impl<M: Modulus> fmt::Display for MInt<M> {
        fn fmt<'a>(&self, f: &mut fmt::Formatter<'a>) -> Result<(), fmt::Error> {
            write!(f, "{}", self.x)
        }
    }
    impl<M: Modulus> FromStr for MInt<M> {
        type Err = ParseIntError;
        #[inline]
        fn from_str(s: &str) -> Result<Self, Self::Err> {
            s.parse::<u32>().map(Self::new)
        }
    }
    impl<M: Modulus> IterScan for MInt<M> {
        type Output = Self;
        #[inline]
        fn scan<'a, I: Iterator<Item = &'a str>>(iter: &mut I) -> Option<Self::Output> {
            iter.next()?.parse::<MInt<M>>().ok()
        }
    }
    impl<M: Modulus> Zero for MInt<M> {
        #[inline]
        fn zero() -> Self {
            Self::new_unchecked(0)
        }
    }
    impl<M: Modulus> One for MInt<M> {
        #[inline]
        fn one() -> Self {
            Self::new_unchecked(1)
        }
    }
    macro_rules! mint_ref_binop {
        ($imp :ident ,$method :ident ,$t :ty ) => {
            impl<M: Modulus> $imp<$t> for &$t {
                type Output = <$t as $imp<$t>>::Output;
                #[inline]
                fn $method(self, other: $t) -> <$t as $imp<$t>>::Output {
                    $imp::$method(*self, other)
                }
            }
            impl<M: Modulus> $imp<&$t> for $t {
                type Output = <$t as $imp<$t>>::Output;
                #[inline]
                fn $method(self, other: &$t) -> <$t as $imp<$t>>::Output {
                    $imp::$method(self, *other)
                }
            }
            impl<M: Modulus> $imp<&$t> for &$t {
                type Output = <$t as $imp<$t>>::Output;
                #[inline]
                fn $method(self, other: &$t) -> <$t as $imp<$t>>::Output {
                    $imp::$method(*self, *other)
                }
            }
        };
    }
    mint_ref_binop!(Add, add, MInt<M>);
    mint_ref_binop!(Sub, sub, MInt<M>);
    mint_ref_binop!(Mul, mul, MInt<M>);
    mint_ref_binop!(Div, div, MInt<M>);
    macro_rules! mint_ref_unop {
        ($imp :ident ,$method :ident ,$t :ty ) => {
            impl<M: Modulus> $imp for &$t {
                type Output = <$t as $imp>::Output;
                #[inline]
                fn $method(self) -> <$t as $imp>::Output {
                    $imp::$method(*self)
                }
            }
        };
    }
    mint_ref_unop!(Neg, neg, MInt<M>);
    macro_rules! mint_ref_op_assign {
        ($imp :ident ,$method :ident ,$t :ty ,$fromimp :ident ,$frommethod :ident ) => {
            impl<M: Modulus> $imp<$t> for $t {
                #[inline]
                fn $method(&mut self, rhs: $t) {
                    *self = $fromimp::$frommethod(*self, rhs);
                }
            }
            impl<M: Modulus> $imp<&$t> for $t {
                #[inline]
                fn $method(&mut self, other: &$t) {
                    $imp::$method(self, *other);
                }
            }
        };
    }
    mint_ref_op_assign!(AddAssign, add_assign, MInt<M>, Add, add);
    mint_ref_op_assign!(SubAssign, sub_assign, MInt<M>, Sub, sub);
    mint_ref_op_assign!(MulAssign, mul_assign, MInt<M>, Mul, mul);
    mint_ref_op_assign!(DivAssign, div_assign, MInt<M>, Div, div);
}
#[derive(Clone, Debug)]
pub struct MemorizedFactorial<M: Modulus> {
    pub fact: Vec<MInt<M>>,
    pub inv_fact: Vec<MInt<M>>,
}
impl<M: Modulus> MemorizedFactorial<M> {
    pub fn new(max_n: usize) -> Self {
        let mut fact = vec![MInt::one(); max_n + 1];
        let mut inv_fact = vec![MInt::one(); max_n + 1];
        for i in 2..=max_n {
            fact[i] = fact[i - 1] * MInt::new(i as u32);
        }
        inv_fact[max_n] = fact[max_n].inv();
        for i in (3..=max_n).rev() {
            inv_fact[i - 1] = inv_fact[i] * MInt::new(i as u32);
        }
        Self { fact, inv_fact }
    }
    #[inline]
    pub fn combination(&self, n: usize, r: usize) -> MInt<M> {
        debug_assert!(n < self.fact.len());
        if r <= n {
            self.fact[n] * self.inv_fact[r] * self.inv_fact[n - r]
        } else {
            MInt::zero()
        }
    }
    #[inline]
    pub fn permutation(&self, n: usize, r: usize) -> MInt<M> {
        debug_assert!(n < self.fact.len());
        if r <= n {
            self.fact[n] * self.inv_fact[n - r]
        } else {
            MInt::zero()
        }
    }
    #[inline]
    pub fn homogeneous_product(&self, n: usize, r: usize) -> MInt<M> {
        debug_assert!(n + r < self.fact.len() + 1);
        if n != 0 && r != 0 {
            self.combination(n + r - 1, r)
        } else {
            MInt::one()
        }
    }
    #[inline]
    pub fn inv(&self, n: usize) -> MInt<M> {
        debug_assert!(n < self.fact.len());
        debug_assert!(n > 0);
        self.inv_fact[n] * self.fact[n - 1]
    }
}
type M = MInt<modulus::Modulo1000000007>;
fn main() {
    #![allow(unused_imports, unused_macros)]
    use std::io::{stdin, stdout, BufWriter, Read as _, Write as _};
    let mut _in_buf = Vec::new();
    stdin().read_to_end(&mut _in_buf).expect("io error");
    let _in_buf = unsafe { String::from_utf8_unchecked(_in_buf) };
    let mut scanner = Scanner::new(&_in_buf);
    macro_rules !scan {() =>{scan !(usize ) } ;(($($t :tt ) ,*) ) =>{($(scan !($t ) ) ,*) } ;([$t :ty ;$len :expr ] ) =>{scanner .scan_vec ::<$t >($len ) } ;([$t :tt ;$len :expr ] ) =>{(0 ..$len ) .map (|_ |scan !($t ) ) .collect ::<Vec <_ >>() } ;([$t :ty ] ) =>{scanner .iter ::<$t >() } ;({$e :expr } ) =>{scanner .mscan ($e ) } ;($t :ty ) =>{scanner .scan ::<$t >() } ;}
    let _out = stdout();
    let mut _out = BufWriter::new(_out.lock());
    macro_rules !print {($($arg :tt ) *) =>(::std ::write !(_out ,$($arg ) *) .expect ("io error" ) ) }
    macro_rules !println {($($arg :tt ) *) =>(::std ::writeln !(_out ,$($arg ) *) .expect ("io error" ) ) }
    macro_rules! echo {
        ($iter :expr ) => {
            echo!($iter, '\n')
        };
        ($iter :expr ,$sep :expr ) => {
            let mut iter = $iter.into_iter();
            if let Some(item) = iter.next() {
                print!("{}", item);
            }
            for item in iter {
                print!("{}{}", $sep, item);
            }
            println!();
        };
    }
    let n = scan!();
    let x = scan!([usize; n]);
    let f = MemorizedFactorial::new(n);
    let mut ans = M::zero();
    let mut acc = M::zero();
    for i in 0..n - 1 {
        acc += f.inv(i + 1);
        ans += M::from(x[i + 1] - x[i]) * acc;
    }
    ans *= f.fact[n - 1];
    println!("{}", ans);
}