Problem:
Score : 300 points

Problem Statement

Snuke has N dogs and M monkeys. He wants them to line up in a row.

As a Japanese saying goes, these dogs and monkeys are on bad terms. ("ken'en no naka", literally "the relationship of dogs and monkeys", means a relationship of mutual hatred.) Snuke is trying to reconsile them, by arranging the animals so that there are neither two adjacent dogs nor two adjacent monkeys.

How many such arrangements there are? Find the count modulo 10^9+7 (since animals cannot understand numbers larger than that).
Here, dogs and monkeys are both distinguishable. Also, two arrangements that result from reversing each other are distinguished.

Constraints

1 ≤ N,M ≤ 10^5

Input

Input is given from Standard Input in the following format:

N M

Output

Print the number of possible arrangements, modulo 10^9+7.

Sample Input 1

2 2

Sample Output 1

8

We will denote the dogs by A and B, and the monkeys by C and D. There are eight possible arrangements: ACBD, ADBC, BCAD, BDAC, CADB, CBDA, DACB and DBCA.

Sample Input 2

3 2

Sample Output 2

12

Sample Input 3

1 8

Sample Output 3

0

Sample Input 4

100000 100000

Sample Output 4

530123477

Solution in Rust (1.42.0) (judge verdict: Accepted)

#![allow(unused_macros)]
#![allow(dead_code)]
#![allow(unused_imports)]

use itertools::Itertools;

const U_INF: usize = 1 << 60;
const I_INF: isize = 1 << 60;

fn main() {
    let mut sc = Scanner::new();
    let n = sc.next_usize();
    let m = sc.next_usize();

    if m.max(n) - m.min(n) > 1 {
        println!("0");
    } else {
        let mut ans = ModInt::new(1);
        for i in 1..=n {
            ans *= ModInt::new(i as isize);
        }
        for i in 1..=m {
            ans *= ModInt::new(i as isize);
        }

        if n == m {
            ans *= ModInt::new(2);
        }

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

pub const MOD: isize = 1000000007;
// pub const MOD: isize = 998244353;

/// 常に設定したModを取り続ける正整数型
#[derive(Debug, Copy, Clone, Ord, PartialOrd, Eq, PartialEq)]
pub struct ModInt {
    /// 保持する値
    value: isize,
}

impl ModInt {
    /// isizeを受け取り、ModIntに変換する
    pub fn new(n: isize) -> Self {
        let mut value = n % MOD;
        if value < 0 {
            value += MOD;
        }
        Self { value }
    }

    /// べき乗計算関数
    /// 二分累乗法を用いるため、計算量はO(log n)
    pub fn pow(self, n: usize) -> Self {
        if n == 0 {
            1.into()
        } else if n == 1 {
            self
        } else if n % 2 == 0 {
            (self * 2.into()).pow(n / 2)
        } else {
            self * self.pow(n - 1)
        }
    }

    /// 逆元を返す
    /// フェルマーの小定理より、べき乗を用いて計算するため、計算量はO(log MOD)
    pub fn inv(self) -> Self {
        self.pow((MOD - 2) as usize)
    }
}

impl std::fmt::Display for ModInt {
    fn fmt(&self, f: &mut std::fmt::Formatter<'_>) -> std::fmt::Result {
        write!(f, "{}", self.value)
    }
}

impl From<usize> for ModInt {
    fn from(n: usize) -> Self {
        Self::new(n as isize)
    }
}

impl From<u64> for ModInt {
    fn from(n: u64) -> Self {
        Self::new(n as isize)
    }
}

impl From<u32> for ModInt {
    fn from(n: u32) -> Self {
        Self::new(n as isize)
    }
}

impl From<u16> for ModInt {
    fn from(n: u16) -> Self {
        Self::new(n as isize)
    }
}

impl From<u8> for ModInt {
    fn from(n: u8) -> Self {
        Self::new(n as isize)
    }
}

impl From<isize> for ModInt {
    fn from(n: isize) -> Self {
        Self::new(n)
    }
}

impl From<i64> for ModInt {
    fn from(n: i64) -> Self {
        Self::new(n as isize)
    }
}

impl From<i32> for ModInt {
    fn from(n: i32) -> Self {
        Self::new(n as isize)
    }
}

impl From<i16> for ModInt {
    fn from(n: i16) -> Self {
        Self::new(n as isize)
    }
}

impl From<i8> for ModInt {
    fn from(n: i8) -> Self {
        Self::new(n as isize)
    }
}

impl std::ops::Add for ModInt {
    type Output = Self;

    fn add(self, rhs: Self) -> Self::Output {
        let mut tmp = self.value + rhs.value;
        if tmp >= MOD {
            tmp %= MOD;
        }

        Self { value: tmp }
    }
}

impl std::ops::AddAssign for ModInt {
    fn add_assign(&mut self, rhs: Self) {
        *self = *self + rhs
    }
}

impl std::ops::Sub for ModInt {
    type Output = ModInt;

    fn sub(self, rhs: Self) -> Self::Output {
        let mut tmp = self.value;
        if tmp < rhs.value {
            tmp += MOD;
        }
        tmp -= rhs.value;
        if tmp >= MOD {
            tmp %= MOD;
        }

        Self { value: tmp }
    }
}

impl std::ops::SubAssign for ModInt {
    fn sub_assign(&mut self, rhs: Self) {
        *self = *self - rhs;
    }
}

impl std::ops::Mul for ModInt {
    type Output = ModInt;

    fn mul(self, rhs: Self) -> Self::Output {
        let mut tmp = self.value * rhs.value;
        if tmp >= MOD {
            tmp %= MOD;
        }

        Self { value: tmp }
    }
}

impl std::ops::MulAssign for ModInt {
    fn mul_assign(&mut self, rhs: Self) {
        *self = *self * rhs;
    }
}

impl std::ops::Div for ModInt {
    type Output = ModInt;

    fn div(self, rhs: Self) -> Self::Output {
        self * rhs.inv()
    }
}

impl std::ops::DivAssign for ModInt {
    fn div_assign(&mut self, rhs: Self) {
        *self = *self / rhs;
    }
}

pub struct Scanner {
    buf: std::collections::VecDeque<String>,
}

impl Scanner {
    pub fn new() -> Self {
        Self {
            buf: std::collections::VecDeque::new(),
        }
    }

    fn scan_line(&mut self) {
        let mut flag = 0;
        while self.buf.is_empty() {
            let mut s = String::new();
            std::io::stdin().read_line(&mut s).unwrap();
            let mut iter = s.split_whitespace().peekable();
            if iter.peek().is_none() {
                if flag >= 5 {
                    panic!("There is no input!");
                }
                flag += 1;
                continue;
            }

            for si in iter {
                self.buf.push_back(si.to_string());
            }
        }
    }

    pub fn next<T: std::str::FromStr>(&mut self) -> T {
        self.scan_line();
        self.buf
            .pop_front()
            .unwrap()
            .parse()
            .unwrap_or_else(|_| panic!("Couldn't parse!"))
    }

    pub fn next_usize(&mut self) -> usize {
        self.next()
    }

    pub fn next_isize(&mut self) -> isize {
        self.next()
    }

    pub fn next_chars(&mut self) -> Vec<char> {
        self.next::<String>().chars().collect()
    }

    pub fn next_string(&mut self) -> String {
        self.next()
    }

    pub fn next_char(&mut self) -> char {
        self.next()
    }

    pub fn next_float(&mut self) -> f64 {
        self.next()
    }
}