Problem:
Score : 500 points

Problem Statement

Count the pairs of length-N sequences consisting of integers between 1 and M (inclusive), A_1, A_2, \cdots, A_{N} and B_1, B_2, \cdots, B_{N}, that satisfy all of the following conditions:

A_i \neq B_i, for every i such that 1\leq i\leq N.

A_i \neq A_j and B_i \neq B_j, for every (i, j) such that 1\leq i < j\leq N.

Since the count can be enormous, print it modulo (10^9+7).

Constraints

1\leq N \leq M \leq 5\times10^5

All values in input are integers.

Input

Input is given from Standard Input in the following format:

N M

Output

Print the count modulo (10^9+7).

Sample Input 1

2 2

Sample Output 1

2

A_1=1,A_2=2,B_1=2,B_2=1 and A_1=2,A_2=1,B_1=1,B_2=2 satisfy the conditions.

Sample Input 2

2 3

Sample Output 2

18

Sample Input 3

141421 356237

Sample Output 3

881613484

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

use std::collections::*;
use std::io::*;
struct StdinReader<R: BufRead> {
    pub reader: R,
    pub buf: String,
}
impl<R: BufRead> StdinReader<R> {
    pub fn new(reader: R) -> Self {
        Self {
            reader,
            buf: String::new(),
        }
    }
}
macro_rules! get {
    ($r:expr, $t:ty) => {
        {
            let mut line = &mut $r.buf;
            line.clear();
            $r.reader.read_line(&mut line).unwrap();
            line.trim().parse::<$t>().unwrap()
        }
    };
    ($r:expr, $($t:ty),*) => {
        {
            let mut line = &mut $r.buf;
            line.clear();
            $r.reader.read_line(&mut line).unwrap();
            let mut iter = line.split_whitespace();
            (
                $(iter.next().unwrap().parse::<$t>().unwrap(),)*
            )
        }
    };
    ($r:expr, $t:ty; $n:expr) => {
        // items in n lines
        (0..$n).map(|_|
                    get!($r, $t)
                   ).collect::<Vec<_>>()
    };
    ($r:expr, $($t:ty),*; $n:expr) => {
        (0..$n).map(|_|
                    get!($r, $($t),*)
                   ).collect::<Vec<_>>()
    };
    ($r:expr, $t:ty ;;) => {
        // items in a line
        {
            let mut line = &mut $r.buf;
            line.clear();
            $r.reader.read_line(&mut line).unwrap();
            line.split_whitespace()
                .map(|t| t.parse::<$t>().unwrap())
                .collect::<Vec<_>>()
        }
    };
    ($r:expr, $t:ty ;; $n:expr) => {
        (0..$n).map(|_| get!($r, $t ;;)).collect::<Vec<_>>()
    };
}
mod modint {
    use std::ops::*;
    pub trait Mod: Copy {
        fn m() -> u64;
    }
    #[derive(Copy, Clone, PartialEq, Eq, PartialOrd, Ord, Hash, Debug)]
    pub struct Modint<M> {
        x: u64,
        phantom: std::marker::PhantomData<M>,
    }
    impl<M: Mod> Modint<M> {
        pub fn new(x: i64) -> Self {
            Modint::new_internal(((x % (M::m() as i64) + M::m() as i64) % M::m() as i64) as u64)
        }
        fn new_internal(x: u64) -> Self {
            Modint {
                x,
                phantom: std::marker::PhantomData,
            }
        }
        pub fn pow(self, mut e: u64) -> Self {
            let mut res = Modint::new_internal(1);
            let mut acc = self;
            while e > 0 {
                if e % 2 != 0 {
                    res *= acc;
                }
                acc *= acc;
                e /= 2;
            }
            res
        }
        pub fn inv(self) -> Self {
            self.pow(M::m() - 2)
        }
    }
    impl<M: Mod, T: Into<Modint<M>>> Add<T> for Modint<M> {
        type Output = Self;
        fn add(self, other: T) -> Self {
            let mut sum = self.x + other.into().x;
            if sum >= M::m() {
                sum -= M::m();
            }
            Modint::new_internal(sum)
        }
    }
    impl<M: Mod, T: Into<Modint<M>>> Sub<T> for Modint<M> {
        type Output = Self;
        fn sub(self, other: T) -> Self {
            let mut diff = self.x as i64 - other.into().x as i64;
            if diff < 0 {
                diff += M::m() as i64;
            }
            Modint::new_internal(diff as u64)
        }
    }
    impl<M: Mod, T: Into<Modint<M>>> Mul<T> for Modint<M> {
        type Output = Self;
        fn mul(self, other: T) -> Self {
            Modint::new((self.x * other.into().x) as i64)
        }
    }
    impl<M: Mod, T: Into<Modint<M>>> AddAssign<T> for Modint<M> {
        fn add_assign(&mut self, other: T) {
            *self = *self + other;
        }
    }
    impl<M: Mod, T: Into<Modint<M>>> SubAssign<T> for Modint<M> {
        fn sub_assign(&mut self, other: T) {
            *self = *self - other;
        }
    }
    impl<M: Mod, T: Into<Modint<M>>> MulAssign<T> for Modint<M> {
        fn mul_assign(&mut self, other: T) {
            *self = *self * other;
        }
    }
    impl<M> std::fmt::Display for Modint<M> {
        fn fmt(&self, f: &mut std::fmt::Formatter) -> std::fmt::Result {
            self.x.fmt(f)
        }
    }
    impl<M: Mod> From<i64> for Modint<M> {
        fn from(x: i64) -> Self {
            Self::new(x)
        }
    }
    impl<M: Mod> From<i32> for Modint<M> {
        fn from(x: i32) -> Self {
            Self::new(x as i64)
        }
    }
    impl<M: Mod> From<usize> for Modint<M> {
        fn from(x: usize) -> Self {
            Self::new(x as i64)
        }
    }
}
macro_rules! define_mod {
    ($ struct_name : ident , $ modulo : expr ) => {
        #[derive(Copy, Clone, PartialEq, Eq, PartialOrd, Ord, Hash, Debug)]
        struct $struct_name {}
        impl modint::Mod for $struct_name {
            #[inline]
            fn m() -> u64 {
                $modulo
            }
        }
    };
}
mod combination {
    use super::modint;
    pub struct CombinationCalculator<M: modint::Mod> {
        fac: Vec<modint::Modint<M>>,
        facinv: Vec<modint::Modint<M>>,
    }
    impl<M: modint::Mod> CombinationCalculator<M> {
        pub fn new(max: usize) -> Self {
            let max = max + 1;
            let mut fac = vec![modint::Modint::new(1); max];
            let mut facinv = vec![modint::Modint::new(1); max];
            for i in 2..max {
                fac[i] = fac[i - 1] * i;
            }
            facinv[max - 1] = fac[max - 1].inv();
            for i in (0..max - 1).rev() {
                facinv[i] = facinv[i + 1] * (i + 1);
            }
            Self { fac, facinv }
        }
        pub fn calc(&self, n: usize, k: usize) -> modint::Modint<M> {
            if n < k {
                return modint::Modint::new(0);
            }
            self.fac[n] * self.facinv[k] * self.facinv[n - k]
        }
        pub fn perm(&self, n: usize, k: usize) -> modint::Modint<M> {
            if n < k {
                return modint::Modint::new(0);
            }
            self.fac[n] * self.facinv[n - k]
        }
    }
}

define_mod!(P, 1_000_000_007);
type Modint = modint::Modint<P>;
type ComCalc = combination::CombinationCalculator<P>;

fn main() {
    let reader = stdin();
    let mut reader = StdinReader::new(reader.lock());
    let out = stdout();
    let mut out = BufWriter::new(out.lock());
    let calc = ComCalc::new(1_000_000);
    let (n, m) = get!(reader, usize, usize);
    let mut a = vec![Modint::new(0); n + 1];
    a[n] = calc.perm(m - n, n - n) * calc.perm(m - n, n - n) * calc.perm(m, n) * calc.calc(n, n);
    for i in (0..n).rev() {
        a[i] =
            calc.perm(m - i, n - i) * calc.perm(m - i, n - i) * calc.perm(m, i) * calc.calc(n, i)
                - a[i + 1];
    }
    writeln!(out, "{}", a[0]);
}