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 Go (1.14.1) (judge verdict: Wrong Answer)

package main

import (
	"bufio"
	"fmt"
	"os"
	"sort"
	"strconv"
)

const N = 1_000_000_007

var fac, finv, inv []int

func main() {
	sc := NewScanner()

	n := sc.ReadInt()
	m := sc.ReadInt()
	MAX := m + 1

	fac = make([]int, MAX)
	fac[0] = 1
	fac[1] = 1
	finv = make([]int, MAX)
	finv[0] = 1
	finv[1] = 1
	inv = make([]int, MAX)
	inv[1] = 1
	for i := 2; i < MAX; i++ {
		fac[i] = fac[i-1] * i % N
		inv[i] = N - inv[N%i]*(N/i)%N
		finv[i] = finv[i-1] * inv[i] % N
	}

	ansForN := make([]int, n+1)
	ansForN[0] = 1
	for ni := 1; ni <= n; ni++ {
		mi := m - n + ni

		ans := fac[mi] * finv[mi-ni]
		ans = ans * ans % N
		for dupNumberCount := 1; dupNumberCount <= ni; dupNumberCount++ {
			caseCount := fac[mi] * finv[mi-dupNumberCount] % N
			caseCount = caseCount * Combi(ni, dupNumberCount) % N
			caseCount = caseCount * ansForN[ni-dupNumberCount] % N
			ans -= caseCount
			ans = (ans + N) % N
		}

		ansForN[ni] = ans
	}

	fmt.Println(ansForN[n])
}

func Combi(n, k int) int {
	if n < k {
		return 0
	}
	if n < 0 || k < 0 {
		return 0
	}
	return fac[n] * (finv[k] * finv[n-k] % N) % N
}

// util
// *   math/simple

func Abs(x int) int {
	if x >= 0 {
		return x
	}
	return -x
}

func Min(values ...int) int {
	if len(values) == 0 {
		panic("no values")
	}
	min := values[0]
	for _, v := range values {
		if v < min {
			min = v
		}
	}
	return min
}

func Max(values ...int) int {
	if len(values) == 0 {
		panic("no values")
	}
	max := values[0]
	for _, v := range values {
		if v > max {
			max = v
		}
	}
	return max
}

func Pow(base int, exponent uint) int {
	answer := 1
	for i := uint(0); i < exponent; i++ {
		answer *= base
	}
	return answer
}

func Ceil(divident, dividor int) int {
	quo := divident / dividor
	rem := divident % dividor

	if rem != 0 {
		if (divident > 0 && dividor > 0) ||
			(divident < 0 && dividor < 0) {
			return quo + 1
		}
	}
	return quo
}

// *   sortutil

func ReverseInts(a []int) {
	sort.Sort(sort.Reverse(sort.IntSlice(a)))
}

func ReverseStrings(a []string) {
	sort.Sort(sort.Reverse(sort.StringSlice(a)))
}

// *   io

type Scanner struct {
	bufScanner *bufio.Scanner
}

func NewScanner() *Scanner {
	bufSc := bufio.NewScanner(os.Stdin)
	bufSc.Split(bufio.ScanWords)
	bufSc.Buffer(nil, 100000000)
	return &Scanner{bufSc}
}

func (sc *Scanner) ReadString() string {
	bufSc := sc.bufScanner
	bufSc.Scan()
	return bufSc.Text()
}

func (sc *Scanner) ReadInt() int {
	bufSc := sc.bufScanner
	bufSc.Scan()
	text := bufSc.Text()

	num, err := strconv.Atoi(text)
	if err != nil {
		panic(err)
	}
	return num
}