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 Kotlin (1.3.71) (judge verdict: Accepted)

import java.io.BufferedReader

fun main() {
    val mod = 1_000_000_007L
    val br = System.`in`.bufferedReader()
    val n = br.readInt()
    val m = br.readInt()
    val dif = (m - n).toLong()
    val dp = LongArray(n + 1)
    dp[0] = 1
    dp[1] = dif
    var f = m.toLong()
    for (x in 2..n) {
        f *= (m - x + 1)
        f %= mod
        dp[x] = (dif * dp[x - 1] + (x - 1) * (dp[x - 2] + dp[x - 1])) % mod
    }
    print((dp.last() * f) % mod)
}

private const val SPACE_INT = ' '.toInt()
private const val ZERO_INT = '0'.toInt()
private const val NL_INT = '\n'.toInt()

private fun BufferedReader.readInt(): Int {
    var ret = read()
    while (ret <= SPACE_INT) {
        ret = read()
    }
    val neg = ret == '-'.toInt()
    if (neg) {
        ret = read()
    }
    ret -= ZERO_INT
    var read = read()
    while (read >= ZERO_INT) {
        ret *= 10
        ret += read - ZERO_INT
        read = read()
    }

    while (read <= SPACE_INT && read != -1 && read != NL_INT) {
        mark(1)
        read = read()
    }
    if (read > SPACE_INT) {
        reset()
    }
    return if (neg) -ret else ret
}