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 Python (3.8.2) (judge verdict: Accepted)

mod = 10 ** 9 + 7

def mod_prepare(N):
    fac = [1, 1]
    finv = [1, 1]
    inv = [0, 1]
    for i in range(2, N + 1):
        fac.append(fac[i - 1] * i % mod)
        inv.append(mod - inv[mod % i] * (mod // i) % mod)
        finv.append(finv[i - 1] * inv[i] % mod)
    return fac, finv

N, M = map(int, input().split())

fac, inv = mod_prepare(M)

ans = 0
sign = 1
for k in range(N + 1):
    ans += sign * fac[M - k] * inv[k] * inv[N - k]
    sign *= -1
    ans %= mod

print(ans * fac[N] * fac[M] * inv[M - N] * inv[M - N] % mod)