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: Time Limit Exceeded)

MOD = 10**9+7
MAXN = 5*(10**5)+5
fact = [1]
ifact = [1]
for i in range(MAXN):
    fact.append(fact[-1] * (i+1) % MOD)
    ifact.append(pow(fact[-1], MOD-2, MOD))
def nCr(n, r):
    return fact[n] * ifact[r] * ifact[n-r] % MOD

def nPr(n, r):
    return fact[n] * ifact[n-r] % MOD

n, m = map(int, input().split())
ans = 0
for k in range(n+1):
    # tmp = pow(nPr(m-k, n-k), 2, MOD) * nPr(m, k) * nCr(n,k) % MOD
    # tmp = nPr(m-k, n-k) * nPr(m, n) * nCr(n,k) % MOD
    tmp = nPr(m-k, n-k) * nCr(n,k) % MOD
    if k%2:
        ans -= tmp
    else:
        ans += tmp
ans = (ans * nPr(m, n) + MOD) % MOD
print(ans)