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 C++ (GCC 9.2.1) (judge verdict: Accepted)

#include <bits/stdc++.h>
#define int long long
#define x first
#define y second
#define getbit(x, i) (((x) >> (i)) & 1)
using namespace std;
typedef pair<int, int> pii;
#define hashset unordered_set
#define hashmap unordered_map
#define newline fast_writechar('\n')
#define unify(arr) arr.resize(unique(arr.begin(), arr.end()) - arr.begin())
#define getbit(x, i) (((x) >> (i)) & 1)

template <typename T>
vector<T> readvector(size_t sz) {
    vector<T> res(sz);
    for (size_t i = 0; i < sz; ++i) {
        cin >> res[i];
    }
    return res;
}
template <typename T>
std::ostream &operator<<(std::ostream &out, const std::vector<T> &v) {
    std::copy(v.begin(), v.end(), std::ostream_iterator<T>(out, " "));
    return out;
}

int mylog(int n) {
    return 63 - __builtin_clzll(n);
}

inline int binPow(int x, int deg, int mod) {
    int ans = 1;
    for (int i = sizeof(deg) * CHAR_BIT - 1; i >= 0; i--) {
        ans *= ans;
        ans %= mod;
        if (getbit(deg, i)) ans *= x;
        ans %= mod;
    }
    return ans;
}

/** Interface */

inline int readInt();
inline int readUInt();
inline void readWord(char *s);
inline int fast_readchar();  // you may use readchar() instead of it

inline void writeInt(int x);
inline void fast_writechar(int x);  // you may use putchar() instead of it
inline void writeWord(const char *s);
inline void fast_flush();

// ====================== END ======================
const int MAXN = 5e5 + 10;
const int MOD = 1e9 + 7;
const int INF = 1e18;


int fact[MAXN], inv_fact[MAXN];

void precalc() {
    fact[0] = 1;
    for (int i = 1; i < MAXN; i++) {
        fact[i] = (fact[i - 1] * i) % MOD;
    }
    inv_fact[MAXN - 1] = binPow(fact[MAXN - 1], MOD - 2, MOD);
    for (int i = MAXN - 1; i > 0; i--) {
        inv_fact[i - 1] = (inv_fact[i] * i) % MOD;
    }
}

int c(int n, int k) {
    return ((fact[n] * inv_fact[k]) % MOD * inv_fact[n - k]) % MOD;
}

int f(int n, int m) {
    int ans = 0;
    for (int i = 0; i <= n; i++) {
        ans += ((i % 2 == 0 ? 1 : -1) * c(n, i) * fact[m - i]) % MOD;
        // cout << ans << endl;
    }
    ans = (ans % MOD) + MOD;
    ans %= MOD;
    // cout << ans << endl;
    return (ans * inv_fact[m - n]) % MOD;
}



void solve() {
    precalc();
    // for (int i = 1; i < 100; i++) {
    //     cout << f(1, i) << endl;
    // }
    int n, m;
    cin >> n >> m;
    int ans = (f(n, m) * ((fact[m] * inv_fact[m - n]) % MOD)) % MOD;
    cout << ans << endl;
}
 
signed main() {
    ios_base::sync_with_stdio(false);
    cin.tie(NULL);
    cout.tie(NULL);
    int t = 1;
    // t = readInt();
    // cin >> t;
    for (int i = 1; i <= t; ++i) {
        // cout << "Case #" << i << ": ";
        solve();
    }
    // fast_flush();
    return 0;
}

/** Read */

static const int buf_size = 4096;

inline int fast_readchar() {
    static char buf[buf_size];
    static int len = 0, pos = 0;
    if (pos == len) pos = 0, len = fread(buf, 1, buf_size, stdin);
    if (pos == len) return -1;
    return buf[pos++];
}

inline int readUInt() {
    int c = fast_readchar(), x = 0;
    while (c <= 32) c = fast_readchar();
    while ('0' <= c && c <= '9') x = x * 10 + c - '0', c = fast_readchar();
    return x;
}

inline int readInt() {
    int s = 1, c = fast_readchar();
    int x = 0;
    while (c <= 32) c = fast_readchar();
    if (c == '-') s = -1, c = fast_readchar();
    while ('0' <= c && c <= '9') x = x * 10 + c - '0', c = fast_readchar();
    return x * s;
}

inline void readWord(char *s) {
    int c = fast_readchar();
    while (c <= 32) c = fast_readchar();
    while (c > 32) *s++ = c, c = fast_readchar();
    *s = 0;
}

/** Write */

static int write_pos = 0;
static char write_buf[buf_size];

inline void fast_writechar(int x) {
    if (write_pos == buf_size) fwrite(write_buf, 1, buf_size, stdout), write_pos = 0;
    write_buf[write_pos++] = x;
}

inline void fast_flush() {
    if (write_pos) fwrite(write_buf, 1, write_pos, stdout), write_pos = 0;
}

inline void writeInt(int x) {
    if (x < 0) fast_writechar('-'), x = -x;

    char s[24];
    int n = 0;
    while (x || !n) s[n++] = '0' + x % 10, x /= 10;
    while (n--) fast_writechar(s[n]);
}

inline void writeWord(const char *s) {
    while (*s) fast_writechar(*s++);
}