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)

//! 尺卂乃卂.卂ﾌ乇乇ㄒ
#include<bits/stdc++.h>
//#include <ext/pb_ds/detail/standard_policies.hpp>
using namespace std;
//Using namespace __gnu_pbds;
//typedef tree<int,null_type,less<int>,rb_tree_tag,tree_order_statistics_node_update> Ordered_set;

#define ll              long long
#define int             long long
#define ld             long double
#define pb              push_back
#define pii             pair<int,int>
#define vi              vector<int>
#define vii             vector<vi>
#define vip            vector<pii>
#define mii             map<int,int>
#define mip             map<pair<int,int>,int>
#define mic             map<char,int> 
#define all(v)          v.begin(),v.end()  
#define pqb             priority_queue<int>
#define pqs             priority_queue<int,vi,greater<int> >
#define setbits(x)      __builtin_popcountll(x)
#define zrobits(x)      __builtin_ctzll(x)
#define lb(x)           (x&(-x))
#define mod             1000000007
#define inf             1e18
#define ps(x,y)         fixed<<setprecision(y)<<x
#define w(x)            int x; cin>>x; while(x--)
#define itr(it,v)          for(auto it:v)
#define show(arr,n)     for(int i=0;i<n;i++) cout<<arr[i]<<" "; cout<<"\n";
#define fi(i,n)         for(int i=0;i<n;i++)
#define fir(i,k,n)       for(int i=k;k<n?i<n:i>n;k<n?i+=1:i-=1)
#define ff               first 
#define ss               second
#define deb(x) cout << #x << "=" << x << endl
#define FIO ios_base::sync_with_stdio(0); cin.tie(0); cout.tie(0);
#define check(x) (x && cout<<"Yes\n")||(cout<<"No\n");
#define fin(s)          freopen(s,"r",stdin);  
#define fout(s)         freopen(s,"w",stdout);

const ld pi = 3.141592653589793238462643383279502884;
const int xd[]={-1,0,1,0};
const int yd[]={0,-1,0,1};
int XX[] = { -1, -1, -1, 0, 0, 1, 1, 1 };
int YY[] = { -1, 0,  1, -1, 1, -1, 0, 1 };

int expo(int a,int b,int m);
int mmi(int a,int m);
void ipgraph(int m);

const int N=5*(1e5)+10;
vii adj(N);
int a[N];
int inv[N];
int fac[N];
int invfac[N];
void infac(){
    fac[0]=fac[1]=1;
    for(int i=2;i<N;i++){
        fac[i]=(i*fac[i-1])%mod;
    }
}
void ininv(){
   inv[0]=inv[1]=1;
   for(int i=2;i<N;i++){
       inv[i]=(inv[mod%i]*(mod-mod/i))%mod;
   } 
}
void ininvfac(){
   invfac[0]=invfac[1]=1;
   for(int i=2;i<N;i++){
       invfac[i]=(inv[i]*invfac[i-1])%mod;
   } 
}
int ncr(int n,int r){
    int ans=(((fac[n]*invfac[r])%mod)*invfac[n-r])%mod;
    return ans;
}
int32_t main(){
    
    FIO
    int n,m; cin>>n>>m;
    infac();
    ininv();
    ininvfac();
    int ans=0;
    for(int j=0;j<=n;j++){
        if(j%2==0){
            ans=(ans+(ncr(n,j)*((ncr(m-j,n-j)*fac[n-j])%mod))%mod)%mod;
        }
        else{
            ans=(ans+mod-(ncr(n,j)*((ncr(m-j,n-j)*fac[n-j])%mod))%mod)%mod;
        }
    }
    cout<<(ans*((ncr(m,n)*fac[n])%mod))%mod<<"\n";
    return 0;

}

void ipgraph(int m){
    int i, u, v;
    while(m--){
          cin>>u>>v;
         u--, v--;
    adj[u].pb(v);
    adj[v].pb(u);
    }
}
int expo(int a,int b,int m){
    if(b==0) return 1;
    if(b==1) return a;
    int val=(expo(a,b/2,m)*expo(a,b/2,m))%m;
    if(b & 1) return (val*a)%m;
    else return val;
}
int mmi(int a,int m){
    return expo(a,m-2,m);
}