lucas定理求组合数+错排模板

int jc[M];
int f[M];

int ksm(int a,int b){
    int res=1;
    while(b){
        if(b&1)res=res*a%mod;
        a=a*a%mod;
        b>>=1;
    }return res%mod;
}
int c(int a,int b){
    return jc[a]%mod*ksm(jc[b]*jc[a-b]%mod,mod-2)%mod;
}
int lucas(int a,int b){
    if(!b)return 1;
    return (lucas(a/mod,b/mod)*c(a%mod,b%mod))%mod;
}
int n,m;
void solve(){
    cin>>n>>m;
    if(n==m){
        cout<<1<<endl;
    }else if(n-m==1){
        cout<<0<<endl;   
    }else if(m==0){
        cout<<f[n]<<endl;
    }else{
        int ans= (f[n-m]%mod*lucas(n,m))%mod;
        cout<<ans<<endl;
    }
}

signed main()
{
  ios::sync_with_stdio(false),cin.tie(0);cout.tie(0);
  int T=1;
  cin>>T;
  f[1]=0;f[2]=1;
  jc[1]=1;jc[2]=2;
  for(int i=3;i<=1e6;i++){
    f[i]=((i-1)*(f[i-1]+f[i-2])%mod)%mod;
    jc[i]=jc[i-1]*i%mod;
  }
  while(T--){
  solve();
  }

  return 0;
}