Cattle off NOIP summer camp seven days - to improve the Group 6C: Placement problems (number of combinations)

Meaning of the questions: A class of N individuals, B class M have personal, now make up a new class C class, to be fair, each drawn from the AB class the same number of people. Now find all the options, and the number of how many.

Idea: That is seeking Σ k * C (N, k ) * C (M, k); ignore the first outer layer k, a combination of two numbers to see how the product and demand. 

Obviously Σ C (N, k) * C (M, k) = C (N + M, N); as C (N, k) = C (N, Nk); N can be selected as the number Nk, M k-selected, so that a number of combinations.

Now look at how to deal with this k. Noting k * C (N, k) = N * C (N-1, k-1); they can engage in the: Σ k * C (N, k) * C (M, k) = Σ N * C (N-1, k-1) * C (M, k) = C (N + M-1, N-1);

Lucas then do it.

#include<bits/stdc++.h>
#define ll long long
#define rep(i,a,b) for(int i=a;i<=b;i++)
using namespace std;
const int Mod=19260817;
const int maxn=19260817;
int f[maxn],rev[maxn];
int qpow(int a,int x){
    int res=1; while(x){
        if(x&1) res=1LL*res*a%Mod;
        x>>=1; a=1LL*a*a%Mod;
    } return res;
}
void init()
{
    f[0]=rev[0]=1;
    rep(i,1,maxn-1) f[i]=1LL*f[i-1]*i%Mod;
    rev[maxn-1]=qpow(f[maxn-1],Mod-2);
    for(int i=maxn-2;i>=1;i--) rev[i]=1LL*rev[i+1]*(i+1)%Mod;
}
int C(int N,int M)
{
    if(N<M) return 0;
    return 1LL*f[N]*rev[M]%Mod*rev[N-M]%Mod;
}
int Lucas(ll N,ll M)
{
    if(M==0) return 1;
    return 1LL*Lucas(N/Mod,M/Mod)*C(N%Mod,M%Mod)%Mod;
}
int main()
{
    init();
    int T; ll N,M;
    scanf("%d",&T);
    while(T--){
        scanf("%lld%lld",&N,&M);
        printf("%d\n",2LL*M%Mod*Lucas(N+M-1,N-1)%Mod);
    }
    return 0;
}