求组合数

第一类时mod为素数

typedef long long LL;

LL n,m,p;

LL quick_mod(LL a, LL b)
{
    LL ans = 1;
    a %= p;
    while(b)
    {
        if(b & 1)
        {
            ans = ans * a % p;
            b--;
        }
        b >>= 1;
        a = a * a % p;
    }
    return ans;
}

LL C(LL n, LL m)
{
    if(m > n) return 0;
    LL ans = 1;
    for(int i=1; i<=m; i++)
    {
        LL a = (n + i - m) % p;
        LL b = i % p;
        ans = ans * (a * quick_mod(b, p-2) % p) % p;
    }
    return ans;
}

LL Lucas(LL n, LL m)
{
    if(m == 0) return 1;
    return C(n % p, m % p) * Lucas(n / p, m / p) % p;
}

第二类时mod可以为合数

typedef long long LL;
const int N = 200005;

bool prime[N];
int p[N];
int cnt;

void isprime()
{
    cnt = 0;
    memset(prime,true,sizeof(prime));
    for(int i=2; i<N; i++)
    {
        if(prime[i])
        {
            p[cnt++] = i;
            for(int j=i+i; j<N; j+=i)
                prime[j] = false;
        }
    }
}

LL quick_mod(LL a,LL b,LL m)
{
    LL ans = 1;
    a %= m;
    while(b)
    {
        if(b & 1)
        {
            ans = ans * a % m;
            b--;
        }
        b >>= 1;
        a = a * a % m;
    }
    return ans;
}

LL Work(LL n,LL p)
{
    LL ans = 0;
    while(n)
    {
        ans += n / p;
        n /= p;
    }
    return ans;
}

LL Solve(LL n,LL m,LL P)
{
    LL ans = 1;
    for(int i=0; i<cnt && p[i]<=n; i++)
    {
        LL x = Work(n, p[i]);
        LL y = Work(n - m, p[i]);
        LL z = Work(m, p[i]);
        x -= (y + z);
        ans *= quick_mod(p[i],x,P);
        ans %= P;
    }
    return ans;
}

int main()
{
    int T;
    isprime();
    cin>>T;
    while(T--)
    {
        LL n,m,P;
        cin>>n>>m>>P;
        n += m - 2;
        m--;
        cout<<Solve(n,m,P)<<endl;
    }
    return 0;
}