HOJ 13101 The Triangle Division of the Convex Polygon（数论求卡特兰数（模不为素数））

　　for i = 1 to k
   　　 q  = s
   　　 num(i) = 0
   　　 while q > 0
      　　  q = q / pi
    　　    num(i) += q
    　　end while
　　end for

#include <climits>
#include <cstdio>
#include <cstring>
#include <cctype>
#include <cmath>
#include <ctime>
#include <cstdlib>
#include <cstdarg>
#include <iostream>
#include <fstream>
#include <iomanip>
#include <sstream>
#include <exception>
#include <stdexcept>
#include <memory>
#include <locale>
#include <bitset>
#include <deque>
#include <list>
#include <map>
#include <set>
#include <queue>
#include <stack>
#include <vector>
#include <algorithm>
#include <iterator>
#include <functional>
#include <string>
#include <complex>
#include <valarray>

using namespace std;

typedef long long ll;

const int N = 1e6+7;

bool tag[N];
int p[N>>3];
int t;

void prime() {
    t = 0;
    memset(tag, 0, sizeof tag);
    p[t++] = 2, tag[4] = 0;
    for(int i = 3; i < N; i += 2) {
        if(!tag[i]) p[t++] = i;
        for(int j = 0, k; j < t && (k = i * p[j]) < N; ++j) {
            tag[k] = 1;
            if(i % p[j] == 0) break;
        }
    }
    return ;
}

int n;
ll m, ans;

int zp[N>>3], mp[N>>3];
int tz, tp;

int Factor(int q[], int u) {   //分解 n!
    int i;
    for( i = 0; i < t && p[i] <= u; ++i) {
        int v = u;
        while(v) {
            v /= p[i];
            q[i] += v;
        }
    }
    return i;
}

void cat(int n) {
    int nn = n + n;
    tz = tp = 0;
    memset(zp, 0, sizeof zp);
    memset(mp, 0, sizeof mp);

    tz = Factor(zp, nn);
    tp = Factor(mp, n);
    tp = Factor(mp, n+1);

    for(int i = 0; i < tp; ++i) zp[i] -= mp[i];

    return ;
}

ll mult_mod(int a, int b, ll m) {
    ll res = 1LL, tt = (ll) a;
    while(b) {
        if(b&1) res = (res * tt) % m;
        tt = tt * tt % m;
        b >>= 1;
    }
    return res;
}

void solve() {
    n -= 2;
    cat(n);
    ans = 1LL;
    for(int i = 0; i < tz; ++i) {
        ans = (ans * mult_mod(p[i], zp[i], m)) % m;
    }
    printf("%I64d\n", ans);
}

int main()
{
#ifdef PIT
    freopen("c.in", "r", stdin);
#endif // PIT
    prime();
    while (~scanf("%d %I64d", &n, &m)) {
        solve();
    }

    return 0;
}