bzoj1485: [HNOI2009]有趣的数列

 1 #include<cstdio>
 2 #include<cstring>
 3 #include<cstdlib>
 4 #include<algorithm>
 5 #include<iostream>
 6 
 7 using namespace std;
 8 
 9 void setIO(const string& s) {
10     freopen((s + ".in").c_str(), "r", stdin);
11     freopen((s + ".out").c_str(), "w", stdout);
12 }
13 template<typename Q> Q read(Q& x) {
14     static char c, f;
15     for(f = 0; c = getchar(), !isdigit(c); ) if(c == ‘-‘) f = 1;
16     for(x = 0; isdigit(c); c = getchar()) x = x * 10 + c - ‘0‘;
17     if(f) x = -x;
18     return x;
19 }
20 template<typename Q> Q read() {
21     static Q x; read(x); return x;
22 }
23 
24 typedef long long LL;
25 const int LIM = 2000000, N = 1000000;
26 
27 int mi[LIM+1], primes[N], tot;
28 bool flag[LIM+1];
29 
30 void get_prime(int n) {
31     for(int i = 2; i <= n; i++) {
32         if(!flag[i]) primes[tot] = i, mi[i] = tot++;
33         for(int j = 0; j < tot; j++) {
34             int k = primes[j];
35             if((LL) i * k > n) break;
36             flag[i * k] = 1;
37             if(i % k == 0) break;
38         }
39     }
40 }
41 
42 int num[N];
43 
44 void add(int x, int sign) {
45     for(int i = 0, k; k = primes[i], k * k <= x; i++) {
46         while(x % k == 0) {
47             num[i] += sign;
48             x /= k;
49         }
50     }
51     if(x ^ 1) num[mi[x]] += sign;
52 }
53 
54 LL qpow(LL a, int b, int p) {
55     a %= p;
56     for(LL c = 1; ; (a *= a) %= p) {
57         if(b & 1) (c *= a) %= p;
58         if(!(b >>= 1)) return c;
59     }
60 }
61 
62 int main() {
63 #ifdef DEBUG
64     freopen("in.txt", "r", stdin);
65     freopen("out.txt", "w", stdout);
66 #endif
67     
68     int n, p;
69     scanf("%d%d", &n, &p);
70     get_prime(n * 2);
71     for(int i = n * 2; i > n; i--) add(i, 1);
72     for(int i = n; i > 1; i--) add(i, -1);
73     add(n + 1, -1);
74     
75     int res = 1;
76     for(int i = 0; i < tot; i++) if(num[i]) {
77         res = (LL) res * qpow(primes[i], num[i], p) % p;
78     }
79     printf("%d\n", res);
80     
81     return 0;
82 }