hdu 6036 NTT取模（板子）+组合数学

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//china no.1
#pragma comment(linker, "/STACK:1024000000,1024000000")
#include <vector>
#include <iostream>
#include <string>
#include <map>
#include <stack>
#include <cstring>
#include <queue>
#include <list>
#include <stdio.h>
#include <set>
#include <algorithm>
#include <cstdlib>
#include <cmath>
#include <iomanip>
#include <cctype>
#include <sstream>
#include <functional>
#include <stdlib.h>
#include <time.h>
#include <bitset>
using namespace std;

#define pi acos(-1)
#define s_1(x) scanf("%d",&x)
#define s_2(x,y) scanf("%d%d",&x,&y)
#define s_3(x,y,z) scanf("%d%d%d",&x,&y,&z)
#define s_4(x,y,z,X) scanf("%d%d%d%d",&x,&y,&z,&X)
#define S_1(x) scan_d(x)
#define S_2(x,y) scan_d(x),scan_d(y)
#define S_3(x,y,z) scan_d(x),scan_d(y),scan_d(z)
#define PI acos(-1)
#define endl '\n'
#define srand() srand(time(0));
#define me(x,y) memset(x,y,sizeof(x));
#define foreach(it,a) for(__typeof((a).begin()) it=(a).begin();it!=(a).end();it++)
#define close() ios::sync_with_stdio(0); cin.tie(0);
#define FOR(x,n,i) for(int i=x;i<=n;i++)
#define FOr(x,n,i) for(int i=x;i<n;i++)
#define fOR(n,x,i) for(int i=n;i>=x;i--)
#define fOr(n,x,i) for(int i=n;i>x;i--)
#define W while
#define sgn(x) ((x) < 0 ? -1 : (x) > 0)
#define bug printf("***********\n");
#define db double
#define ll long long
#define mp make_pair
#define pb push_back
typedef long long LL;
typedef pair <int, int> ii;
const int INF=0x3f3f3f3f;
const LL LINF=0x3f3f3f3f3f3f3f3fLL;
const int dx[]={-1,0,1,0,1,-1,-1,1};
const int dy[]={0,1,0,-1,-1,1,-1,1};
const int maxn=4e3+10;
const int maxx=4e5+10;
const double EPS=1e-8;
const double eps=1e-8;
const int mod=1e9+7;
template<class T>inline T min(T a,T b,T c) { return min(min(a,b),c);}
template<class T>inline T max(T a,T b,T c) { return max(max(a,b),c);}
template<class T>inline T min(T a,T b,T c,T d) { return min(min(a,b),min(c,d));}
template<class T>inline T max(T a,T b,T c,T d) { return max(max(a,b),max(c,d));}
template <class T>
inline bool scan_d(T &ret){char c;int sgn;if (c = getchar(), c == EOF){return 0;}
while (c != '-' && (c < '0' || c > '9')){c = getchar();}sgn = (c == '-') ? -1 : 1;ret = (c == '-') ? 0 : (c - '0');
while (c = getchar(), c >= '0' && c <= '9'){ret = ret * 10 + (c - '0');}ret *= sgn;return 1;}

inline bool scan_lf(double &num){char in;double Dec=0.1;bool IsN=false,IsD=false;in=getchar();if(in==EOF) return false;
while(in!='-'&&in!='.'&&(in<'0'||in>'9'))in=getchar();if(in=='-'){IsN=true;num=0;}else if(in=='.'){IsD=true;num=0;}
else num=in-'0';if(!IsD){while(in=getchar(),in>='0'&&in<='9'){num*=10;num+=in-'0';}}
if(in!='.'){if(IsN) num=-num;return true;}else{while(in=getchar(),in>='0'&&in<='9'){num+=Dec*(in-'0');Dec*=0.1;}}
if(IsN) num=-num;return true;}

void Out(LL a){if(a < 0) { putchar('-'); a = -a; }if(a >= 10) Out(a / 10);putchar(a % 10 + '0');}
void print(LL a){ Out(a),puts("");}
//freopen( "in.txt" , "r" , stdin );
//freopen( "data.txt" , "w" , stdout );
//cerr << "run time is " << clock() << endl;

const int N = 100005;
const int MOD = 985661441;

int e[20],m,k,n;
int g
,ans[20];
int pa[2]
;

namespace NTT
{
const int G = 3;
const int NUM = 20;
int wn[20];
int mul(int x, int y)
{
return (LL)x*y%MOD;
}
int PowMod(int a, int b)
{
int res = 1;
a %= MOD;
while (b)
{
if (b&1) res = mul(res, a);
a = mul(a, a);
b >>= 1;
}
return res;
}
void GetWn()
{
for (int i = 0; i < NUM; i++)
{
int t = 1<<i;
wn[i] = PowMod(G, (MOD-1)/t);
}
}
void Change(int a[], int len)
{
int i, j, k;
for (i = 1, j = len/2; i < len-1; i++)
{
if (i < j) swap(a[i], a[j]);
k = len/2;
while (j >= k)
{
j -= k;
k /= 2;
}
if (j < k) j += k;
}
}
void NTT(int a[], int len, int on)
{
Change(a, len);
int id = 0;
for (int h = 2; h <= len; h <<= 1)
{
id++;
for (int j = 0; j < len; j += h)
{
int w = 1;
for (int k = j; k < j + h/2; k++)
{
int u = a[k] % MOD;
int t = mul(a[k+h/2], w);
a[k] = (u+t) % MOD;
a[k+h/2] = ((u-t)%MOD + MOD) % MOD;
w = mul(w, wn[id]);
}
}
}
if (on == -1)
{
for (int i = 1; i < len/2; i++)
swap(a[i], a[len-i]);
int inv = PowMod(len, MOD-2);
for (int i = 0; i < len; i++)
a[i] = mul(a[i], inv);
}
}
}

int a[N<<3],b[N<<3];
namespace COMB
{
int F[N<<1], Finv[N<<1], inv[N<<1];
void init()
{
inv[1] = 1;
for (int i = 2; i < N<<1; i++)
{
inv[i] = (LL)(MOD - MOD/i) * inv[MOD%i] % MOD;
}
F[0] = Finv[0] = 1;
for (int i = 1; i < N<<1; i++)
{
F[i] = (LL)F[i-1] * i % MOD;
Finv[i] = (LL)Finv[i-1] * inv[i] % MOD;
}
}
int comb(int n, int m)
{
if (m < 0 || m > n) return 0;
return (LL)F
* Finv[n-m] % MOD * Finv[m] % MOD;
}
}
using namespace COMB;

int main()
{
int cas=1,len;
NTT::GetWn();
init();
W(s_2(m,k)!=EOF)
{
n=0;
FOR(1,m,i)
{
scanf("%*d%d",&e[i]);
n+=e[i];
}
++n;//sigma e_i
FOr(0,n,x)
{
g[x]=1;
FOR(1,m,i)
g[x]=(LL)g[x]*comb(e[i]+x-1,x-1)%MOD;
}
FOr(0,n,i)
{
a[i]=i%2?(MOD-Finv[i]):Finv[i];// (-1)^i/i!
b[i]=(LL)g[i]*Finv[i]%MOD;//F(x-i)/(x-i)!
}
len = 1;
while (len < n*2) len <<= 1;//get_len
for(int i=n;i<len;i++) a[i]=b[i]=0;
NTT::NTT(a,len,1);
NTT::NTT(b,len,1);
for(int i=0;i<len;i++) a[i]=NTT::mul(a[i],b[i]);
NTT::NTT(a,len,-1);
for(int i=0;i<n;i++)
a[i]=(LL)a[i]*F[i]%MOD;
me(ans,0);
a
=0;
int pre=1,cur=0;
FOr(1,n,x)
{
pre^=1,cur^=1;//优化，减少内存使用
pa[cur][0]=1;
FOR(1,k,i)
pa[cur][i]=(LL)pa[cur][i-1]*a[x]%MOD;
if(x>1)
FOR(1,k,i)
ans[i]=(ans[i]+(LL)pa[cur][i-1]*pa[pre][k-i+1])%MOD;
}
ans[1]=(ans[1]+pa[cur][k])%MOD;
printf("Case #%d:",cas++);
FOR(1,k,i) printf(" %d",ans[i]);
puts("");
}
}