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Embedded systems, C/C++, GNU/Linux, and Infosec

Sep 3, 2019 - 4 minute read - Comments - solution

2019 CTS

#include<bits/stdc++.h>
#define int long long
#define debug(...) fprintf(stderr,__VA_ARGS__)
#define DEBUG printf("Passing [%s] in LINE %d\n",__FUNCTION__,__LINE__)
#define Debug debug("Passing [%s] in LINE %d\n",__FUNCTION__,__LINE__)
#define all(x) x.begin(),x.end()
#define x first
#define y second
using namespace std;
typedef long long ll;
typedef pair<int,int> pii;
const double eps=1e-8;
const double pi=acos(-1.0);
template<class T>int chkmin(T &a,T b){return a>b?a=b,1:0;}
template<class T>int chkmax(T &a,T b){return a<b?a=b,1:0;}
template<class T>T sqr(T a){return a*a;}
template<class T>T mmin(T a,T b){return a<b?a:b;}
template<class T>T mmax(T a,T b){return a>b?a:b;}
template<class T>T aabs(T a){return a<0?-a:a;}
template<class T>int dcmp(T a,T b){return a>b;}
template<int *a>int cmp_a(int x,int y){return a[x]<a[y];}
#define min mmin
#define max mmax
#define abs aabs
namespace io {
    const int SIZE = (1 << 21) + 1;
    char ibuf[SIZE], *iS, *iT, obuf[SIZE], *oS = obuf, *oT = oS + SIZE - 1, c, qu[55]; int f, qr;
    // getchar
    #define gc() (iS == iT ? (iT = (iS = ibuf) + fread (ibuf, 1, SIZE, stdin), (iS == iT ? EOF : *iS ++)) : *iS ++)
    // print the remaining part
    inline void flush () {
        fwrite (obuf, 1, oS - obuf, stdout);
        oS = obuf;
    }
    // putchar
    inline void putc (char x) {
        *oS ++ = x;
        if (oS == oT) flush ();
    }
    // input a signed integer
    inline bool read (signed &x) {
        for (f = 1, c = gc(); c < '0' || c > '9'; c = gc()) if (c == '-') f = -1;else if(c==EOF)return 0;
        for (x = 0; c <= '9' && c >= '0'; c = gc()) x = x * 10 + (c & 15); x *= f;
        return 1;
    }

    inline bool read (long long &x) {
        for (f = 1, c = gc(); c < '0' || c > '9'; c = gc()) if (c == '-') f = -1;else if(c==EOF)return 0;
        for (x = 0; c <= '9' && c >= '0'; c = gc()) x = x * 10 + (c & 15); x *= f;
        return 1;
    }
    inline bool read (char &x) {
        x=gc();
        return x!=EOF;
    }
    inline bool read(char *x){
        while((*x=gc())=='\n' || *x==' '||*x=='\r')if(*x==EOF)return 0;
        while(!(*x=='\n'||*x==' '||*x=='\r'||*x==EOF))*(++x)=gc();
        *x=0;
        return 1;
    }
    template<typename A,typename ...B>
    inline bool read(A &x,B &...y){
        return read(x)&&read(y...);
    }
    // print a signed integer
    inline bool write (signed x) {
        if (!x) putc ('0'); if (x < 0) putc ('-'), x = -x;
        while (x) qu[++ qr] = x % 10 + '0',  x /= 10;
        while (qr) putc (qu[qr --]);
        return 0;
    }

    inline bool write (long long x) {
        if (!x) putc ('0'); if (x < 0) putc ('-'), x = -x;
        while (x) qu[++ qr] = x % 10 + '0',  x /= 10;
        while (qr) putc (qu[qr --]);
        return 0;
    }
    inline bool write (char x) {
        putc(x);
        return 0;
    }
    inline bool write(const char *x){
        while(*x){putc(*x);++x;}
        return 0;
    }
    inline bool write(char *x){
        while(*x){putc(*x);++x;}
        return 0;
    }
    template<typename A,typename ...B>
    inline bool write(A x,B ...y){
        return write(x)||write(y...);
    }
    //no need to call flush at the end manually!
    struct Flusher_ {~Flusher_(){flush();}}io_flusher_;
}
using io :: read;
using io :: putc;
using io :: write;
int inf;
struct _init_{
    _init_(){
        memset(&inf,0x3f,sizeof(inf));
    }
};
const int p=998244353,yg=3,ig=332748118;
const int N=1<<18,M=N|5;
int fac[200005],inv[200005],invf[200005];
int fpm(int a,int b){
    if(a<0)a+=p;
    int c=1;
    for(;b;b>>=1,a=a*a%p)if(b&1)c=c*a%p;
    return c;
}
int rev[M],f[M],g[M],h[M],s[M],t[M];
void NTT(int *a,int n,int flg){
    for(int i=1;i<n;++i){
        rev[i]=(rev[i>>1]>>1)|((i&1)*(n>>1));
        if(i<rev[i])swap(a[i],a[rev[i]]);
    }    
    for(int i=1;i<n;i<<=1){
        int w=fpm(flg==1?yg:ig,(p-1)/(i<<1)),ww;
        for(int j=0;j<n;j+=i+i){
            ww=1;
            for(int k=0;k<i;++k){
                int u=a[j+k],v=a[j+k+i];
                a[j+k]=(u+ww*v)%p;
                a[j+k+i]=((u-ww*v)%p+p)%p;
                ww=ww*w%p;
            }
        }
    }
    if(flg==-1){
        int w=fpm(n,p-2)%p;
        for(int i=0;i<n;++i)a[i]=a[i]*w%p;
    }
}
int C(int a,int b){return fac[a]*invf[b]%p*invf[a-b]%p;}
signed main(){
#ifdef QAQAutoMaton 
    freopen("pearl.in","r",stdin);
    freopen("pearl.out","w",stdout);
#endif
    int d,n,m;
    read(d,n,m);
    if(n-m*2<0)return write("0\n");
    int XD=d*2+5;
    fac[0]=fac[1]=inv[1]=invf[0]=invf[1]=1;
    for(int i=2;i<=XD;++i){
        fac[i]=fac[i-1]*i%p;
        inv[i]=(p-p/i)*inv[p%i]%p;
        invf[i]=inv[i]*invf[i-1]%p;
    }
    int w=min(n-m*2,d);
    for(int i=0;i<=w;++i){
        h[d-i]=invf[d-i];
    }
    for(int i=0;i<=d;++i)g[i]=invf[i];
    NTT(h,N,1);
    NTT(g,N,1);
    for(int i=0;i<N;++i){g[i]=g[i]*h[i]%p;h[i]=0;}
    NTT(g,N,-1);
    int x=1;
    for(int i=0;i<=w;++i){
        h[i]=g[d-i]*fac[d]%p*invf[i]%p*x%p;
        x=x*(p-2)%p;
    }
    for(int i=0;i<N;++i)g[i]=0;
    int i2=fpm(2,p-2)%p;
    for(int i=0;i<=w;++i)s[0]=(s[0]+h[i])%p;
    h[0]=0;
    for(int i=1;i<=w+1;++i){h[i]=h[i]*invf[i-1]%p;}
    for(int i=1;i<=XD;++i)g[XD-i]=fac[i-1];
    NTT(h,N,1);
    NTT(g,N,1);
    for(int i=0;i<N;++i)f[i]=h[i]*g[i]%p;
    NTT(f,N,-1);
    
    int ans=0;
    t[0]=1;
    for(int i=1;i<=d;++i){
        s[i]=f[XD-i]%p*invf[i]%p*(i&1?p-1:1)%p;
        t[i]=C(d,i);
    }
    NTT(s,N,1);
    NTT(t,N,1);
    for(int i=0;i<N;++i)f[i]=s[i]*t[i]%p;
    NTT(f,N,-1);
    for(int i=0;i<=d;++i){
        ans=(ans+fpm(i+i-d,n)*f[i])%p;
    }
    ans=ans*fpm(i2,d)%p;
    write(ans,'\n');
    return 0;
}

Tags: c++

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