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2020-02-07 13:50:00
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  1. 金神石的块数必须是6的倍数 g(x)=1+x^6+x^{12}+...=\frac 1{1-x^6}
  2. 木神石最多用9块 g(x)=1+x+x^2+...+x^9=\frac{1-x^{10}}{1-x}
  3. 水神石最多用5块 g(x)=1+x+x^2+...+x^5=\frac{1-x^6}{1-x}
  4. 火神石的块数必须是4的倍数 g(x)=1+x^4+x^8+...=\frac 1{1-x^4}
  5. 土神石最多用7块 g(x)=1+x+x^2+...+x^7=\frac{1-x^8}{1-x}

  6. 金神石的块数必须是2的倍数 g(x)=1+x^2+x^4+...=\frac 1{1-x^2}

  7. 木神石最多用1块 g(x)=1+x=\frac{1-x^2}{1-x}
  8. 水神石的块数必须是8的倍数 g(x)=1+x^8+x^{16}+...=\frac 1{1-x^8}
  9. 火神石的块数必须是10的倍数 g(x)=1+x^{10}+x^{20}+...=\frac 1{1-x^{10}}
  10. 土神石最多用3块 g(x)=1+x+x^2+x^3=\frac{1-x^4}{1-x}

\frac 1{1-x^6}\cdot\frac{1-x^{10}}{1-x}\cdot\frac{1-x^6}{1-x}\cdot\frac 1{1-x^4}\cdot\frac{1-x^8}{1-x}\cdot\frac 1{1-x^2}\cdot\frac{1-x^2}{1-x}\cdot\frac 1{1-x^8}\cdot\frac 1{1-x^{10}}\cdot\frac{1-x^4}{1-x}

=\frac1{(1-x)^5}

=\sum_{i=0}^\infty {i+4 \choose 4}x^i

\sum_{i=0}^\infty {i+k-1 \choose k-1}x^i=\frac1{(1-x)^k}

n项的系数是{n+4 \choose 4}需要FFT或NTT

#include<bits/stdc++.h>
namespace ZDY{
    #pragma GCC optimize(3)
    #define il __inline__ __attribute__ ((always_inline))
    #define register
    #define ll long long
    #define ull unsigned long long
    #define db double
    #define sht short
    #define MB template <class T>il
    #define Fur(i,x,y) for(int i(x);i<=y;++i)
    #define Fdr(i,x,y) for(int i(x);i>=y;--i)
    #define fl(i,x) for(int i(head[x]),to;to=e[i].to,i;i=e[i].nxt)
    #define clr(x,y) memset(x,y,sizeof(x))
    #define cpy(x,y) memcpy(x,y,sizeof(x))
    #define fin(s) freopen(s".in","r",stdin)
    #define fout(s) freopen(s".out","w",stdout)
    #define fcin ios::sync_with_stdio(false)
    #define l2(n) ((int)(log2(n)))
    #define inf 2122219134
    MB T ABS(T x){return x>0?x:-x;}
    MB T MAX(T x,T y){return x>y?x:y;}
    MB T MIN(T x,T y){return x<y?x:y;}
    MB T GCD(T x,T y){return y?GCD(y,x%y):x;}
    MB void SWAP(T &x,T &y){T t=x;x=y;y=t;}
}using namespace ZDY;using namespace std;
namespace IO{const int str=1<<20;static char in_buf[str],*in_s,*in_t;bool __=0;il char gc(){return (in_s==in_t)&&(in_t=(in_s=in_buf)+fread(in_buf,1,str,stdin)),in_s==in_t?__=1,EOF:*in_s++;}il void in(string &ch){ch.clear();if(__)return;char c;while((c=gc())!=EOF&&isspace(c));if(c==EOF){__=1;return;}ch+=c;while((c=gc())!=EOF&&!isspace(c))ch+=c;if(c==EOF)__=1;}il void in(char &ch){if(__)return;char c;while((c=gc())!=EOF&&isspace(c));if(c==EOF)__=1;else ch=c;}il void in(char *ch){*ch='\0';if(__)return;char c;while((c=gc())!=EOF&&isspace(c));if(c==EOF){__=1;return;}*ch=c;ch++;while((c=gc())!=EOF&&!isspace(c))*ch=c,ch++;if(c==EOF)__=1;*ch='\0';}template<typename T>il void in(T &x){if(__)return;char c=gc();bool f=0;while(c!=EOF&&(c<'0'||c>'9'))f^=(c=='-'),c=gc();if(c==EOF){__=1;return;}x=0;while(c!=EOF&&'0'<=c&&c<='9')x=x*10+c-48,c=gc();if(c==EOF)__=1;if(f)x=-x;}template<typename T,typename ... arr>il void in(T &x,arr & ... y){in(x),in(y...);}const char ln='\n';static char out_buf[str],*out_s=out_buf,*out_t=out_buf+str;il void flush(){fwrite(out_buf,1,out_s-out_buf,stdout);out_s=out_buf;}il void pt(char c){(out_s==out_t)?(fwrite(out_s=out_buf,1,str,stdout),*out_s++=c):(*out_s++=c);}il void out(const char* s){while(*s)pt(*s++);}il void out(char* s){while(*s)pt(*s++);}il void out(char c){pt(c);}il void out(string s){for(int i=0;s[i];i++)pt(s[i]);}template<typename T>il void out(T x){if(!x){pt('0');return;}if(x<0)pt('-'),x=-x;char a[50],t=0;while(x)a[t++]=x%10,x/= 10;while(t--)pt(a[t]+'0');}template<typename T,typename ... arr>il void out(T x,arr & ... y){out(x),out(y...);}}using namespace IO;
const int N=4000011,P=998244353,G=3,Gi=332748118;
char ch[N];
int n,limit=1,r[N],l=0;
int  n1[N],n2[N],n3[N],n4[N],ans[N];
int pw(int x,int p){
    int ans=1;
    for(;p;p>>=1,x=1ll*x*x%P)
        if(p&1)ans=1ll*ans*x%P;
    return ans;
}
il void ntt(int *A,int typ){
    Fur(i,0,limit-1)
        if(i<r[i])SWAP(A[i],A[r[i]]);
    for(int len=1;len<limit;len<<=1){
        int Wn=pw(~typ?G:Gi,(P-1)/(len<<1));
        for(int i=0;i<limit;i+=(len<<1)){
            int w=1;
            Fur(k,0,len-1){
                int t=1ll*w*A[i+k+len]%P;
                A[i+k+len]=(A[i+k]-t+P)%P;
                A[i+k]=(A[i+k]+t)%P;
                w=1ll*w*Wn%P;
            }
        }
    }
    if(~typ)return;
    int inv=pw(limit,P-2);
    Fur(i,0,limit-1)A[i]=1ll*A[i]*inv%P;
}
il void mul(int *A,int *B){
    ntt(A,1);ntt(B,1);
    Fur(i,0,limit-1)A[i]=1ll*A[i]*B[i]%P;
    ntt(A,-1);
}
int main(){
    in(ch);
    n=strlen(ch);
    while(limit<=n*4)++l,limit<<=1;
    Fur(i,0,limit-1)
        r[i]=(r[i>>1]>>1)|((i&1)<<(l-1));
    Fur(i,0,n-1)n1[i]=n2[i]=n3[i]=n4[i]=ch[n-i-1]-48;
    ++n1[0];
    n2[0]+=2;
    n3[0]+=3;
    n4[0]+=4;
    mul(n1,n2);
    mul(n1,n3);
    mul(n1,n4);
    ll x=0;
    Fdr(i,n-1,0)
        x=x*10+n1[i],ans[i]=x/24,x%=24;
    int len=n;
    Fur(i,0,n-1)ans[i+1]+=ans[i]/10,ans[i]%=10;
    while(ans[len]>9)ans[len+1]+=ans[len]/10,ans[len]%=10,++len;
    Fdr(i,len,0)out(ans[i]);
    flush();
}
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