"JSOI2012" Snack generation function FFT

we construct $f (x) $ of generating function $g (x) $, then obviously $[x^k]g (x) =ok^2+sk+u$

So obviously, the answer is $\sum_{i=1}^{n} [X^m]g^i (x) $

We construct the generating function of the answer $f (x) =\sum_{i=1}^{n} g^i (x) $

According to the geometric series summation formula, $F (x) =\dfrac{1-g (x)}{1-g^{a+1} (x)}$

If you go to geometric series sum, you need polynomial fast power + polynomial inversion, time complexity is obviously $o (m\ log\ m) $.

However, this modulus is not a prime number, so it is not very good to engage.

We can calculate the value of $\sum_{i-1}^{2^k-1}g^i (x) $ in a way that is similar to a fast power.

The time complexity is obviously $o (m\ log\ m\ log\ A) $.

And then it's gone.

The first time I launch a generating function of the problem flattered

1#include <bits/stdc++.h>2 #defineMOD 9982443533 #defineL Long Long4 #defineM 1<<155 #defineG 36 using namespacestd;7 8 l Pow_mod (l x,l k) {9L ans=1;Ten      while(k) { One         if(k&1) ans=ans*x%MOD; AX=x*x%mod; k>>=1; -     } -     returnans; the } - voidChange (L a[],intN) { -      for(intI=0, j=0; i<n-1; i++){ -         if(i<j) Swap (A[i],a[j]); +         intK=n>>1; -          while(j>=k) j-=k,k>>=1; +j+=K; A     } at } - voidNTT (L a[],intNintOn ) { - Change (a,n); -      for(intH=2; h<=n;h<<=1){ -L Wn=pow_mod (G, (mod-1)/h); -          for(intj=0; j<n;j+=h) { inL w=1; -              for(intk=j;k<j+ (h>>1); k++){ toL u=a[k],t=w*a[k+ (h>>1)]%MOD; +a[k]= (u+t)%MOD; -a[k+ (h>>1)]= (u-t+mod)%MOD; thew=w*wn%MOD; *             } $         }Panax Notoginseng     } -     if(on==-1){ theL Inv=pow_mod (n,mod-2); +          for(intI=0; i<n;i++) a[i]=a[i]*inv%MOD; AReverse (A +1, A +n); the     } + } - L m,p,a,o,s,u; $L g[m]={0},gsum[m]={0},ans[m]={0}; $  - intMain () { -Cin>>m>>p>>a>>o>>s>>U; the      for(L i=1; i<=m;i++) g[i]= (o*i*i+s*i+u)%P; -     intlen=1; while(Len<= (m*2)) len<<=1;Wuyigsum[0]=1; theA=min (a,m); -      while(A) { Wu          -         if(a&1){ AboutNTT (Ans,len,1); NTT (G,len,1); $              for(intI=0; i<len;i++) ans[i]=ans[i]*g[i]%MOD; -NTT (ans,len,-1); NTT (g,len,-1); -              for(intI=1; i<=m;i++)  -Ans[i]= (Ans[i]+g[i]+gsum[i])%P; A              for(inti=m+1; i<len;i++) ans[i]=0;  +         } thea>>=1; -          $g[0]++; theNTT (G,len,1); NTT (Gsum,len,1); the          for(intI=0; i<len;i++) gsum[i]=gsum[i]*g[i]%MOD; theNTT (g,len,-1); NTT (gsum,len,-1); theg[0]--; -          for(intI=0; i<len;i++)if(i>m) gsum[i]=0;Elsegsum[i]%=P; in          theNTT (G,len,1);  the          for(intI=0; i<len;i++) g[i]=g[i]*g[i]%MOD; AboutNTT (g,len,-1); the          for(intI=0; i<len;i++)if(i>m) g[i]=0;Elseg[i]%=P; the     } thecout<<ans[m]<<Endl; +}

"JSOI2012" Snack generation function FFT