[51nod 1538] a problem--characteristic polynomial, polynomial modulus

The problem is equivalent to selecting a number of scenarios where the ball is arranged so that the total weight is n

Apparently F[n]=∑f[n-ai]

Here AI will go to 23333, direct write O (N^2logn) of the brute force solution will tle consider using polynomial modulo + multiplication to find x^n mod h (x)

Kathang time limit 5s at the beginning of the machine ran 20s is running but pay attention to the rapid power of the high to the low when the calculation so long as the logn time to take the mold and not 2logn times there is no need for the number of the time to delete this can keep the length of 65536

Preprocessing rotation factor is much faster

#include "bits/stdc++.h" using namespace std;
typedef long Long LL;

const int n=66666,m=1000005,p=104857601,g=3,l=23333;
	int power (int a,int t) {int r=1;
		while (t) {if (t&1) r= (LL) r*a%p;
	A= (LL) a*a%p;t>>=1;
} return R;

} int _wn[25],z[25][n];
	void NTT (int a[],int len,int DFT) {int i,j=len>>1,k,l,u,v,inv;
		for (i=1;i<len-1;i++) {if (i<j) swap (a[i],a[j]);
	For (k=len>>1; (j^=k) <k;k>>=1);
		} if (!_wn[0]) {int c=0,w,wn;
		for (_wn[i=22]=39193363;i;i--) _wn[i-1]= (LL) _wn[i]*_wn[i]%p; For (l=2;l<= (1<<16), l<<=1) for (i=l>>1,wn=_wn[++c],j=0;j< (1<<16); j+=l) for (w=1,k=j;k
	<j+i;k++,w= (LL) w*wn%p) z[c][k]=w;
	} int c=0,*w; for (l=2;l<=len;l<<=1) for (i=l>>1,w=z[++c],j=0;j<len;j+=l) for (k=j;k<j+i;k++) u=A[k],v= (LL) A[
	k+i]*w[k]%p,a[k]= (u+v)%p,a[k+i]= (u-v+p)%P;
		if (dft==-1) {inv=power (len,p-2);
		for (i=0;i<len;i++) a[i]= (LL) a[i]*inv%p; 
	for (i=1;i<len/2;i++) swap (a[i],a[len-i]); }} int W1[n],w2[n],w3[n];
	void Convol (int a[],int b[],int r[],int len) {memcpy (w1,a,len<<2);
	memcpy (W2,B,LEN&LT;&LT;2);
	NTT (w1,len,1);
	NTT (w2,len,1);
	for (int i=0;i<len;i++) w3[i]= (LL) w1[i]*w2[i]%p;
	NTT (w3,len,-1);
memcpy (R,W3,LEN&LT;&LT;2);

} int wi1[n],wi2[n],wi3[n],wi4[n];
	void inverse (int a[],int t[],int len) {if (len==1) {t[0]=power (a[0],p-2); return;}
	Inverse (a,wi1,len>>1);
	memset (wi2,0,len<<3);
	memset (wi3,0,len<<3);
	memcpy (wi2,wi1,len<<1);
	memcpy (WI3,A,LEN&LT;&LT;2);
	NTT (wi2,len<<1,1);
	NTT (wi3,len<<1,1);
	for (int i=0;i< (len<<1); i++) wi4[i]= ((2*wi2[i]-(LL) wi2[i]*wi2[i]%p*wi3[i])%p+p)%P;
	NTT (wi4,len<<1,-1);
memcpy (T,WI4,LEN&LT;&LT;2);

} int wm1[n],wm2[n],wm3[n],wm4[n];
	void modulo (int a[],int b[],int r[],int len) {int dega,degb,degc;
	for (Dega=len;dega&&a[dega]==0;--dega);
	for (DEGB=LEN;DEGB&AMP;&AMP;B[DEGB]==0;--DEGB);
	if (DEGA&LT;DEGB) {for (int i=0;i<len;i++) R[i]=a[i];return;}
	DEGC=DEGA-DEGB; memset (wm1,0, len<<2);
	memset (WM2,0,LEN&LT;&LT;2);
	memset (WM3,0,LEN&LT;&LT;2);
	memset (WM4,0,LEN&LT;&LT;2);
	for (int i=0;i<=degc;i++) wm1[i]=a[dega-i];
	for (int i=0;i<=degb;i++) wm2[i]=b[degb-i];
	Inverse (wm2,wm3,len>>1);
	for (int i=degc+1;i<len;i++) wm3[i]=0;
	Convol (Wm1,wm3,wm4,len);
	memset (WM1,0,LEN&LT;&LT;2);
	for (int i=0;i<=degc;i++) wm1[degc-i]=wm4[i];
	memset (WM2,0,LEN&LT;&LT;2);
	memcpy (WM2,B,DEGB+1&LT;&LT;2);
	Convol (Wm1,wm2,wm3,len);
for (int i=0;i<=dega;i++) r[i]= (a[i]-wm3[i]+p)%P;

} int wl1[n],wl2[n];
	void Sqr (int a[],int d[],int len) {memset (wl1,0,len<<2);
	memset (WL2,0,LEN&LT;&LT;2);
	memcpy (wl1,a,len<<1);
	NTT (wl1,len,1);
	for (int i=0;i<len;i++) wl1[i]= (LL) wl1[i]*wl1[i]%p;
	NTT (wl1,len,-1);
	Modulo (Wl1,d,wl2,len);
memcpy (a,wl2,len<<1);
	} void work (int w[],int mod[],int len,ll t) {int l=0,i;
	while ((1ll<<l) <=t) ++l;
	while ((t>>l) <=l)--l;
	w[t>>l+1]=1;
		while (l>=0) {sqr (W,mod,len);
if ((t>>l) &1) {			for (int i=l;i>=1;i--) w[i]=w[i-1];
			w[0]=0;
			for (int i=0;i<l;i++) w[i]= ((w[i]-(LL) w[l]*mod[i])%p+p;
		w[l]=0;
	}--l;
}} int n,a[m],a,b,w[n],mo[n],res[n];

LL m;
	int main () {cin>>n>>m>>a[1]>>a>>b;
	for (int i=2;i<=n;i++) a[i]= ((LL) a[i-1]*a+b)%l+1;
	for (int i=1;i<=n;i++) if (a[i]<=23333) w[a[i]]++;
	for (int i=mo[l]=1;i<=l;i++) mo[l-i]= (p-w[i])%P;
	Work (RES,MO,1&LT;&LT;16,M+L-1);
	printf ("%d\n", Res[l-1]);
return 0; }