BZOJ4175 : 小G的电话本

#include<cstdio>
#include<cstring>
typedef long long ll;
const int N=262144,K=17,inf=~0U>>2,S=27,M=200010,P=1005060097,G=5;
char s[M];
int n,m,x,i,j,k,C;
int a[N+10],b[N+10],tmp[N],tmp2[N],g[K+1],ng[K+1],inv[N+10],inv2;
int text[M],root,last,pos,need,remain,acnode,ace,aclen,size[M];
inline int min(int a,int b){return a<b?a:b;}
struct node{int st,en,lk,son[S];inline int len(){return min(en,pos+1)-st;}}tree[M];
inline int new_node(int st,int en=inf){return tree[++last].st=st,tree[last].en=en,last;}
inline int acedge(){return text[ace];}
inline void addedge(int node){
  if(need)tree[need].lk=node;
  need=node;
}
inline bool down(int node){
  if(aclen>=tree[node].len())return ace+=tree[node].len(),aclen-=tree[node].len(),acnode=node,1;
  return 0;
}
inline void init(){
  need=last=remain=ace=aclen=0;
  root=acnode=new_node(pos=-1,-1);
}
inline void extend(int c){
  text[++pos]=c;need=0;remain++;
  while(remain){
    if(!aclen)ace=pos;
    if(!tree[acnode].son[acedge()])tree[acnode].son[acedge()]=new_node(pos),addedge(acnode);
    else{
      int nxt=tree[acnode].son[acedge()];
      if(down(nxt))continue;
      if(text[tree[nxt].st+aclen]==c){aclen++;addedge(acnode);break;}
      int split=new_node(tree[nxt].st,tree[nxt].st+aclen);
      tree[acnode].son[acedge()]=split;
      tree[split].son[c]=new_node(pos);
      tree[nxt].st+=aclen;
      tree[split].son[text[tree[nxt].st]]=nxt;
      addedge(split);
    }
    remain--;
    if(acnode==root&&aclen)aclen--,ace=pos-remain+1;
    else acnode=tree[acnode].lk?tree[acnode].lk:root;
  }
}
void dfs(int x,int sum){
  sum+=tree[x].len();
  if(tree[x].en==inf&&pos-sum+1<=n)size[x]=1;
  for(int i=0;i<S;i++)if(tree[x].son[i]){
    int j=tree[x].son[i];
    dfs(j,sum),size[x]+=size[j];
  }
  if(size[x])a[size[x]]=(a[size[x]]+tree[x].len())%P;
}
inline int pow(int a,int b){int t=1;for(;b;b>>=1,a=1LL*a*a%P)if(b&1)t=1LL*t*a%P;return t;}
inline void NTT(int*a,int n,int t){
  for(int i=1,j=0;i<n-1;i++){
    for(int s=n;j^=s>>=1,~j&s;);
    if(i<j){int k=a[i];a[i]=a[j];a[j]=k;}
  }
  for(int d=0;(1<<d)<n;d++){
    int m=1<<d,m2=m<<1,_w=t==1?g[d]:ng[d];
    for(int i=0;i<n;i+=m2)for(int w=1,j=0;j<m;j++){
      int&A=a[i+j+m],&B=a[i+j],t=1LL*w*A%P;
      A=B-t;if(A<0)A+=P;
      B=B+t;if(B>=P)B-=P;
      w=1LL*w*_w%P;
    }
  }
  if(t==-1)for(int i=0,j=inv[n];i<n;i++)a[i]=1LL*a[i]*j%P;
}
void getinv(int*a,int*b,int n){
  if(n==1){b[0]=pow(a[0],P-2);return;}
  getinv(a,b,n>>1);
  int k=n<<1,i;
  for(i=0;i<n;i++)tmp[i]=a[i];
  for(i=n;i<k;i++)tmp[i]=b[i]=0;
  NTT(tmp,k,1),NTT(b,k,1);
  for(i=0;i<k;i++){
    b[i]=(ll)b[i]*(2-(ll)tmp[i]*b[i]%P)%P;
    if(b[i]<0)b[i]+=P;
  }
  NTT(b,k,-1);
  for(i=n;i<k;i++)b[i]=0;
}
inline void getln(int*a,int*b,int n){
  getinv(a,tmp2,n);
  int k=n<<1,i;
  for(i=0;i<n-1;i++)b[i]=(ll)a[i+1]*(i+1)%P;
  for(i=n-1;i<k;i++)b[i]=0;
  NTT(b,k,1),NTT(tmp2,k,1);
  for(i=0;i<k;i++)b[i]=(ll)b[i]*tmp2[i]%P;
  NTT(b,k,-1);
  for(i=n-1;i;i--)b[i]=(ll)b[i-1]*inv[i]%P;b[0]=0;
}
void getexp(int*a,int*b,int n){
  if(n==1){b[0]=1;return;}
  getexp(a,b,n>>1);
  getln(b,tmp,n);
  int k=n<<1,i;
  for(i=0;i<n;i++){tmp[i]=a[i]-tmp[i];if(tmp[i]<0)tmp[i]+=P;}
  if((++tmp[0])==P)tmp[0]=0;
  for(i=n;i<k;i++)tmp[i]=b[i]=0;
  NTT(tmp,k,1),NTT(b,k,1);
  for(i=0;i<k;i++)b[i]=(ll)b[i]*tmp[i]%P;
  NTT(b,k,-1);
  for(i=n;i<k;i++)b[i]=0;
}
int main(){
  scanf("%d%d%s",&m,&x,s+1);
  if(m>x)return puts("0"),0;
  n=std::strlen(s+1);
  for(i=1;i<=n;extend(s[i++]-‘a‘));extend(26);
  pos--,dfs(root,0);
  for(i=0;i<=x;i++)a[i]=1LL*a[i]*i%P;
  C=a[1],j=pow(C,P-2);
  for(i=0;i<x;i++)a[i]=1LL*a[i+1]*j%P;
  for(i=x;i<k;i++)a[i]=0;
  for(g[K]=pow(G,(P-1)/N),ng[K]=pow(g[K],P-2),i=K-1;~i;i--)g[i]=(ll)g[i+1]*g[i+1]%P,ng[i]=(ll)ng[i+1]*ng[i+1]%P;
  for(inv[1]=1,i=2;i<=N;i++)inv[i]=(ll)(P-inv[P%i])*(P/i)%P;inv2=inv[2];
  for(k=1;k<=x;k<<=1);
  getln(a,b,k);
  for(i=0;i<k;i++)b[i]=1LL*b[i]*m%P;
  getexp(b,a,k);
  return printf("%d",1LL*a[x-m]*pow(C,m)%P),0;
}