[省选模拟]Rhyme

考的时候脑子各种短路，用个SAM瞎搞了半天没搞出来，最后中午火急火燎的打了个SPFA才混了点分。

其实这个可以把每个模式串长度为$K-1$的字符串看作一个状态，这个用字符串Hash实现，然后我们发现这实际上可以通过不断转移变成一个DAG，通过topsort即可算出最优解。

我怎么就那么脑残没想到呢..

//rhyme
//by Cydiater
//2017.2.19
#include <iostream>
#include <cstdio>
#include <queue>
#include <map>
#include <cstring>
#include <string>
#include <algorithm>
#include <cstdlib>
#include <cstdio>
#include <ctime>
#include <cmath>
#include <bitset>
#include <set>
#include <vector>
#include <complex>
using namespace std;
#define ll long long
#define up(i,j,n)	for(int i=j;i<=n;i++)
#define down(i,j,n)	for(int i=j;i>=n;i--)
#define cmax(a,b)	a=max(a,b)
#define cmin(a,b)	a=min(a,b)
#define FILE		"rhyme"
#define Auto(i,node)	for(int i=LINK[node];i;i=e[i].next)
#define pii		pair<int,int>
#define Map		map<pii,int>
const int MAXN=3e5+5;
const int oo=0x3f3f3f3f;
const int base1=130069;
const int base2=136027;
const int mod1=9179767;
const int mod2=9832517;
inline int read(){
	char ch=getchar();int x=0,f=1;
	while(ch>'9'||ch<'0'){if(ch=='-')f=-1;ch=getchar();}
	while(ch>='0'&&ch<='9'){x=x*10+ch-'0';ch=getchar();}
	return x*f;
}
int N,K,cnt=1;
char s[MAXN];
struct Hash{
	int bin[MAXN],hash[MAXN],base,mod;
	void Ready(int Base,int Mod){
		base=Base;mod=Mod;
		int len=strlen(s+1);
		bin[0]=1;hash[0]=0;
		up(i,1,len){
			bin[i]=(1LL*bin[i-1]*base)%mod;
			hash[i]=(1LL*hash[i-1]*base%mod+s[i]-17+mod)%mod;
		}
	}
	int get(int L,int R){
		return ((hash[R]-1LL*hash[L-1]*bin[R-L+1]%mod+mod)%mod+mod)%mod;
	}
}h1,h2;
namespace Graph{
	struct edge{
		int y,next;
	}e[MAXN<<1];
	int LINK[MAXN],len=0,deg[MAXN],q[MAXN],head,tail,dis[MAXN];
	bool vis[MAXN];
	pii E[MAXN<<1];
	void reset(){
		len=0;
		memset(LINK,0,sizeof(LINK));
		memset(vis,0,sizeof(vis));
		memset(deg,0,sizeof(deg));
	}
	inline void insert(int x,int y){
		e[++len].next=LINK[x];LINK[x]=len;e[len].y=y;
		deg[y]++;E[len]=make_pair(x,y);
	}
	void Topsort(int cnt){
		head=1;tail=0;
		int tol=len;reset();len=tol;
		up(i,1,tol)insert(E[i].second,E[i].first);
		memset(dis,0,sizeof(dis));
		up(i,1,cnt)if(!deg[i]){
			q[++tail]=i;
			dis[i]=1;
		}
		for(;head<=tail;head++){
			int node=q[head];
			Auto(i,node)if(!--deg[e[i].y]){
				cmax(dis[e[i].y],dis[node]+1);
				q[++tail]=e[i].y;
			}
		}
		up(i,1,cnt)if(deg[i])dis[1]=oo;
	}
}
Map ID;
namespace solution{
	void Prepare(){
		Graph::reset();
		ID.erase(ID.begin(),ID.end());
		cnt=1;
		up(i,1,N){
			using namespace Graph;
			scanf("%s",s+1);int len=strlen(s+1);
			if(len<K)continue;
			h1.Ready(base1,mod1);h2.Ready(base2,mod2);
			pii last=make_pair(h1.get(1,K-1),h2.get(1,K-1)),now;
			if(!ID[last]){
				ID[last]=++cnt;
				insert(1,cnt);
			}
			up(j,K,len){
				now=make_pair(h1.get(j-K+2,j),h2.get(j-K+2,j));
				if(!ID[now]){
					ID[now]=++cnt;
					insert(1,cnt);
				}
				insert(ID[last],ID[now]);
				last=now;
			}
		}
	}
	void Solve(){
		Graph::Topsort(cnt);
		if(Graph::dis[1]==oo){
			puts("INF");
			return;
		}
		printf("%d\n",Graph::dis[1]+K-3==K-2?K-1:Graph::dis[1]+K-3);
	}
}
int main(){
	freopen(FILE".in","r",stdin);
	freopen(FILE".out","w",stdout);
	using namespace solution;
	while(scanf("%d%d",&N,&K)!=EOF){
		Prepare();
		Solve();
	}
	return 0;
}