状压最长公共子序列的DP数组，一维最多K(15)个数，且相邻两个数的差不超过1，2^15种状态，预处理转移
#include<cstdio>
#include<algorithm>
using namespace std;
const int mod=1e9+7;
int n,K,now[25],G[25],To[50005][3],F[2][50005][3],ED[50005],ANS[25],S[25];
char s[1000005];
void dfs(int t,int s){
if (t>K){
for (int i=1; i<=K; i++) {
now[i]=now[i-1];
if (s&(1<<i-1)) now[i]++;
}
ED[s]=now[K];
for (int to=0; to<3; to++){
for (int i=1; i<=K; i++) G[i]=max(max(G[i-1],now[i]),now[i-1]+(to==S[i]));
for (int i=K; i>=1; i--) (To[s][to]<<=1)|=(G[i]-G[i-1]);
}
return;
}
dfs(t+1,s<<1);
dfs(t+1,s<<1|1);
}
int main(){
scanf("%d%d",&n,&K);
scanf("%s",s+1);
for (int i=1; i<=K; i++){
if (s[i]=='N') S[i]=0;
else if (s[i]=='O') S[i]=1;
else S[i]=2;
}
dfs(1,0);
F[0][0][0]=1;
for (int i=0; i<n; i++){
for (int pre=0; pre<(1<<K); pre++)
for (int cas=0; cas<3; cas++)
F[(i+1)%2][pre][cas]=0;
for (int pre=0; pre<(1<<K); pre++)
for (int cas=0; cas<3; cas++)
if (F[i%2][pre][cas]){
for (int to=0; to<3; to++){
int now=To[pre][to],Tocas=cas;
if (to==cas) Tocas++;
else{
if (to==0) Tocas=1;
else Tocas=0;
}
if (Tocas==3) continue;
(F[(i+1)%2][now][Tocas]+=F[i%2][pre][cas])%=mod;
}
}
}
for (int now=0; now<(1<<K); now++)
for (int cas=0; cas<3; cas++)
(ANS[ED[now]]+=F[n%2][now][cas])%=mod;
for (int i=0; i<=K; i++)
printf("%d
",ANS[i]);
return 0;
}