Berlekamp-Massey Algorithm [for Team Problem 5525]

 1 #include<bits/stdc++.h>
 2 using namespace std;
 3 typedef long long ll;
 4 const int N=2010,mod=(int)1e9+7;
 5 ll Base[N][N],a[N],MM[N];
 6 int M,S;
 7 int n,m,k,d[N];
 8 bool vis[N];
 9 ll FPM(ll a,ll b,ll p){
10     ll res=1ll;
11     for(;b;b>>=1,a=a*a%p)
12         if(b&1)res=res*a%p;
13     return res;
14 }
15 ll inv(ll v,ll p){return FPM(v,p-2,p);}
16 void BMA1(){
17     int l=n+1;
18     S=M=n;
19     ll u=0,rev=1;
20     Base[n][n]=1;Base[n+1][n+1]=1;
21     d[n]=n;d[n+1]=n+1;
22     for(int i=n-1;~i;--i,u=0){
23         for(int j=0;j<=n;++j)
24             (u+=Base[i+1][j]*a[n-j]%m)%=m;
25         for(int j=0;j<n;++j){
26             Base[i][j]=(Base[i+1][j+1]-u*rev%m*Base[l][j+1]%m+m)%m;
27         }
28         if(u&&d[i+1]<d[l]){
29             d[i]=d[l]-1;
30             l=i+1,rev=inv(u,m);
31         }
32         else d[i]=d[i+1]-1;
33         if(d[i]<d[M])M=i;
34     }
35 }
36 ll Calc(){
37     ll ans=0;
38     memcpy(MM,Base[M],sizeof MM);
39     vis[M]=1;
40     for(int i=M+1,flag=1;i<n;++i,flag=1){
41         for(int j=n*2;j>=1;--j)
42             MM[j]=MM[j-1];
43         MM[0]=0;
44         for(int j=0;j<=2*n;++j)
45             if(MM[j]!=(j<=n?Base[i][j]:0)){
46                 flag=0;
47                 break;
48             }
49         vis[i]=flag;
50     }
51     for(int i=0;i<n;++i)
52         if(!vis[i]&&d[i]<d[S])
53             S=i;
54     for(int i=0;i<=k;++i){
55         ll res=FPM(m,max(i-d[M],0)+max(i-d[S],0),mod);
56         (res*=(FPM(m,(i>=d[M])+(i>=d[S]),mod)-1+mod)%mod)%=mod;
57         (ans+=res)%=mod;
58     }
59     return (ans+1)%mod;
60 }
61 int main(){
62     scanf("%d%d",&n,&m);
63     for(int i=0;i<n;++i)scanf("%lld",a+i);
64     scanf("%d",&k);
65     BMA1();
66     cout<<Calc()<<endl;
67     return 0;
68 }