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Cod sursa(job #732630)
#include <cstdio>
#include <algorithm>
#include <cstring>
#define KMax 22
#define MMax 1005
#define Mod 9901
using namespace std;
int N, K, M[MMax], DP[KMax];
class Matrix
{
public: int x[KMax][KMax];
Matrix ()
{
memset (x, 0, sizeof (x));
}
Matrix (int v)
{
memset (x, 0, sizeof (x));
for (int k=1; k<=K; ++k) x[k][k]=v;
}
inline void operator = (Matrix y)
{
memcpy (x, y.x, sizeof (y.x));
}
inline Matrix operator * (Matrix y)
{
Matrix z (0);
for (int i=1; i<=K; ++i)
{
for (int j=1; j<=K; ++j)
{
for (int k=1; k<=K; ++k)
{
z.x[i][j]+=(x[i][k]*y.x[k][j]);
if (z.x[i][j]>=Mod) z.x[i][j]%=Mod;
}
}
}
return z;
}
};
Matrix Z (0);
void BuildZ ()
{
Z.x[1][K]=Z.x[K][K]=1;
for (int i=2; i<=K; ++i)
{
Z.x[i][i-1]=1;
}
}
void InitDP ()
{
for (int i=1; i<=K; ++i) DP[i]=1;
}
inline Matrix Pow (Matrix &X, int P)
{
Matrix R (1);
while (P>0)
{
if (P%2==0) X=(X*X), P/=2;
else R=(R*X), --P;
}
return R;
}
inline void Compute (int P)
{
Matrix X; X=Z;
X=Pow (X, P);
int NewDP[KMax]; memset (NewDP, 0, sizeof (NewDP));
for (int i=1; i<=K; ++i)
{
for (int j=1; j<=K; ++j)
{
NewDP[i]=(NewDP[i]+DP[j]*X.x[j][i])%Mod;
}
}
for (int i=1; i<=K; ++i) DP[i]=NewDP[i];
}
void Solve ()
{
BuildZ ();
sort (M+1, M+M[0]+1);
int P=K;
for (int i=1; i<=M[0]; ++i)
{
Compute (M[i]-P);
DP[K]=0; P=M[i];
}
}
void Read ()
{
freopen ("pod.in", "r", stdin);
int Broken; scanf ("%d %d %d", &N, &Broken, &K);
InitDP ();
for (int i=1; i<=Broken; ++i)
{
int P; scanf ("%d", &P); ++P;
if (P<=K)
{
for (int j=P; j<=K; ++j) DP[j]=0;
}
else M[++M[0]]=P;
}
M[++M[0]]=N+2;
}
void Print ()
{
freopen ("pod.out", "w", stdout);
if (N<K) printf ("%d\n", DP[N]);
else printf ("%d\n", DP[K-1]);
}
int main()
{
Read ();
Solve ();
Print ();
return 0;
}