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Cod sursa(job #467344)
#include <cstdio>
#include <algorithm>
using namespace std;
#define Mmax 1010
#define Nmax 1000010
#define Kmax 22
#define MOD 9901
int n, m, k, i;
int v[Mmax], a[Nmax], X[Kmax];
int A[Kmax][Kmax], B[Kmax][Kmax], S[Kmax][Kmax], C[Kmax][Kmax];
void citire () {
scanf ("%d %d %d", &n, &m, &k);
for (i = 1; i <= m; i++)
scanf ("%d", &v[i]);
sort (v + 1, v + m + 1);
}
void brute1 () {
a[0] = 1; int p = 1;
for (i = 1; i <= n; i++) {
while (p <= m && v[p] < i) p++;
if (v[p] != i) {
a[i] = a[i-1];
if (i - k >= 0) {
a[i]+= a[i - k];
if (a[i] >= MOD) a[i]-= MOD;
}
}
}
printf ("%d", a[n]);
}
void prod2 () {
int i, j, l;
for (i = 1; i <= k; i++) {
for (j = 1; j <= k; j++) {
C[i][j] = 0;
for (l = 1; l <= k; l++) {
C[i][j]+= S[i][l] * B[l][j];
C[i][j]%= MOD;
}
}
}
for (i = 1; i <= k; i++)
for (j = 1; j <= k; j++)
S[i][j] = C[i][j];
}
void prod () {
int i, j, l;
for (i = 1; i <= k; i++) {
for (j = 1; j <= k; j++) {
C[i][j] = 0;
for (l = 1; l <= k; l++) {
C[i][j]+= B[i][l] * B[l][j];
C[i][j]%= MOD;
}
}
}
for (i = 1; i <= k; i++)
for (j = 1; j <= k; j++)
B[i][j] = C[i][j];
}
void brute2 () {
if (n < k) {
printf ("%d", 1);
return ;
}
if (n == k) {
printf ("%d", 2);
return ;
}
int i, j;
for (i = 1; i <= k; i++)
X[i] = 1;
X[k]++;
for (i = 1; i <= k; i++)
for (j = 1; j <= i; j++)
B[i][j] = B[i][j] = 1;
for (j = 1; j <= k; j++) {
B[j][k]++;
A[j][k]++;
}
int buc = (n - 1) / k;
for (i = 1; i <= k; i++)
S[i][i] = 1;
for (i = 0; i <= 30; i++) {
if (((buc>>i)&1)) {
prod2 ();
}
prod ();
}
int poz = (n - 1) % k + 1, sol = 0;
for (i = 1; i <= k; i++) {
sol+= X[i] * S[poz][i];
sol%= MOD;
}
printf ("%d", sol);
}
int main () {
freopen ("pod.in", "r", stdin);
freopen ("pod.out", "w", stdout);
citire ();
if (n <= 1000000)
brute1 ();
else {
if (m == 0)
brute2 ();
else
brute2 ();
}
return 0;
}