#include <bits/stdc++.h>
using namespace std;
const int M = 1000000 + 3, N = 1e6 + 10;
int a[N], ch[N], fa[N], dp[N] = {0}, fac[N], invfac[N];
int find (int x) {
return fa[x] == x ? x : fa[x] = find (fa[x]);
}
void add (int &x, int y) {
x += y;
if (x >= M) x -= M;
if (x < 0) x += M;
}
void merge (int i, int j) {
i = find(i), j = find(j);
if (i == j) return;
fa[i] = j;
if (ch[i] == 3 or ch[j] == 3) ch[j] = min(ch[i], ch[j]);
else if (ch[i] != ch[j]) {
cout << "0\n";
exit(0);
}
}
void f(int i, int val) {
i = find(i);
if (ch[i] == 3) ch[i] = val;
else if (ch[i] != val) {
cout << "0\n";
exit(0);
}
}
int fmul (int x, int t) {
if (t == 0) return 1;
long long y = fmul(x, t / 2);
y = y * y % M;
if (t & 1) y = y * x % M;
return y;}
int nCr (int x, int y) {
return fac[x] * 1LL * invfac[y] % M * invfac[x - y] % M;
}
signed main () {
fac[0] = 1;
for (int i = 1; i <= 1000000; i++) fac[i] = fac[i - 1] * 1LL * i % M;
invfac[1000000] = fmul(fac[1000000], M - 2);
for (int i = 999999; i >= 0; i--) invfac[i] = invfac[i + 1] * (i + 1LL) % M;
// cout << invfac[999999] * 1LL * fac[999999] % M<< '\n';
// cout << fac[5] << ' ' << nCr(5, 3) << '\n';return 0;
int n, k;
cin >> n >> k;
for (int i = 1; i <= n; i++) fa[i] = i, ch[i] = 3;
for (int i = 1; i + k - 1 <= n; i++) cin >> a[i];
for (int i = 2; i + k - 1 <= n; i++) {
int dif = a[i] - a[i - 1];
if (dif == 0) merge(i - 1, i + k - 1);
else if (dif == 1) f(i + k - 1, 1), f(i - 1, 0);
else f(i + k - 1, 0), f(i - 1, 1);
}
int left = a[1], wow = 0;
for (int i = 1; i <= k; i++) {
if (ch[find(i)] == 3) wow++;
else if (ch[find(i)] == 1) {
left--;
}
}
cout << nCr (wow, left) << '\n';
}
