#include <bits/stdc++.h>
#define ll long long
#define ar array
#define db double
#define all(x) x.begin(), x.end()
#define sz(x) (int)x.size()
using namespace std;
mt19937 rng(chrono::steady_clock::now().time_since_epoch().count());
#define rint(l, r) uniform_int_distribution<int>(l, r)(rng)
template<typename T> bool ckmin(T &a, const T &b) { return a > b ? a = b, 1 : 0; }
template<typename T> bool ckmax(T &a, const T &b) { return a < b ? a = b, 1 : 0; }
const int mod = 1e6 + 3;
void fadd(int &a, int b) {
a += b;
if (a >= mod) a -= mod;
}
int binpow(int a, int b) {
int r = 1;
for (; b; a = (ll)a*a%mod, b >>= 1) if (b & 1) r = (ll)r*a%mod;
return r;
}
vector<int> facs, invfacs;
void init(int n) {
facs.resize(n+1), invfacs.resize(n+1);
facs[0] = 1;
for (int i = 1; i <= n; i++) facs[i] = (ll)facs[i-1] * i % mod;
invfacs[n] = binpow(facs[n], mod - 2);
for (int i = n - 1; i >= 0; i--) invfacs[i] = (ll)invfacs[i+1] * (i+1) % mod;
}
int choose(int a, int b) {
return ((ll)facs[a] * invfacs[b] % mod) * invfacs[a-b] % mod;
}
void test_case() {
int n, k;
cin >> n >> k;
vector<int> a(n - k + 1);
for (int &x : a) cin >> x;
vector<vector<ar<int, 2>>> adj(n);
for (int i = 0; i < n-k; i++) {
int w = a[i+1] - a[i];
adj[i].push_back({i + k, w});
adj[i + k].push_back({i, -w});
}
vector<int> col(n);
vector<bool> vis(n);
auto dfs = [&](auto&& s, int v) -> void {
vis[v] = 1;
for (auto [u, w] : adj[v]) {
if (!vis[u]) {
col[u] = col[v] + w;
s(s, u);
}
assert(col[u] == (col[v] + w));
}
};
for (int i = 0; i < n; i++) if (!vis[i]) dfs(dfs, i);
vector<int> state(k, -1);
for (int i = 0; i < k; i++) {
int b = 0;
for (int j = i + k; j < n; j += k) {
if (abs(col[j]) > 1) {
cout << 0 << '\n'; return;
}
if (col[j] < 0) b |= 1;
if (col[j] > 0) b |= 2;
}
if (b == 3) {
cout << 0 << '\n'; return;
}
if (b == 1) state[i] = 1;
if (b == 2) state[i] = 0;
}
ar<int, 3> who{};
for (int i = 0; i < k; i++) {
if (state[i] == -1) who[2]++;
else if (state[i] == 0) who[0]++;
else who[1]++;
}
if (who[1] > a[0] || who[2] + who[1] < a[0]) {
cout << 0 << '\n'; return;
}
cout << choose(who[2], a[0] - who[1]) << '\n';
}
int main() {
cin.tie(0)->sync_with_stdio(0);
init(1e6);
int t = 1;
// cin >> t;
while (t--) test_case();
}
