#include <bits/stdc++.h>
using namespace std;
#define fi first
#define se second
#define _size(x) (int)x.size()
#define BIT(i, x) ((x >> i) & 1)
#define MASK(n) ((1 << n) - 1)
#define REP(i, n) for (int i = 0, _n = (n); i < _n; i++)
#define FOR(i, a, b) for (int i = a, _b = (b); i <= _b; i++)
#define FORD(i, a, b) for (int i = a, _b = (b); i >= _b; i--)
#define FORB1(i, mask) for (int i = mask; i > 0; i ^= i & - i)
#define FORB0(i, n, mask) for (int i = ((1 << n) - 1) ^ mask; i > 0; i ^= i & - i)
#define FORALL(i, a) for (auto i: a)
#define fastio ios_base::sync_with_stdio(0); cin.tie(0);
const int mod = 1e6 + 3;
vector<int> root, p, ivp;
int getroot(int u) {
return root[u] == u ? u : (root[u] = getroot(root[u]));
}
bool unite(int u, int v) {
u = getroot(u), v = getroot(v);
if (u == v) return false;
root[v] = u;
return true;
}
int _pow(int a, int x) {
if (!x) return 1;
int t = _pow(a, x / 2);
t = (1LL * t * t) % mod;
if (x % 2) t = (1LL * t * a) % mod;
return t;
}
int C(int k, int n) {
return (1LL * p[n] * ivp[k] * ivp[n - k]) % mod;
}
int main() {
fastio;
int n, k;
cin >> n >> k;
vector<int> a(n - k + 2);
FOR(i, 1, n - k + 1) cin >> a[i];
vector<int> b(n + 1, - 1);
root.resize(n + 1);
FOR(i, 1, n) root[i] = i;
// vector<int> deg(n + 1);
FOR(i, 2, n - k + 1) {
if (a[i] == a[i - 1]) {
unite(i - 1, i + k - 1);
continue;
}
if (a[i] < a[i - 1]) b[i + k - 1] = 0, b[i - 1] = 1;
else b[i + k - 1] = 1, b[i - 1] = 0;
// deg[i - 1]++;
// deg[i + k - 1]++;
}
vector<vector<int>> adj(n + 1);
vector<int> ids;
FOR(i, 1, n) {
adj[getroot(i)].push_back(i);
ids.push_back(getroot(i));
}
sort(ids.begin(), ids.end());
ids.resize(unique(ids.begin(), ids.end()) - ids.begin());
FORALL(id, ids) {
int value = - 1;
FORALL(u, adj[id]) {
if (b[u] == - 1) continue;
if (value == - 1) value = b[u];
else if (value != b[u]) {
cout << 0 << '\n';
return 0;
}
}
if (value == - 1) continue;
FORALL(u, adj[id]) b[u] = value;
}
// int cnt = 0;
// FOR(i, 1, n) if (!deg[i]) cnt++;
p.resize(n + 1);
p[0] = 1;
FOR(i, 1, n) p[i] = (1LL * p[i - 1] * i) % mod;
ivp.resize(n + 1);
ivp[n] = _pow(p[n], mod - 2);
FORD(i, n - 1, 0) ivp[i] = (1LL * ivp[i + 1] * (i + 1)) % mod;
int cnt = 0, sum = 0;
FOR(i, 1, k) if (b[i] == - 1) cnt++; else sum += b[i];
cout << C(a[1] - sum, cnt) << '\n';
return 0;
}
