// Problem: P10066 [CCO2023] Binaria
// Contest: Luogu
// URL: https://www.luogu.com.cn/problem/P10066
// Memory Limit: 1 MB
// Time Limit: 1000 ms
// 
// Powered by CP Editor (https://cpeditor.org)

#include <bits/stdc++.h>
#define pb emplace_back
#define fst first
#define scd second
#define mkp make_pair
#define mems(a, x) memset((a), (x), sizeof(a))

using namespace std;
typedef long long ll;
typedef double db;
typedef unsigned long long ull;
typedef long double ldb;
typedef pair<ll, ll> pii;

const int maxn = 1000100;
const ll mod = 1000003;

inline ll qpow(ll b, ll p) {
	ll res = 1;
	while (p) {
		if (p & 1) {
			res = res * b % mod;
		}
		b = b * b % mod;
		p >>= 1;
	}
	return res;
}

ll n, m, a[maxn], fac[maxn], ifac[maxn];
int b[maxn], fa[maxn];

inline ll C(ll n, ll m) {
	if (n < m || n < 0 || m < 0) {
		return 0;
	} else {
		return fac[n] * ifac[m] % mod * ifac[n - m] % mod;
	}
}

int find(int x) {
	return fa[x] == x ? x : fa[x] = find(fa[x]);
}

inline void merge(int x, int y) {
	x = find(x);
	y = find(y);
	if (x != y) {
		fa[x] = y;
		if (b[y] == -1) {
			b[y] = b[x];
		}
	}
}

void solve() {
	scanf("%lld%lld", &n, &m);
	for (int i = 1; i <= n - m + 1; ++i) {
		scanf("%lld", &a[i]);
	}
	fac[0] = 1;
	for (int i = 1; i <= n; ++i) {
		fac[i] = fac[i - 1] * i % mod;
		fa[i] = i;
		b[i] = -1;
	}
	ifac[n] = qpow(fac[n], mod - 2);
	for (int i = n - 1; ~i; --i) {
		ifac[i] = ifac[i + 1] * (i + 1) % mod;
	}
	ll x = m, y = a[1];
	for (int i = 1; i <= n - m; ++i) {
		if (a[i] != a[i + 1]) {
			b[find(i)] = (a[i] == a[i + 1] + 1 ? 1 : 0);
		} else {
			merge(i, i + m);
		}
	}
	for (int i = 1; i <= m; ++i) {
		if (b[find(i)] != -1) {
			--x;
			y -= (b[find(i)] == 1);
		}
	}
	printf("%lld\n", C(x, y));
}

int main() {
	int T = 1;
	// scanf("%d", &T);
	while (T--) {
		solve();
	}
	return 0;
}