// author : daohuyenchi
#ifdef LOCAL
#include "D:\C++ Submit\debug.h"
#else
#define debug(...)
#endif
#include <bits/stdc++.h>
using namespace std;
#define ull unsigned long long
#define db double
#define i32 int32_t
#define i64 int64_t
#define ll long long
//
#define fi first
#define se second
// #define int long long // consider carefully
//
#define pii pair <int, int>
#define pll pair <ll, ll>
#define PAIR make_pair
#define TUP make_tuple
// TIME IS LIMITED ...
#define rep(i, a, b) for (int i = (a), _b = (b); i <= _b; ++i)
#define repd(i, b, a) for (int i = (b), _a = (a); i >= _a; --i)
#define repv(v, H) for(auto &v: H)
// REFLECT ON THE PAST ...
#define RESET(c, x) memset(c, x, sizeof(c))
#define MASK(i) (1LL << (i))
#define BIT(mask, i) (((mask) >> (i)) & 1LL)
#define ONBIT(mask, i) ((mask) | (1LL << (i)))
#define OFFBIT(mask, i) ((mask) &~ (1LL << (i)))
#define COUNTBIT __builtin_popcountll
// 30 / 1 / 2024 ? love is zero... start from zero
#define vi vector <int>
#define vll vector <ll>
#define Lower lower_bound
#define Upper upper_bound
#define all(v) (v).begin(), (v).end()
#define special(H) (H).resize(distance(H.begin(), unique(all(H))))
//
#define sp ' '
#define nl '\n'
#define EL { cerr << '\n'; }
#define yes "YES"
#define no "NO"
#define Log2(n) (63 - __builtin_clzll(n))
#define left __left__
#define right __right__
#define lps(id) ((id) << 1)
#define rps(id) ((id) << 1 | 1)
//____________________________________________________________________
template <class X, class Y> bool maximize(X &a, const Y &b)
{ if(a < b) return a = b, true; else return false; }
template <class X, class Y> bool minimize(X &a, const Y &b)
{ if(a > b) return a = b, true; else return false; }
template <class... T>
void print(T&&... n)
{ using exp = int[]; exp{ 0, (cerr << n << sp, 0)... }; cerr << nl; }
template <class T, class... C>
void assign(int n, T v, C&&... a)
{ using e = int[]; e { (a.assign(n, v), 0)...}; }
template <class... C>
void resize(int n, C&&... a)
{ using e = int[]; e { (a.resize(n), 0)...}; }
template <class T>
using vector2d = vector<vector<T>>;
template <class T>
using vector3d = vector<vector2d<T>>;
template <class T> int ssize(T &a) { return (int) a.size(); }
//____________________________________________________________________
mt19937 rng(chrono::steady_clock().now().time_since_epoch().count());
const long long MOD = 1e6 + 3;
// const int MOD[2] = {1000000009, 998244353};
template<class X> void modmize(X &x, long long cur_Mod = MOD) {
if(x >= cur_Mod) x -= cur_Mod;
if(x < 0) x += cur_Mod;
}
int mod_plus(int A, int B) { modmize(A += B); return A; }
const long long oo = 1e18 + 7;
const long long LINF = 1e18 + 7;
const int IINF = 2e9;
const int nmax = 2e5 + 10;
const int MAX = 1e6;
const int base = 311;
const double eps = 1e-6;
const int block = 500;
static const double PI = acos(-1.0);
//____________________________________________________________________
int n, k;
int x[nmax], a[nmax];
struct DSU {
vector<int> parent;
void Init(int _n) {
parent.assign(_n + 1, -1);
return;
}
void Reset(int _n = 0) {
for (int i = 1; i <= _n; ++i) {
parent[i] = -1;
}
}
int Find(int u) {
return (parent[u] < 0 ? u : parent[u] = Find(parent[u]));
}
int Son(int u) {
u = Find(u);
return - parent[u];
}
bool Merge(int u, int v) {
u = Find(u);
v = Find(v);
if(u == v) return false;
if(parent[u] > parent[v]) swap(u, v);
parent[u] += parent[v];
parent[v] = u;
return true;
}
} dsu;
int64_t Pow(ll a, ll b) {
ll cur = 1;
for(; b > 0; b >>= 1) {
if(b & 1LL) cur = cur * a % MOD;
a = a * a % MOD;
}
return cur;
}
struct combinatorics {
vector<ll> fac, ifac;
void init(int _n) {
fac.assign(_n + 5, 0);
ifac.assign(_n + 5, 0);
fac[0] = 1;
for (int i = 1; i <= _n; ++i) {
fac[i] = fac[i - 1] * i % MOD;
}
ifac[_n] = Pow(fac[_n], MOD - 2);
for (int i = _n - 1; i >= 0; --i) {
ifac[i] = ifac[i + 1] * (i + 1) % MOD;
}
}
// n choose k
ll ncr(int n, int k) {
if (k > n) return 0;
if (k == 0 && n == 0) return 1;
if (k == 0) return 1;
if (n == 0) return 0;
return fac[n] * ifac[k] % MOD * ifac[n - k] % MOD;
}
// n permutation k
ll npr(int n, int k) {
if (k > n) return 0;
return fac[n] * ifac[n - k] % MOD;
}
// (k, n) = 0 if k > n
// (k, n) = n * nf[k] * (k - 1, n - 1)
// sigma (i, n) = 2 ^ n :i = 0 -> n
// sigma (k, i) = (k + 1, n + 1) :i = 0 -> n
// sigma (i, n + i) = (m, n + m + 1) :i = 0 -> m
// sigma {(i, n) ^ 2} = (n, 2n) :i = 0 -> n
// sigma {k * (k, n)} = n * 2 ^ (n - 1) :i = 1 -> n
// x[1] + x[2] + .. + x[n] = m (x[i] >= 0) => (n - 1, m + n - 1)
// x[1] + x[2] + .. + x[n] <= m (x[i] >= 0) => (n, m + n)
// cell(u, v) -> cell(x, y) => (x - u, x + y - u - v)
// choose len elements in n elements (not need to be diifer) = ncr(n - 1 + len, len)
// the number of regular bracket strings of length 2⋅n is equal to (1 / (n + 1)) * ncr(2 * n, n)
} C;
void tintingyn()
{
cin >> n >> k;
rep (i, k, n) {
cin >> x[i];
}
C.init(1e6);
dsu.Init(n);
memset(a, -1, sizeof a);
rep (i, n - k + 1, n - 1) {
if (x[i] != x[i + 1]) {
if (abs(x[i] - x[i + 1]) > 1) {
cout << 0 << nl;
exit(0);
}
if (x[i + 1] > x[i]) a[i + 1] = 1, a[i - k + 1] = 0;
else a[i + 1] = 0, a[i - k + 1] = 1;
}
else {
dsu.Merge(i + 1, i - k + 1);
}
}
vector2d < int > List;
assign(n + 2, vector < int > (), List);
rep (i, 1, n) {
List[dsu.Find(i)].push_back(i);
}
rep (i, 1, n) {
if (dsu.Find(i) == i) {
int ok = -1;
repv (v, List[i]) {
if (ok == -1) {
if (a[v] != -1) ok = a[v];
}
else {
if (ok != a[v]) {
cout << 0 << nl;
exit(0);
}
}
}
if (ok != -1) {
repv (v, List[i]) {
a[v] = ok;
}
}
else {
}
}
}
int cnt = 0;
int sum = x[k];
vector < bool > vis(n + 2, 0);
rep (i, 1, k) {
int p = dsu.Find(i);
if (a[p] != -1) sum -= a[p];
else cnt++;
vis[p] = 1;
}
ll ans = C.ncr(cnt, sum);
// rep (i, k + 1, n) {
// int p = dsu.Find(i);
// if (vis[p] == 0) {
// vis[p] = 1;
// ans = ans * Pow(2, dsu.Son(p)) % MOD;
// }
// }
cout << ans << nl;
}
signed main() {
ios_base::sync_with_stdio(0); cin.tie(0); cout.tie(0);
//________________________________________________________________
#define TASK "2"
if(fopen(TASK".inp", "r"))
{ freopen(TASK".inp", "r", stdin); freopen(TASK".out", "w", stdout); }
//________________________________________________________________
// CODE FROM HERE ...!
int num_test = 1;
// cin >> num_test;
while(num_test--) {
tintingyn();
}
cerr << '\n' << "Time elapsed: " << (1.0 * clock() / CLOCKS_PER_SEC) << " s\n" << nl;
return 0;
}
