#include <bits/stdc++.h>
using namespace std;
using ll = long long;
#define int long long
#define FOR(i, a, b) for (int i = (a); i <= (b); i++)
#define FORD(i, a, b) for (int i = (b); i >= (a); i --)
#define REP(i, n) for (int i = 0; i < (a); ++i)
#define REPD(i, n) for (int i = (a) - 1; i >= 0; --i)
#define MASK(i) (1LL << (i))
#define BIT(x, i) (((x) >> (i)) & 1)
constexpr ll LINF = (1ll << 60);
constexpr int INF = (1ll << 30);
constexpr int Mod = 1e6 + 3;
mt19937 rng(chrono::steady_clock::now().time_since_epoch().count());
/*
Phu Trong from Nguyen Tat Thanh High School for gifted student
*/
template <class X, class Y>
bool minimize(X &x, const Y &y){
X eps = 1e-9;
if (x > y + eps) {x = y; return 1;}
return 0;
}
template <class X, class Y>
bool maximize(X &x, const Y &y){
X eps = 1e-9;
if (x + eps < y) {x = y; return 1;}
return 0;
}
#define MAX 1000005
int N, K, M;
int A[MAX];
int inv[MAX], fac[MAX];
int power(int a, int exp){
int res = 1;
for (;exp > 0; a = (a * a) % Mod, exp >>= 1) if(exp & 1){
res = (res * a) % Mod;
}
return res;
}
void genFac(int n){
fac[0] = 1;
for (int i = 1; i <= n; ++i) fac[i] = fac[i - 1] * i % Mod;
inv[n] = power(fac[n], Mod - 2);
for (int i = n - 1; i >= 0; --i) inv[i] = inv[i + 1] * (i + 1) % Mod;
}
int C(int n, int k){
if (n < k || k < 0) return 0;
return fac[n] * inv[k] % Mod * inv[n - k] % Mod;
}
void mul(int &x, int y){
x = (1ll * x * y) % Mod;
}
void add(int &x, int y){
x += y;
if (x >= Mod) x -= Mod;
}
vector<int> G[MAX];
int col[MAX];
int vis[MAX];
void paint(int u, int c){
vis[u] = 1; col[u] = c;
for (int&v : G[u]) if(!vis[v]){
paint(v, c);
}
}
void process(void){
cin >> N >> K;
M = N - K + 1;
for (int i = 1; i <= M; ++i) cin >> A[i];
genFac(N);
for (int i = 1; i <= N; ++i) col[i] = -1;
for (int i = 1; i < M; ++i){
if(A[i] == A[i + 1]){
G[i].push_back(i + K);
G[i + K].push_back(i);
}
else if(A[i] + 1 == A[i + 1]){
col[i] = 0, col[i + K] = 1;
}
else if(A[i] - 1 == A[i + 1]){
col[i] = 1, col[i + K] = 0;
}
else return void(cout << 0);
}
vector<int> vis(K + 5);
for (int i = 1; i <= N; ++i){
if (~col[i]){
paint(i, col[i]);
}
}
for (int i = 1; i < M; ++i){
if (A[i] == A[i + 1]){
if(col[i] != col[i + K]) return void(cout << 0);
}
else if (A[i] < A[i + 1]) {
if(!(col[i] == 0 && col[i + K] == 1)) return void(cout << 0);
}
else{
if(!(col[i] == 1 && col[i + K] == 0)) return void(cout << 0);
}
}
int need = A[1], emp = 0;
for (int i = 1; i <= K; ++i){
if (col[i] == -1) emp++;
else if(col[i] == 1) need--;
}
assert(emp >= 0);
cout << C(emp, need);
}
signed main(){
#define name "Whisper"
cin.tie(nullptr) -> sync_with_stdio(false);
//freopen(name".inp", "r", stdin);
//freopen(name".out", "w", stdout);
process();
return (0 ^ 0);
}
