/*#pragma GCC optimize("O3")
#pragma GCC optimization("Ofast,unroll-loops")
#pragma GCC target("avx2,bmi,bmi2,lzcnt,popcnt")*/
#include <bits/stdc++.h>
//#include "jumps.h"
/*#include <ext/pb_ds/assoc_container.hpp>
#include <ext/pb_ds/tree_policy.hpp>*/
#define ll long long
#define ll1 long long
#define ull unsigned long long
#define dou long double
#define str string
#define vll vector<ll>
#define vi vector<int>
#define pll pair<ll, ll>
#define vpll vector<pair<ll, ll>>
#define vbool vector<bool>
#define vstr vector<str>
#define vvll vector<vll>
#define pb push_back
#define pf push_front
#define endl "\n"
#define fr first
#define se second
// #define sortcmp(a) sort(a.begin(), a.end(), cmp)
#define sort(a) sort(a.begin(), a.end())
#define reverse(a) reverse(a.begin(), a.end())
#define speed ios_base::sync_with_stdio(0);cin.tie(0);cout.tie(0)
#define ordered_set tree<ll, null_type, less_equal<ll>, rb_tree_tag, tree_order_statistics_node_update>
using namespace std;
//using namespace __gnu_pbds;
const ll INF = 1e9+7;
const int lg = 20;
//const ll MOD = 1e9+7;
//const ll MOD2 = 998244353;
const ll MOD2 = 1e6+3;
mt19937 rng(1488);
ll randll(ll l, ll r) {
return uniform_int_distribution<ll>(l, r)(rng);
}
ll f(ll n) {
ll fk = 1;
for (int i = 2; i <= n; i ++) {
fk *= i;
fk %= MOD2;
}
return fk;
}
ll bp(ll b, ll n) {
if (n == 1) return b;
if (n % 2 == 1) return b*bp(b, n-1)%MOD2;
ll c = bp(b, n/2);
return c*c%MOD2;
}
int main() {
speed;
ll n, k;
cin >> n >> k;
vll a(n-k+1);
for (int i = 0; i < n-k+1; i ++) {
cin >> a[i];
}
vll c(n, -1);
bool q = 1;
vpll v;
for (int i = 1; i < n-k+1; i ++) {
if (a[i] == a[i-1]) {
v.pb({i-1, i+k-1});
continue;
}
if (a[i] < a[i-1]) {
c[i+k-1] = 0;
if (c[i-1] != -1) q = 0;
c[i-1] = 1;
}
else {
c[i-1] = 0;
if (c[i+k-1] != -1) q = 0;
c[i+k-1] = 1;
}
}
//cout << q << endl;
for (auto i : v) {
if (c[i.fr] != -1) {
if (c[i.se] != -1 && c[i.se] != c[i.fr]) q = 0;
c[i.se] = c[i.fr];
}
}
reverse(v);
for (auto i : v) {
if (c[i.se] != -1) {
if (c[i.fr] != -1 && c[i.fr] != c[i.se]) q = 0;
c[i.fr] = c[i.se];
}
}
ll res = 0;
ll s = 0;
for (int i = 0; i < k; i ++) {
if (c[i] == -1) res ++;
else s += c[i];
}
s = a[0]-s;
if (s > res) q = 0;
if (!q) {
cout << 0 << endl;
return 0;
}
cout << f(res)*bp(f(res-s)*f(s)%MOD2, MOD2-2)%MOD2;
}
