#include <bits/stdc++.h>

using namespace std;
using ll = long long;

int main() {
    ios::sync_with_stdio(false);
    cin.tie(nullptr);

    int n, k;
    cin >> n >> k;

    vector<int> s(n - k + 1), a(n, -1);
    vector<int> nxt(n);

    for (int i = 0; i < size(s); ++i) {
        cin >> s[i];
    }

    for (int i = 0; i + 1 < size(s); ++i) {
        if (s[i] == s[i + 1]) {
            nxt[i] = 0; // same
        } else if (s[i] > s[i + 1]) {
            nxt[i] = 1; // a[i] = 1, a[i + k] = 0
            a[i] = 1, a[i + k] = 0;
        } else {
            nxt[i] = -1; // a[i] = 0, a[i + k] = 1;
            a[i] = 0, a[i + k] = 1;
        }
    }

    for (int i = 0; i < size(s) - 1; ++i) {
        if (a[i] != -1 && nxt[i] == 0) {
            a[i + k] = a[i];
        }
    }

    for (int i = int(size(s)) - 2; i >= 0; --i) {
        if (a[i + k] != -1 && nxt[i] == 0) {
            a[i] = a[i + k];
        }
    }

    int free = 0, sum = 0;

    for (int i = 0; i < k; ++i) {
        if (a[i] != -1) {
            sum += a[i];
        } else {
            free += 1;
        }
    }

    constexpr int MOD = 1e6 + 3;

    if (sum > s[0] || sum + free < s[0]) {
        cout << "0\n";
        return 0;
    }

    int N = free, K = s[0] - sum;

    vector<int> fact(n + 1), ifact(n + 1), I(n + 1);

    fact[0] = ifact[0] = fact[1] = ifact[1] = I[0] = I[1] = 1;

    for (int i = 2; i <= n; ++i) {
        I[i] = 1LL * I[MOD % i] * (MOD - MOD / i) % MOD;
        fact[i] = 1LL * fact[i - 1] * i % MOD;
        ifact[i] = 1LL * ifact[i - 1] * I[i] % MOD;
    }

    int ans = 1LL * fact[N] * ifact[K] % MOD * ifact[N - K] % MOD;

    cout << ans << '\n';

    return 0;
}