#include <bits/stdc++.h>

using namespace std;

#define ll long long
#define flt double
#define all(a) a.begin(), a.end()
#define rall(a) a.rbegin(), a.rend()

mt19937 rnd(234);
const ll inf = 1e9;

const ll mod = 1e6 + 3;

ll bin_pow(ll x, ll n) {
    if (n == 0) {
        return 1;
    }
    ll a = bin_pow(x, n / 2);
    a = (a * a) % mod;
    if (n & 1) {
        a = (a * x) % mod;
    }
    return a;
}

ll rev(ll x) {
    return bin_pow(x, mod - 2);
}

vector<ll> fct;
vector<ll> rv_fct;

void build_fct(int n) {
    fct.resize(n + 1);
    rv_fct.resize(n + 1);
    fct[0] = 1;
    rv_fct[0] = 1;
    for (int i = 1; i <= n; i += 1) {
        fct[i] = (fct[i - 1] * i) % mod;
        rv_fct[i] = rev(fct[i]);
    }
}

ll cnk(int n, int k) {
    if (k < 0 || k > n) {
        return 0;
    }
    return fct[n] * rv_fct[k] % mod * rv_fct[n - k] % mod;
}

int n, k;
vector<ll> a;

ll solve() {
    build_fct(n + 100);
    if (k == 1) {
        return 1;
    }
    vector<ll> d(n + 1, 0);
    for (int i = 0; i < n - k + 1; i += 1) {
        d[i + k] = d[i] + a[i];
    }
    vector<pair<ll, ll>> bebra(k, {-inf, inf});
    for (int i = 0; i + 1 <= n; i += 1) {
        int x = i % k;
        // int y = (i + 1) % k;
        ll dx = d[i];
        ll dy = d[i + 1];
        bebra[x].first = max(bebra[x].first, dx - dy);
        bebra[x].second = min(bebra[x].second, dx + 1 - dy);
    }
    int bg = 0;
    int cnk_n = 0;
    for (int i = 0; i + 1 < k; i += 1) {
        if (bebra[i].first == 1) {
            bg += 1;
        } else if (bebra[i].second == 1) {
            cnk_n += 1;
        }
    }
    ll rs = 0;
    ll l = -bebra[k - 1].second;
    ll r = -bebra[k - 1].first;
    for (ll t = l; t <= r; t += 1) {
        rs = (rs + cnk(cnk_n, t - bg)) % mod;
    }
    return rs;
}

int32_t main() {
    if (1) {
        ios::sync_with_stdio(0);
        cin.tie(0);
        cout.tie(0);
    }
    cin >> n >> k;
    a.assign(n - k + 1, 0);
    for (int i = 0; i < n - k + 1; i += 1) {
        cin >> a[i];
    }
    cout << solve() << "\n";
    return 0;
}