#include <bits/stdc++.h>

#define f first
#define s second
#define pb push_back
#define mp make_pair

using namespace std;

typedef long long ll;
typedef pair<int, int> pii;
typedef pair<long long, long long> pll;

const int N = 3000500, inf = 1e9, mod = 1e6 + 3;
const ll INF = 1e18;

int sum(int a, int b) {
    a += b;
    if (a >= mod)
        a -= mod;
    return a;
}

int sub(int a, int b) {
    a -= b;
    if (a < 0)
        a += mod;
    return a;
}

int mult(int a, int b) {
    return 1ll * a * b % mod;
}

int bp(int a, int b) {
    int res = 1;
    while (b) {
        if (b & 1)
            res = mult(res, a);
        a = mult(a, a);
        b >>= 1;
    }
    return res;
}

int inv(int x) {
    return bp(x, mod - 2);
}

int n, k;
int a[N], b[N], f[N];
int c[N];

void no() {
    cout << "0\n";
    exit(0);
}

int C(int k, int n) {
    if (0 <= k && k <= n)
        return mult(f[n], inv(mult(f[k], f[n - k])));
    return 0;
}

void solve() {
    f[0] = 1;
    for (int i = 1; i < N; i++)
        f[i] = mult(f[i - 1], i);
    cin >> n >> k;
    for(int i = 0; i < n - k + 1; i++)
        cin >> a[i];
    for (int i = 0; i + 1 < n - k + 1; i++) {
        if (a[i] == a[i + 1])
            continue;
        if (abs(a[i] - a[i + 1]) > 1)
            no();
        int x, y;
        if (a[i] < a[i + 1])
            x = 1, y = 2;
        else
            x = 2, y = 1;
        if (b[i] == 0)
            b[i] = x;
        if (b[i + k] == 0)
            b[i + k] = y;
        if (b[i] != x || b[i + k] != y)
            no();
    }
    for (int i = 0; i + 1 < n - k + 1; i++) {
        if (a[i] == a[i + 1]) {
            if (b[i] != 0 && b[i + k] == 0)
                b[i + k] = b[i];
            if (b[i + k] != 0 && b[i] == 0)
                b[i] = b[i + k];
            if (b[i] != b[i + k])
                no();
        }
    }
    for (int i = n - k; i >= 0; i--) {
        if (a[i] == a[i + 1]) {
            if (b[i] != 0 && b[i + k] == 0)
                b[i + k] = b[i];
            if (b[i + k] != 0 && b[i] == 0)
                b[i] = b[i + k];
            if (b[i] != b[i + k])
                no();
        }
    }
    int x = 0, y = 0;
    for (int i = 0; i < k; i++) {
        if (b[i] == 0)
            y++;
        else
            x += b[i] - 1;
    }
    cout << C(a[0] - x, y) << "\n";
}

int main() {
#ifdef DEBUG
    freopen("input.txt", "r", stdin);
#endif
    ios_base::sync_with_stdio(false);
    int t = 1;
//    cin >> t;
    for (int i = 1; i <= t; i++) {
//        cout << "Case #" << i << endl;
        solve();
    }
}