#include <bits/stdc++.h>
#define int long long
using namespace std;
const long long N = 2e5 + 5;
int a[N];
int b[N];
int f[N];
const int mod = 1e6 + 3;
int po(int n, int k = mod - 2)
{
if (k == 0)
return 1;
else if (k & 1)
return n * po((n * n) % mod, k / 2) % mod;
return po((n * n) % mod, k / 2);
}
int ncr(int n, int k)
{
return ((f[n] * po(f[k]) % mod) * po(f[n - k])) % mod;
}
void solve()
{
int n, k;
cin >> n >> k;
for (int i = 0; i < n - k + 1; i++)
{
cin >> b[i];
}
for (int i = 0; i <= n; i++)
{
a[i] = -1;
}
for (int i = 0; i + k < n; i++)
{
// cout << b[i] << ' ' << b[i + 1] << endl;
if (b[i] == b[i + 1])
{
continue;
}
else if (b[i] + 1 == b[i + 1])
{
a[i] = 0;
a[i + k] = 1;
}
else if (b[i] == b[i + 1] + 1)
{
a[i] = 1;
a[i + k] = 0;
}
else
{
cout << 0;
return;
}
}
int choices = 0;
int sum = 0;
for (int i = 0; i < k; i++)
{
if (a[i] == -1)
{
choices++;
}
else
{
sum += a[i];
}
}
// for (int i = 0; i < n; i++)
// {
// cout << a[i] << ' ' << endl;
// }
// cout << sum << ' ' << b[0] << endl;
cout << ncr(choices, b[0] - sum);
}
signed main()
{
f[0] = 1;
for (int i = 1; i < N; i++)
{
f[i] = (f[i - 1] * i) % mod;
}
ios_base::sync_with_stdio(0);
cin.tie(NULL);
cout.tie(NULL);
int t = 1;
// cin >> t;
for (int i = 1; i <= t; i++)
{
// cout << "Case #" << i << ':' << ' ';
solve();
cout << endl;
}
return 0;
}
