This submission is migrated from previous version of oj.uz, which used different machine for grading. This submission may have different result if resubmitted.
#include<bits/stdc++.h>
using namespace std;
mt19937_64 rng(chrono::high_resolution_clock::now().time_since_epoch().count());
namespace Random
{
	#define int long long
	int Rand(int l , int r)
		{
			return uniform_int_distribution<int>(l , r)(rng);
		} 
	#undef int 
}
using i64 = long long;
using ui64 = unsigned long long;
#define MASK(x) ((i64)(1) << (x))
#define BIT(mask , x) (((mask) >> (x)) & (1))
#define sz(x) (x).size()
#define all(x) (x).begin() , (x).end()
#define FOR(i ,a , b) for (int i = (a); i <= (b); ++i)
#define FORD(i , a , b) for (int i = (b); i >= (a); --i)
#define REP(i , a , b) for (int i = (a); i < (b); ++i)
#define REPD(i , a , b) for (int i = (b) - 1 ; i >= (a); --i)
template <class T> 
    void compress(vector<T> &a)
    {
        sort(a.begin() , a.end());
        a.resize(unique(a.begin() , a.end()) - a.begin());
        return;
    }
template<class T>
    void printArr(T& container , string separator = "" , string finish = "\n")
    {
        for (auto& item : container) cout << item << separator;
        cout << finish;
    }
template<class T>
    bool maximize(T &a , T b) {if (a < b) return a = b , true; else return false;}
template<class T>
    bool minimize(T &a , T b) {if (a > b) return a = b , true; else return false;}
template<class T>
    T gcd(T x , T y) {while (y) swap(y , x %= y); return x;}
template<class T>
    T lcm(T x , T y) {return (x * y) / gcd(x , y);}
//... INPUT
    void INPUT(string name)
    {
    	iostream::sync_with_stdio(false); cin.tie(0);
    	if (!fopen((name + ".inp").c_str() , "r")) return;
    	freopen((name + ".inp").c_str() , "r" , stdin);
    	freopen((name + ".out").c_str() , "w+" , stdout);
    	return;
    }
const int maxn = 1e6;
int a[maxn + 2] ;
int n , k;
//... MOD OPERATOR
	const int MOD = 1e6 + 3;
	int add(int a , int b)
	{
		return (a + b >= MOD ? a + b - MOD : a + b);
	}
	int mul(int a , int b)
	{
		return (i64)a * b % MOD;
	}
	int _pow(int a , int b)
	{
		int res = 1;
		for (; b ; b >>= 1 , a = mul(a,a))
			if (b&1) res = mul(res,a);
		return res;
	}
	int fac[maxn + 2] , inv[maxn + 2];
	void pre()
	{
		fac[0] = 1;
		FOR(i,1,maxn) fac[i] = mul(fac[i - 1] , i);
		inv[maxn] = _pow(fac[maxn] , MOD - 2);
		FORD(i,1,maxn) inv[i - 1] = mul(inv[i] , i);
		return;
	}
	int C(int x , int y)
	{
		if (x > y) return 0;
		return fac[y] * inv[x] % MOD * inv[y - x] % MOD;
	}
int s[maxn + 2] ;
int32_t main()
{
	INPUT("main");
		cin >> n >> k;
		pre();
		FOR(i,1,n-k+1) cin >> a[i];
		FOR(i,1,n) s[i] = -1;
		FORD(i,1,n-k)
		{
			if (abs(a[i] - a[i + 1]) == 0) s[i] = s[i + k];
			if (abs(a[i] - a[i + 1]) == 1) 
			{
				if (a[i] > a[i + 1])
				{
					if (s[i + k] == 1)
					{
						cout << 0;
						return 0;
					}
					s[i] = 1;
				}
				if (a[i] < a[i + 1])
				{
					if (s[i + k] == 0)
					{
						cout << 0;
						return 0;
					}
					s[i] = 0;
				}
			}
			if (abs(a[i] - a[i + 1]) >= 2)
					{
						cout << 0;
						return 0;
					}
		}
		int answer = 0 , s1 = a[1] , s2 = 0;
		FOR(i,1,k)
		{
			if (s[i] == 1) s1--;
				else if (s[i] == -1) ++s2;
		}
		cout << C(s1 , s2);
	cerr << "\nTIME RUN : " << 1000 * clock() / CLOCKS_PER_SEC << "MS\n";
	return 0;
}
Compilation message (stderr)
Main.cpp: In function 'int32_t main()':
Main.cpp:134:7: warning: unused variable 'answer' [-Wunused-variable]
  134 |   int answer = 0 , s1 = a[1] , s2 = 0;
      |       ^~~~~~
Main.cpp: In function 'void INPUT(std::string)':
Main.cpp:55:13: warning: ignoring return value of 'FILE* freopen(const char*, const char*, FILE*)' declared with attribute 'warn_unused_result' [-Wunused-result]
   55 |      freopen((name + ".inp").c_str() , "r" , stdin);
      |      ~~~~~~~^~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Main.cpp:56:13: warning: ignoring return value of 'FILE* freopen(const char*, const char*, FILE*)' declared with attribute 'warn_unused_result' [-Wunused-result]
   56 |      freopen((name + ".out").c_str() , "w+" , stdout);
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