#include<bits/stdc++.h>
#define fi first
#define se second
#define eb emplace_back
#define mp make_pair
using namespace std;
typedef long double ld;
typedef long long ll;
typedef unsigned long long ull;
typedef __int128 i128;
template<typename T,typename U>
T ceil(T x, U y) {return (x>0?(x+y-1)/y:x/y);}
template<typename T,typename U>
T floor(T x, U y) {return (x>0?x/y:(x-y+1)/y);}
template<class T,class S>
bool chmax(T &a,const S b) {return (a<b?a=b,1:0);}
template<class T,class S>
bool chmin(T &a,const S b) {return (a>b?a=b,1:0);}
int popcnt(int x) {return __builtin_popcount(x);}
int popcnt(ll x)  {return __builtin_popcountll(x);}
int topbit(int x) {return (x==0?-1:31-__builtin_clz(x));}
int topbit(ll x)  {return (x==0?-1:63-__builtin_clzll(x));}
int lowbit(int x) {return (x==0?-1:__builtin_ctz(x));}
int lowbit(ll x)  {return (x==0?-1:__builtin_ctzll(x));}

#define int long long
#define rep(i,a,b) for(int i=(a);i<=(b);i++)
#define per(i,a,b) for(int i=(a);i>=(b);i--)
typedef pair<int,int> pii; 
typedef vector<int> vi;
typedef vector<pii> vp;
typedef tuple<int,int,int> tiii;
int read() {
  int x=0,w=1; char c=getchar(); 
  while(!isdigit(c)) {if(c=='-') w=-1; c=getchar();}
  while(isdigit(c)) {x=x*10+(c-'0'); c=getchar();}
  return x*w;
}

const int N=1e6+5,mod=1e6+3;
int n,k,s[N],sum,cnt,flag;
vi p[N];

int ksm(int x,int y,int r=1) {
  for(;y;y>>=1,x=x*x%mod) if(y&1) r=r*x%mod;
  return r;
}

signed main() {
  n=read(), k=read(), flag=1;
  rep(i,k,n) s[i]=read(); sum=s[k];
  rep(i,k+1,n) if(abs(s[i]-s[i-1])>1) flag=0;
  rep(i,k+1,n) p[i%k].eb(s[i]-s[i-1]);
  rep(i,0,k-1) {
    int mn=0,mx=0,cur=0;
    for(int x:p[i]) {
      cur+=x;
      chmin(mn,cur);
      chmax(mx,cur);
    }
    if(mn<-1||mx>1) flag=0;
    else if(mn==-1&&mx==1) flag=0;
    else if(mn==-1) sum--;
    else if(!mn&&!mx) cnt++;
  }
  if(cnt<sum) flag=0;
  if(!flag) return puts("0"), 0;
  int prod=1;
  rep(i,1,sum) prod=prod*i%mod;
  prod=ksm(prod,mod-2);
  rep(i,1,sum) prod=prod*(cnt-i+1)%mod;
  printf("%lld\n",prod);
  return 0;
}