#include "bits/stdc++.h"
using namespace std;
#ifdef N_N_C
#include "debug.h"
#else
#define cebug(...) "Arya"
#endif
#define int long long
const int N=1e6+5;
const int mod=1e6+3;
int n,k,a[N],f[N],inv[N],b[N];
int powmod(int a, int k, int m){
int ans=1;
while(k){
if(k&1) ans=(ans*a)%m;
a=(a*a)%m;
k/=2;
}
return ans;
}
int C(int n, int k){
if(n<k || k<0) return 0;
return f[n]*inv[k]%mod*inv[n-k]%mod;
}
void sol(){
cin>>n>>k;
for(int i=k; i<=n; i++) cin>>a[i];
memset(b,-1,sizeof(b));
for(int i=k+1; i<=n; i++){
if(a[i]==a[i-1]+1){
if(b[i-k]==1){
cout<<"0";
return;
}
b[i-k]=0;
b[i]=1;
}else if(a[i]==a[i-1]){
if(b[i-k]==1) b[i]=1;
if(b[i-k]==0) b[i]=0;
}else if(a[i]==a[i-1]-1){
if(b[i-k]==0){
cout<<"0";
return;
}
b[i-k]=1;
b[i]=0;
}else{
cout<<"0";
return;
}
}
for(int i=n; i>=k+1; i--) if(a[i]==a[i-1]) b[i]=b[i-k]=max(b[i],b[i-k]);
int sz=0,cnt=0;
for(int i=1; i<=k; i++){
if(b[i]==-1) sz++;
if(b[i]==1) cnt++;
}
cout<<C(sz,a[k]-cnt);
}
signed main(){
ios_base::sync_with_stdio(false);
cin.tie(NULL);
// freopen(".inp", "r", stdin);
// freopen(".out", "w", stdout);
f[0]=1;
for(int i=1; i<N; i++) f[i]=(f[i-1]*i)%mod;
inv[0]=1;
for(int i=1; i<N; i++) inv[i]=powmod(f[i],mod-2,mod);
int tt=1;
//cin>>tt;
while(tt--){
sol();
}
cerr << "\nTime elapsed: " << 1000.0 * clock() / CLOCKS_PER_SEC << " ms.\n";
return 0;
}
