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>
#define el '\n'
#define fi first
#define sc second
#define int ll
#define pii pair<int, int>
#define all(v) v.begin(), v.end()
using namespace std;
using ll=long long;
using ull=unsigned long long;
using ld=long double;
const int mod=1e6+3;
const int N=1e6+11;
int n, k, a[N], ned[N], f[N];
int po(int a, int b)
{
int r=1;
while(b)
{
if(b&1) r=r*a%mod;
b/=2;
a=a*a%mod;
}
return r%mod;
}
void sol()
{
cin >> n >> k;
for(int i=1;i<=n-k+1;i++) cin >> a[i];
for(int i=1;i<=n;i++) ned[i]=-1;
for(int i=1;i<=n-k;i++)
{
if(abs(a[i]-a[i+1])>=2)
{
cout << 0;
return;
}
if(a[i]>a[i+1])
{
if(ned[i]==0)
{
cout << 0;
return;
}
ned[i]=1;
}
else if(a[i]<a[i+1])
{
if(ned[i]==1)
{
cout << 0;
return;
}
ned[i]=0;
}
else if(a[i]==a[i+1]) ned[i]=ned[i+k];
}
f[0]=1;
int s1=a[1], s2=0;
for(int i=1;i<=k;i++)
{
if(ned[i]==1) s1--;
else if(ned[i]==-1) s2++;
}
for(int i=1;i<=k;i++) f[i]=f[i-1]*i%mod;
if(s1>s2) cout << 0;
else cout << f[s2]*po(f[s1], mod-2)%mod*po(f[s2-s1], mod-2)%mod;
}
signed main()
{
// freopen("divisor.INP", "r", stdin);
// freopen("divisor.OUT", "w", stdout);
ios_base::sync_with_stdio(0);
cin.tie(0);
int t=1;
//cin >> t;
while(t--)
{
sol();
}
}
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