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>
#ifdef LOCAL
#include "D:\debug.h"
#else
#define cebug(...) "Orz_chUoNgnn_khanhtb_0x2ee08"
#endif
using namespace std;
#define int long long
#define fi first
#define se second
#define pb push_back
#define ll long long
#define ii pair<int, int>
#define vi vector<int>
#define vll vector<ll>
#define vii vector<ii>
#define cd complex<double>
const ll mod = 1e6 + 3;
const ll INF = 1e18L + 5;
const double PI = acos(-1);
const int block = 320;
const int N = 1e6;
int tc, tt = 1;
int n, k;
ll a[N + 5], b[N + 5];
vi g[N + 5];
int vis[N + 5];
ll powmod(ll a, ll b) {
ll ans = 1;
while(b) {
if(b & 1) ans = ans * a % mod;
a = a * a % mod;
b /= 2;
}
return ans;
}
void dfs(int root, int u, int par) {
cerr<<root<<' '<<u<<'\n';
b[u] = b[root];
vis[u] = true;
for(auto v: g[u])
if(!vis[v]) dfs(root, v, u);
}
void solve() {
cin>>n>>k;
memset(b, -1, sizeof(b));
for(int i=1; i<=n-k+1; i++)
cin>>a[i];
for(int i=2; i<=n-k+1; i++) {
if(abs(a[i] - a[i - 1]) > 1) {
cout<<0<<'\n';
return;
}
if(a[i] == a[i - 1]) {
g[i + k - 1].pb(i - 1);
g[i - 1].pb(i + k - 1);
}
if(a[i] > a[i - 1]) {
if(b[i - 1] == 1 || b[i + k - 1] == 0) {
cout<<0<<'\n';
return;
}
b[i - 1] = 0;
b[i + k - 1] = 1;
}
if(a[i] < a[i - 1]) {
if(b[i - 1] == 0 || b[i + k - 1] == 1) {
cout<<0<<'\n';
return;
}
b[i - 1] = 1;
b[i + k - 1] = 0;
}
}
for(int i=1; i<=n; i++)
cerr<<b[i]<<' ';
cerr<<'\n';
for(int i=1; i<=n; i++)
if(b[i] != -1 && !vis[i]) dfs(i, i, -1);
ll ans = 1, sum = 0, cnt = 0;
for(int i=1; i<=k; i++) {
if(b[i] == -1) cnt++;
else sum += b[i];
}
if(sum > a[1] || sum > cnt) {
cout<<0<<'\n';
return;
}
sum = a[1] - sum;
for(int i=cnt; i>=cnt - sum + 1; i--) ans = ans * i % mod;
ll dem = 1;
for(int i=1; i<=sum; i++) dem = dem * i % mod;
ans = ans * powmod(dem, mod - 2) % mod;
cout<<ans;
}
signed main() {
ios_base::sync_with_stdio(0);
cin.tie(0); cout.tie(0);
for(tc=1; tc<=tt; tc++) solve();
cerr<<"\nTime elapsed: "<<1000.0*clock()/CLOCKS_PER_SEC<<" ms.\n";
return 0;
}
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