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;
#define fi first
#define se second
#define pb push_back
#define mp make_pair
#define foru(i, l, r) for(int i = l; i <= r; i++)
#define ford(i, r, l) for(int i = r; i >= l; i--)
#define __TIME (1.0 * clock() / CLOCKS_PER_SEC)
typedef pair<int, int> ii;
typedef pair<ii, int> iii;
typedef pair<ii, ii> iiii;
const int N = 1e6 + 5;
const int oo = 1e9, mod = 1e6 + 3;
int n, m, k, fact[N], inv[N], a[N], color[N];
string s;
vector<int> arr;
long long binpow(long long a, long long b) {
a %= mod;
long long res = 1;
while (b > 0) {
if (b & 1)
res = res * a % mod;
a = a * a % mod;
b >>= 1;
}
return res;
}
int comb(int k, int n) {
if (k > n || k < 0) return 0;
return (fact[n] * ((inv[k] * inv[n - k]) % mod)) % mod;
}
void process() {
cin >> n >> k;
foru(i, 1, n - k + 1) cin >> a[i];
fact[0] = inv[0] = 1;
foru(i, 1, n) fact[i] = (fact[i - 1] * i) % mod;
inv[n] = binpow(fact[n], mod - 2);
ford(i, n - 1, 1) inv[i] = (inv[i + 1] * (i + 1)) % mod;
foru(i, 1, n) color[i] = 2;
ford(i, n - k, 1) {
if (abs(a[i] - a[i + 1]) > 1) {
cout << 0 << '\n'; return;
}
if (a[i] == a[i + 1]) color[i] = color[i + k];
else if (a[i] > a[i + 1]) {
if (color[i + k] == 1) {
cout << 0 << '\n'; return;
}
color[i] = 1;
} else {
if (color[i + k] == 0) {
cout << 0 << '\n'; return;
}
color[i] = 0;
}
}
int ans = 0;
foru(i, 1, k) a[1] -= (color[i] == 1), ans += color[i] == 2;
cout << comb(a[1], ans);
return;
}
signed main() {
cin.tie(0)->sync_with_stdio(false);
//freopen(".inp", "r", stdin);
//freopen(".out", "w", stdout);
process();
cerr << "Time elapsed: " << __TIME << " s.\n";
return 0;
}
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