// #pragma GCC optimize("O3", "unroll-loops")
// #pragma GCC target("avx2", "bmi", "bmi2", "lzcnt", "popcnt")
#include <bits/stdc++.h>
#define ldb long double
//#define double ldb
#define db double
#define unomap unordered_map
#define unoset unordered_set
#define endl '\n'
#define str string
#define strstr stringstream
#define sz(a) (int)a.size()
#define ll long long
//#define int ll
#define pii pair <int, int>
#define pll pair <ll, ll>
#define Unique(a) a.resize(unique(all(a)) - a.begin())
#define ull unsigned ll
#define fir first
#define sec second
#define idc cin.ignore()
#define lb lower_bound
#define ub upper_bound
#define all(s) s.begin(), s.end()
#define rev reverse
#define gcd __gcd
#define pushb push_back
#define popb pop_back
#define pushf push_front
#define popf pop_front
#define mul2x(a, x) a << x
#define div2x(a, x) a >> x
#define lcm(a, b) (a / __gcd(a, b) * b)
#define log_base(x, base) log(x) / log(base)
#define debug cerr << "No errors!"; exit(0);
#define forw(i, a, b) for (int i = a; i <= b; ++i)
#define forw2(i, a, b) for (ll i = a; i <= b; ++i)
#define fors(i, a, b) for (int i = a; i >= b; --i)
#define fors2(i, a, b) for (ll i = a; i >= b; --i)
#define pqueue priority_queue
#define sqrt sqrtl
#define i128 __int128
#define popcount __builtin_popcountll
#define BIT(x, i) (((x) >> (i)) & 1)
#define MASK(x) ((1LL) << (x))
#define want_digit(x) cout << fixed << setprecision(x);
#define excuting_time 1000.0 * clock() / CLOCKS_PER_SEC
#define mapa make_pair
using namespace std;
// const int MOD = 1e9 + 7; // 998244353
const int MOD = 1e6 + 3;
const int inf = 1e9;
const ll INF = 1e18; // MASK(63) - 1
const int N = 4e5;
mt19937_64 rng(chrono::steady_clock::now().time_since_epoch().count());
ll random(const ll &L, const ll &R) {
return uniform_int_distribution<ll> (L, R) (rng);
}
int n, a[N + 5], m, lim;
const int LIM = 8e5;
ll fact[LIM + 5], invfact[LIM + 5], invNum[N + 5];
ll powmod(ll a, ll b) {
ll res = 1;
while (b) {
if (b & 1) res = res * a % MOD;
a = a * a % MOD;
b >>= 1;
}
return res;
}
ll C(ll n, ll k) {
if (k < 0 || k > n) return 0;
return fact[n] * invfact[k] % MOD * invfact[n - k] % MOD;
}
void build() {
fact[0] = 1;
forw (i, 1, LIM) fact[i] = fact[i - 1] * i % MOD;
invfact[LIM] = powmod(fact[LIM], MOD - 2);
fors (i, LIM - 1, 0) invfact[i] = invfact[i + 1] * (i + 1) % MOD;
invNum[1] = 1;
forw (i, 2, N + 1) invNum[i] = MOD - MOD / i * invNum[MOD % i] % MOD;
}
ll catalan(ll n) {
return C(2 * n, n) * invNum[n + 1] % MOD;
}
const int N4 = 4e3;
ll dp[N4 + 5];
void sub4() {
dp[0] = 1;
for (int i = 2; i <= lim; i += 2) {
for (int j = i - 1; j >= 1 && a[j] + m >= a[i]; j -= 2) {
(dp[i] += dp[j - 1] * catalan((i - j - 1) / 2)) %= MOD;
}
}
cout << dp[lim] << endl;
}
void sub5() {
}
void solve() {
cin >> n >> m;
lim = n << 1;
forw (i, 1, lim) cin >> a[i];
build();
if (n <= 2e3) sub4();
else sub5();
}
signed main() {
ios::sync_with_stdio(false), cin.tie(nullptr);
srand(time(NULL));
#define name "test"
/*
if (fopen(name".INP", "r")) {
freopen(name".INP", "r", stdin);
freopen(name".OUT", "w", stdout);
}
*/
bool testCase = false;
int numTest = 1;
// cin >> numTest;
forw (i, 1, numTest) {
if (testCase) cout << "Case " << i << ": ";
solve();
}
return 0;
}
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