Submission #4822871

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Source Code Expand

#include <bits/stdc++.h>
using namespace std;

using VS = vector<string>;    using LL = long long;
using VI = vector<int>;       using VVI = vector<VI>;
using PII = pair<int, int>;   using PLL = pair<LL, LL>;
using VL = vector<LL>;        using VVL = vector<VL>;

#define ALL(a)  begin((a)),end((a))
#define RALL(a) (a).rbegin(), (a).rend()
#define SZ(a) int((a).size())
#define SORT(c) sort(ALL((c)))
#define RSORT(c) sort(RALL((c)))
#define UNIQ(c) (c).erase(unique(ALL((c))), end((c)))
#define FOR(i, s, e) for (int(i) = (s); (i) < (e); (i)++)
#define FORR(i, s, e) for (int(i) = (s); (i) > (e); (i)--)
//#pragma GCC optimize ("-O3") 
#ifdef YANG33
#include "mydebug.hpp"
#else
#define DD(x) 
#endif
const int INF = 1e9;                          const LL LINF = 1e16;
const LL MOD = 1000000007;                    const double PI = acos(-1.0);
int DX[8] = { 0, 0, 1, -1, 1, 1, -1, -1 };    int DY[8] = { 1, -1, 0, 0, 1, -1, 1, -1 };

/* -----  2019/04/04  Problem: ABC 042 D / Link: http://abc042.contest.atcoder.jp/tasks/abc042_d  ----- */


template <std::uint_least32_t MODULO> class modint {
public:
using uint32 = std::uint_least32_t; using uint64 = std::uint_least64_t; using iint64 = std::int_fast64_t; class optimize_tag_t {}; static constexpr optimize_tag_t optimize_tag{}; public:using value_type = uint32; value_type a; static constexpr value_type cst(iint64 x) noexcept { x %= static_cast<iint64>(MODULO); if (x < static_cast<iint64>(0)) { x += static_cast<iint64>(MODULO); }return static_cast<value_type>(x); }constexpr modint(optimize_tag_t, const value_type &x) noexcept : a(x) {}constexpr modint() noexcept : a(static_cast<value_type>(0)) {}constexpr modint(const iint64 &x) noexcept : a(cst(x)) {}constexpr modint operator+(const modint &o) const noexcept { return modint(optimize_tag, a + o.a < MODULO ? a + o.a : a + o.a - MODULO); }constexpr modint operator-(const modint &o) const noexcept { return modint(optimize_tag, a < o.a ? a + MODULO - o.a : a - o.a); }constexpr modint operator*(const modint &o) const noexcept { return modint(optimize_tag, static_cast<value_type>(static_cast<uint64>(a) * static_cast<uint64>(o.a) % static_cast<uint64>(MODULO))); }constexpr modint operator/(const modint &o) const { return modint(optimize_tag, static_cast<value_type>(static_cast<uint64>(a) * static_cast<uint64>((~o).a) % static_cast<uint64>(MODULO))); }modint &operator+=(const modint &o) noexcept { if ((a += o.a) >= MODULO)a -= MODULO; return *this; }modint &operator-=(const modint &o) noexcept { if (a < o.a)a += MODULO; a -= o.a; return *this; }modint &operator*=(const modint &o) noexcept { a = static_cast<value_type>(static_cast<uint64>(a) * static_cast<uint64>(o.a) % static_cast<uint64>(MODULO)); return *this; }modint &operator/=(const modint &o) { a = static_cast<uint64>(a) * (~o).a % MODULO; return *this; }constexpr modint inverse() const noexcept { assert(a != static_cast<value_type>(0) && "0 does not have inverse"); return pow(static_cast<uint64>(MODULO - static_cast<value_type>(2))); }constexpr modint operator~() const noexcept { return inverse(); }constexpr modint operator-() const noexcept { if (a == static_cast<value_type>(0)) { return modint(optimize_tag, static_cast<value_type>(0)); } else { return modint(optimize_tag, MODULO - a); } }modint &operator++() noexcept { if (++a == MODULO) { a = static_cast<value_type>(0); }return *this; }modint &operator--() noexcept { if (a == static_cast<value_type>(0)) { a = MODULO; }--a; return *this; }constexpr bool operator==(const modint &o) const noexcept { return a == o.a; }constexpr bool operator!=(const modint &o) const noexcept { return a != o.a; }constexpr bool operator<(const modint &o) const noexcept { return a < o.a; }constexpr bool operator<=(const modint &o) const noexcept { return a <= o.a; }constexpr bool operator>(const modint &o) const noexcept { return a > o.a; }constexpr bool operator>=(const modint &o) const noexcept { return a >= o.a; }constexpr explicit operator bool() const noexcept { return a; }constexpr explicit operator value_type() const noexcept { return a; }modint pow(iint64 inx) const noexcept { if (inx < 0)assert(a != static_cast<value_type>(0) && "not pow index < 0"); uint64 x = inx; uint64 t = a, u = 1; while (x) { if (x & 1)u = u * t % MODULO; t = (t * t) % MODULO; x >>= 1; }return modint(optimize_tag, static_cast<value_type>(u)); }
constexpr value_type get() const noexcept { return a; }
};
using mint = modint<MOD>;
const mint mintzero = mint(0); const mint mintone = mint(1);
mint modinv(mint a) { return mintone / mint(a); }
vector<mint> fact, inv_fact;

void init_fact(int n) {
	fact.resize(n);
	fact[0] = mintone;
	for (int i = 1; i < n; i++) {
		fact[i] = fact[i - 1] * mint(i);
	}
	inv_fact.resize(n);
	inv_fact[n - 1] = modinv(fact[n - 1]);
	for (int i = n - 2; i >= 0; i--) {
		inv_fact[i] = mint(i + 1) * inv_fact[i + 1];
	}
}
mint nCr(int n, int r) {
	if (n < r || n < 0 || r < 0) return mintzero;
	return fact[n] * inv_fact[r] * inv_fact[n - r];
}

int main() {
	cin.tie(0);
	ios_base::sync_with_stdio(false);

	init_fact(200005);
	LL H, W, A, B; cin >> H >> W >> A >> B;
	mint ans = 0;
	FOR(i, 0, H - A) {
		mint sub = (nCr(B - 1 + i, B - 1)*nCr(W - B - 1 + H - 1 - i, W - B - 1));
		ans += sub;
	}

	cout << ans.get() << endl;

	return 0;
}

Submission Info

Judge Result