Submission #2169462


Source Code Expand

#include <bits/stdc++.h>

#define _overload(_1,_2,_3,name,...) name
#define _rep(i,n) _range(i,0,n)
#define _range(i,a,b) for(int i=int(a);i<int(b);++i)
#define rep(...) _overload(__VA_ARGS__,_range,_rep,)(__VA_ARGS__)

#define _rrep(i,n) _rrange(i,n,0)
#define _rrange(i,a,b) for(int i=int(a)-1;i>=int(b);--i)
#define rrep(...) _overload(__VA_ARGS__,_rrange,_rrep,)(__VA_ARGS__)

#define _all(arg) begin(arg),end(arg)
#define uniq(arg) sort(_all(arg)),(arg).erase(unique(_all(arg)),end(arg))
#define getidx(ary,key) lower_bound(_all(ary),key)-begin(ary)
#define clr(a,b) memset((a),(b),sizeof(a))
#define bit(n) (1LL<<(n))
#define popcount(n) (__builtin_popcountll(n))

using namespace std;

template<class T>bool chmax(T &a, const T &b) { return (a < b) ? (a = b, 1) : 0;}
template<class T>bool chmin(T &a, const T &b) { return (b < a) ? (a = b, 1) : 0;}

using ll = long long;
using R = long double;
const R EPS = 1e-9L; // [-1000,1000]->EPS=1e-8 [-10000,10000]->EPS=1e-7
inline int sgn(const R& r) {return (r > EPS) - (r < -EPS);}
inline R sq(R x) {return sqrt(max(x, 0.0L));}

const int dx[8] = {1, 0, -1, 0, 1, -1, -1, 1};
const int dy[8] = {0, 1, 0, -1, 1, 1, -1, -1};

// Problem Specific Parameter:


template<int MOD> struct ModInt {
	static const int Mod = MOD;
	unsigned x;
	ModInt(): x(0) {}
	ModInt(signed sig) {int sigt = sig % MOD; if (sigt < 0) sigt += MOD; x = sigt; }
	ModInt(signed long long sig) { int sigt = sig % MOD; if (sigt < 0) sigt += MOD; x = sigt; }
	int getval() const { return int(x); }
	inline int extgcd(int a, int b, int& x, int& y) {x = 1, y = 0; int g = a; if (b != 0) g = extgcd(b, a % b, y, x), y -= a / b * x; return g;}


	ModInt &operator+=(ModInt that) { if ((x += that.x) >= MOD) x -= MOD; return *this; }
	ModInt &operator-=(ModInt that) { if ((x += MOD - that.x) >= MOD) x -= MOD; return *this; }
	ModInt &operator*=(ModInt that) { x = 1LL * x * that.x % MOD; return *this; }
	ModInt &operator/=(ModInt that) { int y, d; extgcd(that.x, MOD, y, d); return x = 1LL * x * y % MOD; return *this;}

	ModInt operator+(ModInt that) const { return ModInt(*this) += that; }
	ModInt operator-(ModInt that) const { return ModInt(*this) -= that; }
	ModInt operator*(ModInt that) const { return ModInt(*this) *= that; }
	ModInt operator/(ModInt that) const { return ModInt(*this) /= that; }
};

using mint = ModInt<1000000007>;

const int limit = 100000;
mint I[limit + 10];
void inv_table(int n) {I[1] = 1LL; rep(i, 2, n + 1) I[i] = I[mint::Mod % i] * (mint::Mod - mint::Mod / i);}

mint F[limit + 10], IF[limit + 10];
void fact_table(int n) {F[0] = IF[0] = 1LL; rep(i, 1, n + 1) F[i] = F[i - 1] * i, IF[i] = IF[i - 1] * I[i];}

inline mint comb(int n, int k) {return F[n] * IF[k] * IF[n - k];}


void init() {
	inv_table(limit);
	fact_table(limit);
}

mint dp[5010][5010][2];

int main(void) {
	init();

	int n, a, b, c;
	cin >> n >> a >> b >> c;

	dp[0][0][0] = mint(1);

	rep(block, n + 1)rep(three, n + 1)rep(state, 2) {
		if (dp[block][three][state].getval() == 0) continue;

		if (state == 0) {
			// 2222
			// 232 ... 3333 ... 232 first
			dp[block][three][1] += dp[block][three][0];
		} else {
			// 232 ... 3333 ... 232 middle
			dp[block][three + 1][1] += dp[block][three][1];
			// 232 ... 3333 ... 232 last
			dp[block + 1][three][0] += dp[block][three][1];
		}
	}

	// ca 2222  cb 232232 cc 3333 cd 333333 ce 3113 cf 11

	// a = ce + cf
	// b = 2 * ca + 2 * cb
	// c = cb + 2 * cc + 3 * cd + ce

	// block = ca + cb
	// three = cb + 2 * cc

	mint ans;
	rep(three, n + 1)rep(ce, n + 1) {
		if (b % 2 != 0) continue;
		const int block = b / 2;
		if (dp[block][three][0].getval() == 0) continue;
		if (a - ce < 0) continue;
		const int cf = a - ce;
		if (c - three - ce < 0 or (c - three - ce) % 3 != 0) continue;
		const int cd = (c - three - ce) / 3;

		mint cur = dp[block][three][0];
		mint coef = comb(block + cd + ce + cf, block) * comb(cd + ce + cf, cd) * comb(ce + cf, ce);
		ans += coef * cur;
	}

	cout << ans.getval() << endl;
	return 0;
}

Submission Info

Submission Time
Task J - 123 Pairs
User Hec
Language C++14 (GCC 5.4.1)
Score 1500
Code Size 4121 Byte
Status AC
Exec Time 311 ms
Memory 197632 KB

Judge Result

Set Name Sample All
Score / Max Score 0 / 0 1500 / 1500
Status
AC × 2
AC × 52
Set Name Test Cases
Sample example0.txt, example1.txt
All 000.txt, 001.txt, 002.txt, 003.txt, 004.txt, 005.txt, 006.txt, 007.txt, 008.txt, 009.txt, 010.txt, 011.txt, 012.txt, 013.txt, 014.txt, 015.txt, 016.txt, 017.txt, 018.txt, 019.txt, 020.txt, 021.txt, 022.txt, 023.txt, 024.txt, 025.txt, 026.txt, 027.txt, 028.txt, 029.txt, 030.txt, 031.txt, 032.txt, 033.txt, 034.txt, 035.txt, 036.txt, 037.txt, 038.txt, 039.txt, 040.txt, 041.txt, 042.txt, 043.txt, 044.txt, 045.txt, 046.txt, 047.txt, 048.txt, 049.txt, example0.txt, example1.txt
Case Name Status Exec Time Memory
000.txt AC 301 ms 197504 KB
001.txt AC 288 ms 197504 KB
002.txt AC 288 ms 197504 KB
003.txt AC 295 ms 197504 KB
004.txt AC 288 ms 197504 KB
005.txt AC 288 ms 197504 KB
006.txt AC 296 ms 197504 KB
007.txt AC 279 ms 197504 KB
008.txt AC 288 ms 197504 KB
009.txt AC 296 ms 197504 KB
010.txt AC 277 ms 197504 KB
011.txt AC 281 ms 197504 KB
012.txt AC 277 ms 197504 KB
013.txt AC 65 ms 197504 KB
014.txt AC 65 ms 197504 KB
015.txt AC 279 ms 197504 KB
016.txt AC 84 ms 197504 KB
017.txt AC 145 ms 197504 KB
018.txt AC 81 ms 197504 KB
019.txt AC 169 ms 197504 KB
020.txt AC 181 ms 197504 KB
021.txt AC 298 ms 197504 KB
022.txt AC 237 ms 197504 KB
023.txt AC 295 ms 197504 KB
024.txt AC 304 ms 197504 KB
025.txt AC 296 ms 197504 KB
026.txt AC 299 ms 197504 KB
027.txt AC 305 ms 197504 KB
028.txt AC 297 ms 197504 KB
029.txt AC 297 ms 197504 KB
030.txt AC 303 ms 197504 KB
031.txt AC 305 ms 197504 KB
032.txt AC 293 ms 197504 KB
033.txt AC 263 ms 197504 KB
034.txt AC 172 ms 197504 KB
035.txt AC 250 ms 197504 KB
036.txt AC 164 ms 197504 KB
037.txt AC 60 ms 197504 KB
038.txt AC 311 ms 197504 KB
039.txt AC 272 ms 197504 KB
040.txt AC 272 ms 197504 KB
041.txt AC 292 ms 197504 KB
042.txt AC 290 ms 197504 KB
043.txt AC 60 ms 197632 KB
044.txt AC 60 ms 197504 KB
045.txt AC 60 ms 197504 KB
046.txt AC 60 ms 197504 KB
047.txt AC 60 ms 197504 KB
048.txt AC 60 ms 197504 KB
049.txt AC 60 ms 197504 KB
example0.txt AC 60 ms 197504 KB
example1.txt AC 64 ms 197504 KB