답안 #96517

# 제출 시각 아이디 문제 언어 결과 실행 시간 메모리
96517 2019-02-10T05:50:01 Z qkxwsm 힘 센 거북 (IZhO11_turtle) C++14
45 / 100
2000 ms 70292 KB
#pragma GCC optimize ("O3")
#pragma GCC target ("sse4")
#include <bits/stdc++.h>
#include <ext/pb_ds/tree_policy.hpp>
#include <ext/pb_ds/assoc_container.hpp>
#include <ext/rope>

using namespace std;
using namespace __gnu_pbds;
using namespace __gnu_cxx;

random_device(rd);
mt19937 rng(rd());
const long long FIXED_RANDOM = chrono::steady_clock::now().time_since_epoch().count();

struct custom_hash
{
	template<class T>
	unsigned long long operator()(T v) const
	{
		unsigned long long x = v;
		x += FIXED_RANDOM;
		// x += 11400714819323198485ull;
		// x = (x ^ (x >> 30)) * 13787848793156543929ull;
		x = (x ^ (x >> 27)) * 10723151780598845931ull;
		return x ^ (x >> 31);
	}
};

template<class T> using ordered_set = tree<T, null_type, less<T>, rb_tree_tag, tree_order_statistics_node_update>;
template<class T, class U> using hash_table = gp_hash_table<T, U, custom_hash>;

template<class T>
T randomize(T mod)
{
	return (uniform_int_distribution<T>(0, mod - 1))(rng);
}
template<class T>
void readi(T &x)
{
	x = 0;
	bool negative = false;
	char c = ' ';
	while (c < '-')
	{
		c = getchar();
	}
	if (c == '-')
	{
		negative = true;
		c = getchar();
	}
	while (c >= '0')
	{
		x = x * 10 + (c - '0');
		c = getchar();
	}
	if (negative)
	{
		x = -x;
	}
}
template<class T>
void printi(T output)
{
	if (output == 0)
	{
		putchar('0');
		return;
	}
	if (output < 0)
	{
		putchar('-');
		output = -output;
	}
	int buf[20], n = 0;
	while(output)
	{
		buf[n] = ((output % 10));
		output /= 10;
		n++;
	}
	for (n--; n >= 0; n--)
	{
		putchar(buf[n] + '0');
	}
	return;
}
template<class T>
void ckmin(T &a, T b)
{
	a = min(a, b);
}
template<class T>
void ckmax(T &a, T b)
{
	a = max(a, b);
}
long long expo(long long a, long long e, long long mod)
{
	return ((e == 0) ? 1 : ((expo(a * a % mod, e >> 1, mod)) * ((e & 1) ? a : 1) % mod));
}
template<class T, class U>
void nmod(T &x, U mod)
{
	if (x >= mod) x -= mod;
}
template<class T>
T gcd(T a, T b)
{
	return (b ? gcd(b, a % b) : a);
}

#define y0 ___y0
#define y1 ___y1
#define MP make_pair
#define PB push_back
#define LB lower_bound
#define UB upper_bound
#define fi first
#define se second
#define DBG(x) cerr << #x << " = " << (x) << endl
#define SZ(x) ((int) ((x).size()))
#define FOR(i, a, b) for (auto i = (a); i < (b); i++)
#define FORD(i, a, b) for (auto i = (a) - 1; i >= (b); i--)
#define ALL(x) (x).begin(), (x).end()

const long double PI = 4.0 * atan(1.0);
const long double EPS = 1e-9;

#define MAGIC 347
#define SINF 10007
#define CO 1000007
#define INF 1000000007
#define BIG 1000000931
#define LARGE 1696969696967ll
#define GIANT 2564008813937411ll
#define LLINF 2696969696969696969ll
#define MAXN 600013

typedef long long ll;
typedef long double ld;
typedef pair<int, int> pii;
typedef pair<ll, ll> pll;
typedef pair<ld, ld> pdd;
typedef vector<int> vi;
typedef vector<ll> vl;
typedef vector<ld> vd;
typedef vector<pii> vpi;
typedef vector<pll> vpl;
typedef vector<pdd> vpd;

int N, M, K, T;
ll MOD;
pii coor[MAXN];
ll num[22];
ll dp[2013][2013];
ll ans = 0;
ll phi;
vpl primes;
hash_table<ll, vpl> factors;
pair<ll, vpl> fact[MAXN];

ll choose(ll a, ll b)
{
	// cerr << a << ' ' << b << ' ' << dp[a][b] << endl;
	ll res = fact[a].fi;
	res *= expo(fact[b].fi, phi - 1, MOD); res %= MOD;
	res *= expo(fact[a - b].fi, phi - 1, MOD); res %= MOD;
	FOR(i, 0, SZ(primes))
	{
		res *= expo(primes[i].fi, fact[a].se[i].se - fact[a - b].se[i].se - fact[b].se[i].se, MOD); res %= MOD;
	}
	// if (dp[a][b] != res)
	// {
	// 	cerr << "dead " << a << ' ' << b << ' ' << dp[a][b] << ' ' << res << endl; exit(0);
	// }
	return res;
	// cerr << a << ' ' << b << endl;
}

int32_t main()
{
	ios_base::sync_with_stdio(0); cin.tie(0);
	// cout << fixed << setprecision(10);
	// cerr << fixed << setprecision(10);
	// if (fopen("file.in", "r"))
	// {
	// 	freopen ("file.in", "r", stdin);
	// 	freopen ("file.out", "w", stdout);
	// }
	cin >> N >> M >> K >> T >> MOD;
	if (MOD == 1)
	{
		cout << "0\n";
		return 0;
	}
	int mod = MOD;
	for (int i = 2; i * i <= mod; i++)
	{
		if (mod % i) continue;
		primes.PB({i, 0});
		while(mod % i == 0)
		{
			mod /= i;
			primes.back().se++;
		}
	}
	if (mod != 1)
	{
		primes.PB({mod, 1});
	}
	for (int i = 1; i * i <= MOD; i++)
	{
		if (MOD % i) continue;
		mod = i;
		for (pll p : primes)
		{
			factors[i].PB({p.fi, 0});
			if (i * i != MOD) factors[MOD / i].PB({p.fi, p.se});
			while(mod % p.fi == 0)
			{
				mod /= p.fi;
				factors[i].back().se++;
				if (i * i  != MOD) factors[MOD / i].back().se--;
			}
		}
	}
	// for (auto p : factors)
	// {
	// 	cerr << "factor " << p.fi << ":";
	// 	for (auto q : p.se)
	// 	{
	// 		cerr << ' ' << q.fi << ',' << q.se;
	// 	}
	// 	cerr << endl;
	// }
	FOR(i, 0, K)
	{
		cin >> coor[i].fi >> coor[i].se;
	}
	dp[0][0] = 1;
	FOR(i, 1, 2010)
	{
		dp[i][0] = dp[i][i] = 1;
		FOR(j, 1, i) dp[i][j] = (dp[i - 1][j] + dp[i - 1][j - 1]) % MOD;
	}
	sort(coor, coor + K);
	FOR(i, 0, K + 1)
	{
		ll take = (i <= T ? 1 : 0) - num[i]; take += MOD; nmod(take, MOD);
		num[i] = take;
		FOR(j, i + 1, K + 1)
		{
			num[j] += take * dp[j][i];
			num[j] %= MOD; nmod(take, MOD);
		}
		// DBG(num[i]);
	}
	fact[0].fi = 1;
	fact[0].se = factors[1];
	FOR(i, 1, N + M + 2)
	{
		ll g = gcd((ll) i, MOD); vpl f = factors[g];
		fact[i].fi = fact[i - 1].fi * (i / g); fact[i].fi %= MOD;
		fact[i].se = fact[i - 1].se;
		FOR(j, 0, SZ(fact[i].se))
		{
			fact[i].se[j].se += f[j].se;
		}
		// cerr << i << ' ' << fact[i].fi;
		// for (auto p : fact[i].se)
		// {
		// 	cerr << ' ' << p.fi << ',' << p.se;
		// }
		// cerr << endl;
	}
	phi = MOD;
	for (pll p : primes)
	{
		phi /= p.fi;
		phi *= (p.fi - 1);
	}
	// DBG(phi);
	FOR(mask, 0, (1 << K))
	{
		ll cur = num[__builtin_popcount(mask)];
		pii block = MP(0, 0);
		FOR(i, 0, K)
		{
			if (!(mask & (1 << i))) continue;
			if (coor[i].se < block.se)
			{
				cur = 0;
				break;
			}
			cur *= choose(coor[i].fi - block.fi + coor[i].se - block.se, coor[i].se - block.se);
			block = coor[i];
			cur %= MOD;
		}
		cur *= choose(N - block.fi + M - block.se, N - block.fi);
		cur %= MOD;
		// DBG(cur);
		ans += cur; nmod(ans, MOD);
	}
	cout << ans << '\n';
	// cerr << "time elapsed = " << (clock() / (CLOCKS_PER_SEC / 1000)) << " ms" << endl;
	return 0;
}
/* READ READ READ
* int overflow, maxn too small, special cases (n=1?, two distinct?), cin.tie() interactive
* reread the problem, try small cases
* note down possible sources of error as you go
* do smth instead of nothing
*/
# 결과 실행 시간 메모리 Grader output
1 Correct 62 ms 41948 KB Output is correct
2 Correct 63 ms 42152 KB Output is correct
3 Correct 62 ms 41976 KB Output is correct
4 Correct 211 ms 41980 KB Output is correct
5 Execution timed out 2061 ms 41968 KB Time limit exceeded
6 Correct 84 ms 42104 KB Output is correct
7 Correct 314 ms 42152 KB Output is correct
8 Correct 67 ms 42104 KB Output is correct
9 Correct 1139 ms 42384 KB Output is correct
10 Execution timed out 2016 ms 42616 KB Time limit exceeded
11 Correct 454 ms 48444 KB Output is correct
12 Execution timed out 2097 ms 60912 KB Time limit exceeded
13 Incorrect 276 ms 65528 KB Output isn't correct
14 Execution timed out 2096 ms 51472 KB Time limit exceeded
15 Execution timed out 2106 ms 51448 KB Time limit exceeded
16 Execution timed out 2080 ms 68736 KB Time limit exceeded
17 Execution timed out 2085 ms 67832 KB Time limit exceeded
18 Execution timed out 2020 ms 70240 KB Time limit exceeded
19 Execution timed out 2060 ms 70292 KB Time limit exceeded
20 Execution timed out 2092 ms 70236 KB Time limit exceeded