답안 #96520

# 제출 시각 아이디 문제 언어 결과 실행 시간 메모리
96520 2019-02-10T06:10:43 Z qkxwsm 힘 센 거북 (IZhO11_turtle) C++14
45 / 100
2000 ms 70152 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))
	{
		assert(fact[a].se[i].se - fact[a - b].se[i].se - fact[b].se[i].se >= 0);
		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 64 ms 42108 KB Output is correct
2 Correct 64 ms 42060 KB Output is correct
3 Correct 62 ms 42028 KB Output is correct
4 Correct 205 ms 41976 KB Output is correct
5 Execution timed out 2053 ms 42076 KB Time limit exceeded
6 Correct 78 ms 42100 KB Output is correct
7 Correct 320 ms 42108 KB Output is correct
8 Correct 67 ms 42132 KB Output is correct
9 Correct 1129 ms 42380 KB Output is correct
10 Execution timed out 2048 ms 42616 KB Time limit exceeded
11 Correct 429 ms 48244 KB Output is correct
12 Execution timed out 2094 ms 60848 KB Time limit exceeded
13 Incorrect 285 ms 65564 KB Output isn't correct
14 Execution timed out 2011 ms 51432 KB Time limit exceeded
15 Execution timed out 2016 ms 51444 KB Time limit exceeded
16 Execution timed out 2032 ms 68732 KB Time limit exceeded
17 Execution timed out 2061 ms 67780 KB Time limit exceeded
18 Execution timed out 2033 ms 70136 KB Time limit exceeded
19 Execution timed out 2031 ms 70132 KB Time limit exceeded
20 Execution timed out 2041 ms 70152 KB Time limit exceeded