Submission #96534

# Submission time Handle Problem Language Result Execution time Memory
96534 2019-02-10T06:52:00 Z qkxwsm Energetic turtle (IZhO11_turtle) C++14
60 / 100
2000 ms 75604 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[69][69];
ll ans = 0;
ll phi;
vpl primes;
hash_table<ll, vpl> factors;
pair<ll, vpl> fact[MAXN];
ll ifact[MAXN];
vl pows[MAXN];

ll choose(ll a, ll b)
{
	// cerr << a << ' ' << b << ' ' << dp[a][b] << endl;
	ll res = fact[a].fi;
	res *= ifact[b]; res %= MOD;
	res *= ifact[a - b]; 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 *= pows[fact[a].se[i].se - fact[a - b].se[i].se - fact[b].se[i].se][i]; res %= MOD;
		// 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, 42)
	{
		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];
		if(gcd(i / g, MOD) != 1) while(true){};
		fact[i].fi = (fact[i - 1].fi * ((ll) i / g)) % 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);
	}
	FOR(i, 0, SZ(primes))
	{
		pows[0].PB(1);
	}
	FOR(i, 1, N + M + 2)
	{
		pows[i] = pows[i - 1];
		FOR(j, 0, SZ(primes))
		{
			pows[i][j] *= primes[j].fi;
			pows[i][j] %= MOD;
		}
	}
	FOR(i, 0, N + M + 2)
	{
		ifact[i] = expo(fact[i].fi, phi - 1, MOD);
	}
	// 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
*/
# Verdict Execution time Memory Grader output
1 Correct 35 ms 33416 KB Output is correct
2 Correct 35 ms 33272 KB Output is correct
3 Correct 35 ms 33256 KB Output is correct
4 Correct 42 ms 33192 KB Output is correct
5 Correct 253 ms 33340 KB Output is correct
6 Correct 45 ms 33372 KB Output is correct
7 Correct 55 ms 33272 KB Output is correct
8 Correct 43 ms 33380 KB Output is correct
9 Correct 102 ms 34012 KB Output is correct
10 Correct 161 ms 34732 KB Output is correct
11 Correct 329 ms 47324 KB Output is correct
12 Correct 975 ms 75604 KB Output is correct
13 Execution timed out 2009 ms 33272 KB Time limit exceeded
14 Execution timed out 2099 ms 33272 KB Time limit exceeded
15 Execution timed out 2077 ms 33400 KB Time limit exceeded
16 Execution timed out 2013 ms 33340 KB Time limit exceeded
17 Execution timed out 2089 ms 33272 KB Time limit exceeded
18 Execution timed out 2099 ms 33372 KB Time limit exceeded
19 Execution timed out 2009 ms 33276 KB Time limit exceeded
20 Execution timed out 2054 ms 33344 KB Time limit exceeded