Submission #96521

# Submission time Handle Problem Language Result Execution time Memory
96521 2019-02-10T06:11:11 Z qkxwsm Energetic turtle (IZhO11_turtle) C++14
35 / 100
2000 ms 142208 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;
	return dp[a][b];
	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
*/
# Verdict Execution time Memory Grader output
1 Correct 61 ms 41976 KB Output is correct
2 Correct 62 ms 42104 KB Output is correct
3 Correct 59 ms 41976 KB Output is correct
4 Correct 179 ms 42068 KB Output is correct
5 Execution timed out 2066 ms 42140 KB Time limit exceeded
6 Correct 78 ms 41976 KB Output is correct
7 Correct 275 ms 42104 KB Output is correct
8 Correct 72 ms 41980 KB Output is correct
9 Runtime error 129 ms 85556 KB Execution killed with signal 11 (could be triggered by violating memory limits)
10 Runtime error 136 ms 86208 KB Execution killed with signal 11 (could be triggered by violating memory limits)
11 Runtime error 205 ms 97656 KB Execution killed with signal 11 (could be triggered by violating memory limits)
12 Runtime error 363 ms 123048 KB Execution killed with signal 11 (could be triggered by violating memory limits)
13 Runtime error 341 ms 132544 KB Execution killed with signal 11 (could be triggered by violating memory limits)
14 Runtime error 211 ms 104148 KB Execution killed with signal 11 (could be triggered by violating memory limits)
15 Runtime error 228 ms 104056 KB Execution killed with signal 11 (could be triggered by violating memory limits)
16 Runtime error 399 ms 139000 KB Execution killed with signal 11 (could be triggered by violating memory limits)
17 Runtime error 376 ms 137368 KB Execution killed with signal 11 (could be triggered by violating memory limits)
18 Runtime error 427 ms 142016 KB Execution killed with signal 11 (could be triggered by violating memory limits)
19 Runtime error 391 ms 141984 KB Execution killed with signal 11 (could be triggered by violating memory limits)
20 Runtime error 413 ms 142208 KB Execution killed with signal 11 (could be triggered by violating memory limits)