#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];
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);
}
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);
if (ifact[i] * fact[i].fi % MOD != 1) while(true) {};
}
// 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 |
33292 KB |
Output is correct |
| 2 |
Correct |
37 ms |
33400 KB |
Output is correct |
| 3 |
Correct |
35 ms |
33204 KB |
Output is correct |
| 4 |
Correct |
42 ms |
33272 KB |
Output is correct |
| 5 |
Correct |
261 ms |
33328 KB |
Output is correct |
| 6 |
Correct |
37 ms |
33372 KB |
Output is correct |
| 7 |
Correct |
48 ms |
33316 KB |
Output is correct |
| 8 |
Correct |
34 ms |
33364 KB |
Output is correct |
| 9 |
Correct |
98 ms |
34008 KB |
Output is correct |
| 10 |
Correct |
157 ms |
34808 KB |
Output is correct |
| 11 |
Correct |
286 ms |
47416 KB |
Output is correct |
| 12 |
Correct |
867 ms |
75640 KB |
Output is correct |
| 13 |
Execution timed out |
2045 ms |
72380 KB |
Time limit exceeded |
| 14 |
Execution timed out |
2078 ms |
48960 KB |
Time limit exceeded |
| 15 |
Execution timed out |
2031 ms |
48856 KB |
Time limit exceeded |
| 16 |
Execution timed out |
2048 ms |
77760 KB |
Time limit exceeded |
| 17 |
Execution timed out |
2024 ms |
76384 KB |
Time limit exceeded |
| 18 |
Execution timed out |
2016 ms |
80248 KB |
Time limit exceeded |
| 19 |
Execution timed out |
2040 ms |
80248 KB |
Time limit exceeded |
| 20 |
Execution timed out |
2077 ms |
80404 KB |
Time limit exceeded |
