#include <bits/stdc++.h>
using namespace std;
#define m_p make_pair
#define all(x) (x).begin(),(x).end()
#define sz(x) ((int)(x).size())
#define fi first
#define se second
typedef long long ll;
mt19937 rnd(chrono::steady_clock::now().time_since_epoch().count());
mt19937 rnf(2106);
const int N = 600005, K = 22;
int ast(int x, int n, int M)
{
int ans = 1;
while (n)
{
if (n % 2 == 1)
ans = (ans * 1LL * x) % M;
x = (x * 1LL * x) % M;
n /= 2;
}
return ans;
}
int M;
vector<pair<int, int> > p;
vector<int> pp;
vector<vector<int> > r;
vector<int> g[N];
vector<int> u[N];
void pre()
{
int x = M;
for (int i = 2; i * i <= x; ++i)
{
if (x % i == 0)
{
p.push_back(m_p(i, 0));
pp.push_back(1);
while (x % i == 0)
{
x /= i;
p.back().se++;
pp.back() *= i;
}
}
}
if (x > 1)
{
p.push_back(m_p(x, 1));
pp.push_back(x);
}
for (int i = 0; i < sz(p); ++i)
{
r.push_back({});
for (int j = 0; j < sz(p); ++j)
{
if (i == j)
{
r.back().push_back(0);
}
else
{
r.back().push_back(ast(pp[i], pp[j] - pp[j] / p[j].fi - 1, pp[j]));
}
}
}
g[0].assign(sz(p), 1);
u[0].assign(sz(p), 0);
for (int i = 1; i < N; ++i)
{
u[i].resize(sz(p));
for (int j = 0; j < sz(p); ++j)
u[i][j] = u[i - 1][j];
g[i].resize(sz(p));
for (int j = 0; j < sz(p); ++j)
{
int x = i;
while (x % p[j].fi == 0)
{
u[i][j]++;
x /= p[j].fi;
}
g[i][j] = (g[i - 1][j] * 1LL * x) % pp[j];
}
}
}
map<pair<int, int>, int> memo;
int C(int n, int k)
{
if (memo.find(m_p(n, k)) != memo.end())
return memo[m_p(n, k)];
static vector<int> a;
a.resize(sz(p));
for (int j = 0; j < sz(p); ++j)
{
int yans = (g[n][j] * 1LL * ast((g[k][j] * 1LL * g[n - k][j]) % pp[j], pp[j] - pp[j] / p[j].fi - 1, pp[j])) % pp[j];
int uu = u[n][j] - u[n - k][j] - u[k][j];
if (uu >= p[j].se)
yans = 0;
else
yans = (yans * 1LL * ast(p[j].fi, uu, pp[j])) % pp[j];
a[j] = yans;
}
static vector<int> x;
x.resize(sz(p));
for (int j = 0; j < sz(p); ++j)
{
x[j] = a[j];
for (int k = 0; k < j; ++k)
x[j] = ((x[j] - x[k]) * 1LL * r[k][j]) % pp[j];
}
int ans = 0;
for (int j = sz(p) - 1; j >= 0; --j)
{
ans = (ans + x[j]) % M;
if (j - 1 >= 0)
ans = (ans * 1LL * pp[j - 1]) % M;
}
return memo[m_p(n, k)] = ans;
}
int n, m, k, t;
pair<int, int> a[K];
int q[K];
int yans[K];
void solv()
{
cin >> n >> m >> k >> t >> M;
for (int i = 0; i < k; ++i)
cin >> a[i].fi >> a[i].se;
pre();
sort(a, a + k);
for (int x = 0; x < (1 << k); ++x)
{
vector<pair<int, int> > v;
v.push_back(m_p(0, 0));
for (int i = 0; i < k; ++i)
{
if ((x & (1 << i)))
v.push_back(a[i]);
}
v.push_back(m_p(n, m));
bool z = true;
for (int i = 0; i < sz(v) - 1; ++i)
{
if (!(v[i].fi <= v[i + 1].fi && v[i].se <= v[i + 1].se))
{
z = false;
break;
}
}
if (!z)
continue;
int ans = 1;
for (int i = 0; i < sz(v) - 1; ++i)
ans = (ans * 1LL * C(v[i + 1].fi - v[i].fi + v[i + 1].se - v[i].se, v[i + 1].fi - v[i].fi)) % M;
q[sz(v) - 2] = (q[sz(v) - 2] + ans) % M;
}
for (int i = k; i >= 0; --i)
{
yans[i] = q[i];
for (int j = i + 1; j <= k; ++j)
{
yans[i] = (yans[i] - yans[j] * 1LL * C(j, i)) % M;
}
}
int ans = 0;
for (int i = 0; i <= t; ++i)
ans = (ans + yans[i]) % M;
ans = (ans + M) % M;
cout << ans << "\n";
}
int main()
{
#ifdef SOMETHING
freopen("input.txt", "r", stdin);
//freopen("output.txt", "w", stdout);
#endif // SOMETHING
ios_base::sync_with_stdio(false), cin.tie(0);
int tt = 1;
//cin >> tt;
while (tt--)
solv();
return 0;
}
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Correct |
131 ms |
65968 KB |
Output is correct |
| 2 |
Correct |
131 ms |
66052 KB |
Output is correct |
| 3 |
Correct |
135 ms |
66000 KB |
Output is correct |
| 4 |
Correct |
124 ms |
65988 KB |
Output is correct |
| 5 |
Correct |
352 ms |
66128 KB |
Output is correct |
| 6 |
Correct |
96 ms |
65944 KB |
Output is correct |
| 7 |
Correct |
111 ms |
65976 KB |
Output is correct |
| 8 |
Correct |
97 ms |
66064 KB |
Output is correct |
| 9 |
Correct |
156 ms |
66196 KB |
Output is correct |
| 10 |
Correct |
222 ms |
66116 KB |
Output is correct |
| 11 |
Correct |
111 ms |
66024 KB |
Output is correct |
| 12 |
Correct |
217 ms |
66064 KB |
Output is correct |
| 13 |
Correct |
132 ms |
65996 KB |
Output is correct |
| 14 |
Correct |
219 ms |
66048 KB |
Output is correct |
| 15 |
Correct |
376 ms |
66120 KB |
Output is correct |
| 16 |
Correct |
381 ms |
66064 KB |
Output is correct |
| 17 |
Correct |
187 ms |
66036 KB |
Output is correct |
| 18 |
Correct |
859 ms |
66176 KB |
Output is correct |
| 19 |
Correct |
885 ms |
66200 KB |
Output is correct |
| 20 |
Correct |
375 ms |
66104 KB |
Output is correct |
