Submission #475411

#TimeUsernameProblemLanguageResultExecution timeMemory
475411SamAndEnergetic turtle (IZhO11_turtle)C++17
90 / 100
2100 ms66144 KiB
#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]; } } } int C(int n, int 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 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; }
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