#include #include using namespace std; using namespace atcoder; typedef modint998244353 mint; typedef long long ll; // https://tjkendev.github.io/procon-library/cpp/convex_hull_trick/li_chao_tree_dynamic.html class LiChaoTree { struct Line { ll a, b; ll f(ll x) const { return a*x + b; } Line(ll a, ll b) : a(a), b(b) {} }; struct Node { Node *left, *right; Line line; Node(Line line) : left(nullptr), right(nullptr), line(line) {} }; const ll inf = 1e16L; const Line inf_line = Line{0, inf}; Node* root; ll xl, xr; Node* _add_line(Node *nd, Line line, ll l, ll r) { if(l == r) return nullptr; ll m = (l + r) >> 1; if(nd == nullptr) return new Node(line); bool left = (line.f(l) <= nd->line.f(l)); bool mid = (line.f(m) <= nd->line.f(m)); bool right = (line.f(r) <= nd->line.f(r)); if(left && right) { nd->line = line; return nd; } if(!left && !right) { return nd; } if(mid) { swap(nd->line, line); } if(left != mid) { nd->left = _add_line(nd->left, line, l, m); } else { nd->right = _add_line(nd->right, line, m, r); } return nd; } Node* _add_segment_line(ll a, ll b, Node *nd, Line line, ll l, ll r) { if(r <= a || b <= l) { return nd; } if(a <= l && r <= b) { return _add_line(nd, line, l, r); } if(nd == nullptr) { nd = new Node(inf_line); } ll m = (l + r) >> 1; nd->left = _add_segment_line(a, b, nd->left, line, l, m); nd->right = _add_segment_line(a, b, nd->right, line, m, r); return nd; } ll _query(ll k, ll l, ll r) { Node *nd = root; ll s = inf; while(r-l > 0 && nd != nullptr) { ll m = (l + r) >> 1; s = min(s, nd->line.f(k)); if(k < m) { r = m; nd = nd->left; } else { l = m; nd = nd->right; } } return s; } public: // [xl, xr) LiChaoTree(ll xl, ll xr) : xl(xl), xr(xr), root(nullptr) {} void add_line(ll a, ll b) { Line line = Line{a, b}; root = _add_line(root, line, xl, xr); } void add_segment_line(ll a, ll b, ll l, ll r) { Line line = Line{a, b}; root = _add_segment_line(l, r, root, line, xl, xr); } ll query(ll x) { return _query(x, xl, xr); } }; // isprime bool isprime(ll n){ if (n == 1) return false; for (ll i = 2; i * i <= n; i++){ if (n % i == 0) return false; } return true; } // importrandom // don't forget randomjumon // and also isprime ll RandomMod(ll l, ll r){ ll ret = l + rand() % (r - l); while (!isprime(ret)) ret = l + rand() % (r - l); return ret; } ll randrange(ll l, ll r){ return l + rand() % (r - l); } // ----- // defcomp template vector compress(vector &X) { vector vals = X; sort(vals.begin(), vals.end()); vals.erase(unique(vals.begin(), vals.end()), vals.end()); return vals; } // ----- // importbisect template int bisect_left(vector &X, T v){ return lower_bound(X.begin(), X.end(), v) - X.begin(); } template int bisect_right(vector &X, T v){ return upper_bound(X.begin(), X.end(), v) - X.begin(); } // ----- int main(){ srand((unsigned)time(NULL)); // Rolling Hash typedef dynamic_modint<0> mint1; typedef dynamic_modint<1> mint2; int mod1 = RandomMod(7e8, 1e9); int mod2 = RandomMod(7e8, 1e9); mint1::set_mod(mod1); mint2::set_mod(mod2); mint1 b1 = randrange(100, 200); mint2 b2 = randrange(100, 200); int MAX_m = 1000000; vector b1l(MAX_m+1); b1l[0] = 1; for (int i=0; i b2l(MAX_m+1); b2l[0] = 1; for (int i=0; i> n >> m; vector a(n); vector b(m); vector c(m); vector over; for (int i=0; i> a[i]; over.push_back(a[i]); } for (int i=0; i> b[i]; over.push_back(b[i]); } for (int i=0; i> c[i]; } vector p = compress(over); vector t1(n+1); vector t2(n+1); { mint1 x1 = 0; mint2 x2 = 0; for (int i=0; i u1(m+1); vector u2(m+1); { mint1 x1 = 0; mint2 x2 = 0; for (int i=0; i linemax(m); for (int i=0; i 1){ int targ = (ub + lb) / 2; mint1 kt1 = t1[targ-i]; mint2 kt2 = t2[targ-i]; mint1 ku1 = u1[targ] - u1[i] * b1l[targ - i]; mint2 ku2 = u2[targ] - u2[i] * b2l[targ - i]; if (kt1 == ku1 && kt2 == ku2){ lb = targ; }else{ ub = targ; } } linemax[i] = lb;\ } LiChaoTree lc(0, m+1); vector dp(m+1, 1e18); for (int i=0; i 0){ val = lc.query(i); } dp[i] = val; //cout << i << " " << val << endl; if (i < m && linemax[i] > i){ lc.add_segment_line(c[i], dp[i] - i * c[i], i, linemax[i] + 1); } } if (dp[m] >= 1e16) cout << -1 << endl; else cout << dp[m] << endl; }