#include using namespace std; using ll = int64_t; using pll = pair; const ll LINF = 0x1fffffffffffffff; template< typename T > struct LiChaoTree { struct Line { T a, b; Line(T a, T b) : a(a), b(b) {} inline T get(T x) const { return a * x + b; } inline bool over(const Line &b, const T &x) const { return get(x) < b.get(x); } }; vector< T > xs; vector< Line > seg; int sz; LiChaoTree(const vector< T > &x, T INF) : xs(x) { sz = 1; while(sz < xs.size()) sz <<= 1; while(xs.size() < sz) xs.push_back(xs.back() + 1); seg.assign(2 * sz - 1, Line(0, INF)); } void update(Line &x, int k, int l, int r) { int mid = (l + r) >> 1; auto latte = x.over(seg[k], xs[l]), malta = x.over(seg[k], xs[mid]); if(malta) swap(seg[k], x); if(l + 1 >= r) return; else if(latte != malta) update(x, 2 * k + 1, l, mid); else update(x, 2 * k + 2, mid, r); } void update(T a, T b) { // ax+b Line l(a, b); update(l, 0, 0, sz); } T query(T x) { // xs[k] int k = lower_bound(xs.begin(), xs.end(), x) - xs.begin(); k += sz - 1; T ret = seg[k].get(x); while(k > 0) { k = (k - 1) >> 1; ret = min(ret, seg[k].get(x)); } return ret; } }; signed main(){ ll n, C; cin >> n >> C; vector a(n); for(pll& i : a) cin >> i.first >> i.second; vector dp1(n+1); vector dp2(n+1); dp1[0] = LINF; vector x1(n), x2(n); for(ll i = 0; i < n; i++){ x1[i] = a[i].first + C * (i + 1); x2[i] = i + 1; } sort(x1.begin(), x1.end()); x1.erase(unique(x1.begin(), x1.end()), x1.end()); LiChaoTree cht1(x1, LINF), cht2(x2, LINF); for(ll i = 0; i < n; i++){ const auto [A, B] = a[i]; cht1.update(-i, dp2[i] + C * i * (i + 1) / 2); dp1[i + 1] = cht1.query(A + C * (i + 1)) + A * (i + 1) + B + C * i * (i + 1) / 2; if(i){ cht2.update(a[i - 1].first - C * i, dp1[i] - a[i - 1].first * i + C * i * (i - 1) / 2); dp2[i + 1] = min(dp1[i + 1], cht2.query(i + 1) + C * (i + 1) * (i + 2) / 2); } else dp2[i + 1] = dp1[i + 1]; } cout << dp2[n] << endl; }