#pragma GCC optimize("O3") #pragma GCC optimize("unroll-loops") #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include using namespace std; //#define int long long typedef long long ll; typedef unsigned long long ul; typedef unsigned int ui; //constexpr ll mod = 998244353; constexpr ll mod = 1000000007; const ll INF = mod * mod; typedef pairP; #define rep(i,n) for(int i=0;i=0;i--) #define Rep(i,sta,n) for(int i=sta;i=1;i--) #define Rep1(i,sta,n) for(int i=sta;i<=n;i++) #define all(v) (v).begin(),(v).end() typedef pair LP; template void chmin(T& a, T b) { a = min(a, b); } template void chmax(T& a, T b) { a = max(a, b); } template void cinarray(vector& v) { rep(i, v.size())cin >> v[i]; } template void coutarray(vector& v) { rep(i, v.size()) { if (i > 0)cout << " "; cout << v[i]; } cout << "\n"; } ll mod_pow(ll x, ll n, ll m = mod) { if (n < 0) { ll res = mod_pow(x, -n, m); return mod_pow(res, m - 2, m); } if (abs(x) >= m)x %= m; if (x < 0)x += m; //if (x == 0)return 0; ll res = 1; while (n) { if (n & 1)res = res * x % m; x = x * x % m; n >>= 1; } return res; } //mod should be <2^31 struct modint { int n; modint() :n(0) { ; } modint(ll m) { if (m < 0 || mod <= m) { m %= mod; if (m < 0)m += mod; } n = m; } operator int() { return n; } }; bool operator==(modint a, modint b) { return a.n == b.n; } bool operator<(modint a, modint b) { return a.n < b.n; } modint operator+=(modint& a, modint b) { a.n += b.n; if (a.n >= mod)a.n -= (int)mod; return a; } modint operator-=(modint& a, modint b) { a.n -= b.n; if (a.n < 0)a.n += (int)mod; return a; } modint operator*=(modint& a, modint b) { a.n = ((ll)a.n * b.n) % mod; return a; } modint operator+(modint a, modint b) { return a += b; } modint operator-(modint a, modint b) { return a -= b; } modint operator*(modint a, modint b) { return a *= b; } modint operator^(modint a, ll n) { if (n == 0)return modint(1); modint res = (a * a) ^ (n / 2); if (n % 2)res = res * a; return res; } ll inv(ll a, ll p) { return (a == 1 ? 1 : (1 - p * inv(p % a, a)) / a + p); } modint operator/(modint a, modint b) { return a * modint(inv(b, mod)); } modint operator/=(modint& a, modint b) { a = a / b; return a; } const int max_n = 1 << 21; modint fact[max_n], factinv[max_n]; void init_f() { fact[0] = modint(1); for (int i = 0; i < max_n - 1; i++) { fact[i + 1] = fact[i] * modint(i + 1); } factinv[max_n - 1] = modint(1) / fact[max_n - 1]; for (int i = max_n - 2; i >= 0; i--) { factinv[i] = factinv[i + 1] * modint(i + 1); } } modint comb(int a, int b) { if (a < 0 || b < 0 || a < b)return 0; return fact[a] * factinv[b] * factinv[a - b]; } modint combP(int a, int b) { if (a < 0 || b < 0 || a < b)return 0; return fact[a] * factinv[a - b]; } ll gcd(ll a, ll b) { a = abs(a); b = abs(b); if (a < b)swap(a, b); while (b) { ll r = a % b; a = b; b = r; } return a; } using ld = long double; //typedef long double ld; typedef pair LDP; const ld eps = 1e-10; const ld pi = acosl(-1.0); template void addv(vector& v, int loc, T val) { if (loc >= v.size())v.resize(loc + 1, 0); v[loc] += val; } /*const int mn = 2000005; bool isp[mn]; vector ps; void init() { fill(isp + 2, isp + mn, true); for (int i = 2; i < mn; i++) { if (!isp[i])continue; ps.push_back(i); for (int j = 2 * i; j < mn; j += i) { isp[j] = false; } } }*/ //[,val) template auto prev_itr(set& st, T val) { auto res = st.lower_bound(val); if (res == st.begin())return st.end(); res--; return res; } //[val,) template auto next_itr(set& st, T val) { auto res = st.lower_bound(val); return res; } using mP = pair; mP operator+(mP a, mP b) { return { a.first + b.first,a.second + b.second }; } mP operator+=(mP& a, mP b) { a = a + b; return a; } mP operator-(mP a, mP b) { return { a.first - b.first,a.second - b.second }; } mP operator-=(mP& a, mP b) { a = a - b; return a; } LP operator+(LP a, LP b) { return { a.first + b.first,a.second + b.second }; } LP operator+=(LP& a, LP b) { a = a + b; return a; } LP operator-(LP a, LP b) { return { a.first - b.first,a.second - b.second }; } LP operator-=(LP& a, LP b) { a = a - b; return a; } mt19937 mt(time(0)); const string drul = "DRUL"; string senw = "SENW"; //DRUL,or SENW int dx[4] = { 1,0,-1,0 }; int dy[4] = { 0,1,0,-1 }; //----------------------------------------- struct LiChaoTree { struct Node { ll l, r; Node* chl; Node* chr; LP val; Node(ll l, ll r) :l(l), r(r) { val = { 0,4*INF }; chl = chr = NULL; } }; Node* root; LiChaoTree(ll le,ll ri) { root = new Node(le,ri); } ll calc(LP a, ll x) { return a.first * x + a.second; } void add(Node* node, LP a) { if (!node)return; ll l = node->l, r = node->r; ll m = (l + r) / 2; //そのノードでの最小値 if (calc(node->val, m) > calc(a, m))swap(node->val, a); if (r - l == 1)return; //左側をさらに更新しなきゃ if (calc(node->val, l) > calc(a, l)) { if (!node->chl)node->chl = new Node(l, m); add(node->chl, a); } else if (calc(node->val, r) > calc(a, r)) { if (!node->chr)node->chr = new Node(m, r); add(node->chr, a); } } void add(LP a) { add(root, a); } ll query(int x) { ll ret = INF; Node* node = root; while (node) { ret = min(ret, calc(node->val, x)); ll m = (node->l + node->r) / 2; if (x < m) { node = node->chl; } else { node = node->chr; } } return ret; } }; void solve() { int n; ll c; cin >> n >> c; vector a(n), b(n); rep(i, n)cin >> a[i] >> b[i]; vector dp(n + 1,INF); dp[0] = 0; LiChaoTree lt1(-1200000000000,0), lt2(0,n+1); rep(i, n+1) { if (i > 0) { dp[i] = lt2.query(i); dp[i] += ((ll)i * i - i) / 2 * c; } if (i < n) { LP cur; cur.first = i; cur.second = dp[i] + ((ll)i * i - i) / 2 * c; lt1.add(cur); ll s = lt1.query(-a[i] - i * c); s += a[i] * i + b[i] + ((ll)i * i + i) / 2 * c; //cout << "?? " << s << "\n"; cur.first = a[i] - i*c; cur.second = s - i * a[i] + ((ll)i * i + i) / 2 * c; lt2.add(cur); } } //coutarray(dp); cout << dp[n] << "\n"; } signed main() { ios::sync_with_stdio(false); cin.tie(0); //cout << fixed << setprecision(10); //init_f(); //init(); //expr(); //while(true) //int t; cin >> t; rep(i, t) solve(); return 0; }