import std.conv, std.functional, std.range, std.stdio, std.string; import std.algorithm, std.array, std.bigint, std.bitmanip, std.complex, std.container, std.math, std.mathspecial, std.numeric, std.regex, std.typecons; import core.bitop; class EOFException : Throwable { this() { super("EOF"); } } string[] tokens; string readToken() { for (; tokens.empty; ) { if (stdin.eof) { throw new EOFException; } tokens = readln.split; } auto token = tokens.front; tokens.popFront; return token; } int readInt() { return readToken.to!int; } long readLong() { return readToken.to!long; } real readReal() { return readToken.to!real; } bool chmin(T)(ref T t, in T f) { if (t > f) { t = f; return true; } else { return false; } } bool chmax(T)(ref T t, in T f) { if (t < f) { t = f; return true; } else { return false; } } int binarySearch(alias pred, T)(in T[] as) { int lo = -1, hi = cast(int)(as.length); for (; lo + 1 < hi; ) { const mid = (lo + hi) >> 1; (unaryFun!pred(as[mid]) ? hi : lo) = mid; } return hi; } int lowerBound(T)(in T[] as, T val) { return as.binarySearch!(a => (a >= val)); } int upperBound(T)(in T[] as, T val) { return as.binarySearch!(a => (a > val)); } // class Func = TX -> TY // for any f, g: Func, x -> sgn(g(x) - f(x)) must be monotone class LiChaoTree(Func) { import std.algorithm : swap; alias TX = Func.TX; alias TY = Func.TY; const(TX) L, R; class Tree { Tree l, r; Func f; this(Func f) { this.f = f; } } Tree root; // [L, R) this(TX L, TX R) { assert(L < R, "LiChaoTree: L < R must hold"); this.L = L; this.R = R; } // Add g to the whole [L, R) void add(Func g) { root = add(root, L, R, g); } // Add g to [a, b) void add(TX a, TX b, Func g) { root = add(root, L, R, a, b, g); } // Get max at a TY opCall(TX a) { TY mx = TY.min; TX l = L, r = R; for (Tree u = root; u; ) { if (u.f) { const fX = u.f(a); if (mx < fX) mx = fX; } const mid = l + (r - l) / 2; if (a < mid) { u = u.l; r = mid; } else { u = u.r; l = mid; } } return mx; } private: Tree add(Tree u0, TX l, TX r, Func g) { if (!u0) return new Tree(g); TY gL = g(l), gR = g(r); for (Tree u = u0; ; ) { TY fL = u.f ? u.f(l) : TY.min, fR = u.f ? u.f(r) : TY.min; if (fL >= gL && fR >= gR) return u0; if (fL <= gL && fR <= gR) { u.f = g; return u0; } if (r - l == 1) { if (fL <= gL) { u.f = g; } return u0; } const mid = l + (r - l) / 2; TY fMid = u.f(mid), gMid = g(mid); if (fMid < gMid) { swap(u.f, g); if (!g) return u0; if (gL < fL) { if (!u.l) { u.l = new Tree(g); return u0; } u = u.l; r = mid; gL = fL; gR = fMid; } else { if (!u.r) { u.r = new Tree(g); return u0; } u = u.r; l = mid; gL = fMid; gR = fR; } } else { if (fL < gL) { if (!u.l) { u.l = new Tree(g); return u0; } u = u.l; r = mid; gR = gMid; } else { if (!u.r) { u.r = new Tree(g); return u0; } u = u.r; l = mid; gL = gMid; } } } } Tree add(Tree u, TX l, TX r, TX a, TX b, Func g) { if (b <= l || r <= a) return u; if (a <= l && r <= b) return add(u, l, r, g); if (u && u.f && u.f(l) >= g(l) && u.f(r) >= g(r)) return u; if (!u) u = new Tree(null); const mid = l + (r - l) / 2; u.l = add(u.l, l, mid, a, b, g); u.r = add(u.r, mid, r, a, b, g); return u; } } // y = p x + q class Line { alias TX = long; alias TY = long; long p, q; this(long p, long q) { this.p = p; this.q = q; } TY opCall(TX x) { return p * x + q; } } enum INF = 10L^^18; enum LIM_CN = 10L^^12 + 10L^^11 + 10; void main() { try { for (; ; ) { const N = readInt(); const C = readLong(); auto A = new long[N]; auto B = new long[N]; foreach (i; 0 .. N) { A[i] = readLong(); B[i] = readLong(); } /* min_{j<=i} (dp[j] + A[i] (i - j) + C (i - j) (i - j + 1) / 2) = min_{j<=i} ((dp[j] + C j (j - 1) / 2) - j (A[i] + C i)) + A[i] i + C i (i + 1) / 2 min_i (DP[i] + A[i] (j - i - 1) + C (j - i - 1) (j - i) / 2) = min_i ((DP[i] - A[i] (i + 1) + C i (i + 1) / 2) + (A[i] - C i) j) + C j (j - 1) / 2 */ auto lct = new LiChaoTree!Line(-LIM_CN, LIM_CN); auto LCT = new LiChaoTree!Line(0, N + 1); void add(int j, long val) { lct.add(new Line(-(-j), -(val + C * j * (j - 1) / 2))); } void ADD(int i, long val) { LCT.add(new Line(-(A[i] - C * i), -(val - A[i] * (i + 1) + C * i * (i + 1) / 2))); } auto dp = new long[N + 1]; dp[] = INF; foreach (i; 0 .. N + 1) { dp[i] = (i == 0) ? 0 : (-LCT(i) + C * i * (i - 1) / 2); add(i, dp[i]); if (i == N) { break; } long mn = -lct(A[i] + C * i) + A[i] * i + C * i * (i + 1) / 2; debug { writeln(i, ": ", mn, " ", mn + A[i] + B[i]); } ADD(i, mn + A[i] + B[i]); } debug { writeln("dp = ", dp); } writeln(dp[N]); debug { auto brt = new long[N + 1]; brt[] = INF; brt[0] = 0; foreach (i; 0 .. N) { long mn = INF; foreach (j; 0 .. i + 1) { // [j, i) const long l = i - j; chmin(mn, brt[j] + A[i] * l + C * (l * (l + 1) / 2)); } writeln(i, ": ", mn, " ", mn + A[i] + B[i]); mn += A[i] + B[i]; foreach (j; i + 1 .. N + 1) { // [i + 1, j) const long l = j - (i + 1); chmin(brt[j], mn + A[i] * l + C * (l * (l + 1) / 2)); } } writeln("brt = ", brt); } } } catch (EOFException e) { } }