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)); } // floor(a / b) Int divFloor(Int)(Int a, Int b) { return a / b - (((a ^ b) < 0 && a % b != 0) ? 1 : 0); } // ceil(a / b) Int divCeil(Int)(Int a, Int b) { return a / b + (((a ^ b) > 0 && a % b != 0) ? 1 : 0); } enum INF = 10L^^18; 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(); } /* C k^2 + (A[i] - A[j] - C (i + j + 1)) k + (-A[i] * (i + 1) + A[j] * j + C (i * (i + 1) / 2 + j * (j + 1) / 2)) */ long calc(int i, int j) { const p = A[i] - A[j] - C * (i + j + 1); const q = -A[i] * (i + 1) + A[j] * j + C * (1L * i * (i + 1) / 2 + 1L * j * (j + 1) / 2); long mn = INF; void check(long k) { if (i + 1 <= k && k <= j) { chmin(mn, (C * k + p) * k + q); } } check(i + 1); check(j); check(divFloor(-p, 2 * C)); check(divCeil(-p, 2 * C)); return mn; } auto dp = new long[N]; foreach (i; 0 .. N) { dp[i] = A[i] * i + C * i * (i + 1) / 2; } auto que = new int[N]; int qb, qe; foreach (j; 0 .. N) { long here(int i) { return dp[i] + calc(i, j); } bool cmp(int i0, int i1) { int lo = j + 1, hi = N; for (; lo + 1 < hi; ) { const mid = (lo + hi) / 2; const res0 = dp[i0] + calc(i0, mid); const res1 = dp[i1] + calc(i1, mid); const resj = dp[j] + calc(j, mid); if (res0 >= res1 && !(res1 >= resj)) return false; if (!(res0 >= res1) && res1 >= resj) return true; ((res0 >= res1) ? hi : lo) = mid; } return false; } for (; qe - qb >= 2 && here(que[qb]) >= here(que[qb + 1]); ++qb) {} if (qe - qb >= 1) { chmin(dp[j], here(que[qb])); } dp[j] += A[j] + B[j]; for (; qe - qb >= 2 && cmp(que[qe - 2], que[qe - 1]); --qe) {} que[qe++] = j; } debug { writeln("dp = ", dp); } long ans = INF; foreach (i; 0 .. N) { chmin(ans, dp[i] + A[i] * (N - i - 1) + C * (N - i - 1) * (N - i) / 2); } writeln(ans); debug { long calcBrute(int i, int j) { long mn = INF; foreach (k; i + 1 .. j + 1) { long cost; cost += A[i] * (k - i - 1) + C * (k - i - 1) * (k - i) / 2; cost += A[j] * (j - k) + C * (j - k) * (j - k + 1) / 2; chmin(mn, cost); } return mn; } foreach (i; 0 .. N) foreach (j; i + 1 .. N) { assert(calc(i, j) == calcBrute(i, j)); } auto brt = new long[N]; brt[] = INF; foreach (i; 0 .. N) { chmin(brt[i], A[i] * i + C * i * (i + 1) / 2); } foreach (i; 0 .. N) { brt[i] += A[i] + B[i]; foreach (j; i + 1 .. N) { chmin(brt[j], brt[i] + calcBrute(i, j)); } } writeln("brt = ", brt); long brtAns = INF; foreach (i; 0 .. N) { chmin(brtAns, brt[i] + A[i] * (N - i - 1) + C * (N - i - 1) * (N - i) / 2); } writeln("brtAns = ", brtAns); foreach (i; 0 .. N) foreach (j; i + 1 .. N) { foreach (k; j + 1 .. N - 1) { if (brt[i] + calcBrute(i, k) >= brt[j] + calcBrute(j, k)) { assert(brt[i] + calcBrute(i, k + 1) >= brt[j] + calcBrute(j, k + 1)); } } } } } } catch (EOFException e) { } }