using System; using System.Linq; using System.Collections.Generic; using Debug = System.Diagnostics.Debug; using StringBuilder = System.Text.StringBuilder; using Number = System.Int64; namespace Program { public class Solver { public void Solve() { var n = sc.Integer(); var k = sc.Integer(); var u = sc.Long(); var a = sc.Long(n - 1); Array.Sort(a); var ok = false; var l = 0; var r = n - 1; for (int _ = 0; _ < 20; _++) { var m = (l + r) / 2; var v = u + a[m]; var s = new Set(); s.IsMultiSet = true; for (int i = n - 2; i >= 0; i--) if (i != m) s.Add(a[i]); var cnt = 0; while (s.Count >= 2) { var min = s[0]; s.RemoveAt(0); var lb = s.UpperBound(v - min); if (lb < s.Count) { cnt++; s.RemoveAt(lb); } } if (cnt < k) { ok = true; r = m; } else l = m; } if (!ok) IO.Printer.Out.WriteLine(-1); else IO.Printer.Out.WriteLine(a[r]); } public IO.StreamScanner sc = new IO.StreamScanner(Console.OpenStandardInput()); static T[] Enumerate(int n, Func f) { var a = new T[n]; for (int i = 0; i < n; ++i) a[i] = f(i); return a; } static public void Swap(ref T a, ref T b) { var tmp = a; a = b; b = tmp; } } } #region main static class Ex { static public string AsString(this IEnumerable ie) { return new string(System.Linq.Enumerable.ToArray(ie)); } static public string AsJoinedString(this IEnumerable ie, string st = " ") { return string.Join(st, ie); } static public void Main() { var solver = new Program.Solver(); solver.Solve(); Program.IO.Printer.Out.Flush(); } } #endregion #region Ex namespace Program.IO { using System.IO; using System.Text; using System.Globalization; public class Printer: StreamWriter { static Printer() { Out = new Printer(Console.OpenStandardOutput()) { AutoFlush = false }; } public static Printer Out { get; set; } public override IFormatProvider FormatProvider { get { return CultureInfo.InvariantCulture; } } public Printer(System.IO.Stream stream) : base(stream, new UTF8Encoding(false, true)) { } public Printer(System.IO.Stream stream, Encoding encoding) : base(stream, encoding) { } public void Write(string format, T[] source) { base.Write(format, source.OfType().ToArray()); } public void WriteLine(string format, T[] source) { base.WriteLine(format, source.OfType().ToArray()); } } public class StreamScanner { public StreamScanner(Stream stream) { str = stream; } public readonly Stream str; private readonly byte[] buf = new byte[1024]; private int len, ptr; public bool isEof = false; public bool IsEndOfStream { get { return isEof; } } private byte read() { if (isEof) return 0; if (ptr >= len) { ptr = 0; if ((len = str.Read(buf, 0, 1024)) <= 0) { isEof = true; return 0; } } return buf[ptr++]; } public char Char() { byte b = 0; do b = read(); while ((b < 33 || 126 < b) && !isEof); return (char)b; } public string Scan() { var sb = new StringBuilder(); for (var b = Char(); b >= 33 && b <= 126; b = (char)read()) sb.Append(b); return sb.ToString(); } public string ScanLine() { var sb = new StringBuilder(); for (var b = Char(); b != '\n'; b = (char)read()) if (b == 0) break; else if (b != '\r') sb.Append(b); return sb.ToString(); } public long Long() { if (isEof) return long.MinValue; long ret = 0; byte b = 0; var ng = false; do b = read(); while (b != 0 && b != '-' && (b < '0' || '9' < b)); if (b == 0) return long.MinValue; if (b == '-') { ng = true; b = read(); } for (; true; b = read()) { if (b < '0' || '9' < b) return ng ? -ret : ret; else ret = ret * 10 + b - '0'; } } public int Integer() { return (isEof) ? int.MinValue : (int)Long(); } public double Double() { var s = Scan(); return s != "" ? double.Parse(s, CultureInfo.InvariantCulture) : double.NaN; } private T[] enumerate(int n, Func f) { var a = new T[n]; for (int i = 0; i < n; ++i) a[i] = f(); return a; } public char[] Char(int n) { return enumerate(n, Char); } public string[] Scan(int n) { return enumerate(n, Scan); } public double[] Double(int n) { return enumerate(n, Double); } public int[] Integer(int n) { return enumerate(n, Integer); } public long[] Long(int n) { return enumerate(n, Long); } } } #endregion #region Compair static public class Pair { static public Pair Create(FT f, ST s) where FT : IComparable where ST : IComparable { return new Pair(f, s); } static public Pair Min(Pair p, Pair q) where FT : IComparable where ST : IComparable { return (p.CompareTo(q) <= 0) ? p : q; } static public Pair Max(Pair p, Pair q) where FT : IComparable where ST : IComparable { return (p.CompareTo(q) >= 0) ? p : q; } } public struct Pair: IComparable> where FT : IComparable where ST : IComparable { public FT x; public ST y; public Pair(FT f, ST s) : this() { x = f; y = s; } public int CompareTo(Pair other) { var cmp = x.CompareTo(other.x); return cmp != 0 ? cmp : y.CompareTo(other.y); } public override string ToString() { return string.Format("{0} {1}", x, y); } } #endregion #region Set public class Set: ICollection { public Set() { cmp = Comparer.Default; } public Set(IComparer comparer) { cmp = comparer; } public Set(Comparison compare) { cmp = Comparer.Create(compare); } AVLTree tree = new AVLTree(); IComparer cmp; /// /// 値の重複を許すならばtrue,そうでなければfalse /// public bool IsMultiSet { get; set; } /// /// コレクションのサイズ. O(1) /// public int Count { get { return tree.Count; } } /// /// 要素の追加.成功した場合true,そうでなければfalse.O(logN) /// public bool Add(T item) { var v = new Node() { Key = item }; var lb = LowerBound(item); if (!IsMultiSet && UpperBound(item) != lb) return false; tree.Insert(v, lb); return true; } /// /// 要素の削除.成功した場合true,そうでなければfalse.O(logN) /// public bool Remove(T item) { var lb = LowerBound(item); var ub = UpperBound(item); if (ub == lb) return false; tree.RemoveAt(lb); return true; } /// /// 0-indexed で k 番目に小さい要素を削除.成功した場合true,そうでなければfalse.O(logN) /// public bool RemoveAt(int k) { if (k < 0 || k >= Count) return false; tree.RemoveAt(k); return true; } /// /// 0-indexed で k 番目に小さい要素を返す.O(logN) /// public T this[int index] { get { if (index < 0 || index >= Count) throw new IndexOutOfRangeException(); var t = tree.Find(tree.root, index); return t.Key; } } /// /// 要素があるなら true,そうでなければfalse /// public bool Contains(T item) { return UpperBound(item) != LowerBound(item); } /// /// itemの値以上の要素の最小のインデックスを返す.O(logN) /// public int LowerBound(T item) { return tree.root.LowerBound(item, cmp); } /// /// itemの値より大きい要素の最小のインデックスを返す.O(logN) /// public int UpperBound(T item) { return tree.root.UpperBound(item, cmp); } /// /// O(N)でなめる /// public T[] Items { get { var ret = new T[Count]; int ptr = 0; walk(tree.root, ret, ref ptr); return ret; } } public bool IsReadOnly { get { return false; } } void walk(Node root, T[] a, ref int ptr) { if (root.cnt == 0) return; walk(root.lst, a, ref ptr); a[ptr++] = root.Key; walk(root.rst, a, ref ptr); } void ICollection.Add(T item) { Add(item); } public void Clear() { tree.root = tree.NIL; } public void CopyTo(T[] array, int arrayIndex) { ((ICollection)Items).CopyTo(array, arrayIndex); } public IEnumerator GetEnumerator() { return ((ICollection)Items).GetEnumerator(); } System.Collections.IEnumerator System.Collections.IEnumerable.GetEnumerator() { return ((ICollection)Items).GetEnumerator(); } class Node: AVLTreeNode, IKey { public T Key { get; set; } public override Node Push() { return this; } } } #endregion #region AVLTree public abstract class AVLTreeNode: BinaryTreeNode where T : AVLTreeNode { public int rank; public override void Update() { cnt = 1 + lst.cnt + rst.cnt; rank = 1 + Math.Max(lst.rank, rst.rank); } } public class AVLTree: Tree where T : AVLTreeNode, new() { protected override T insert(T t, T v, int k) { t = t.Push(); if (t.cnt == 0) { v.cnt = 1; v.lst = NIL; v.rst = NIL; v.Update(); return v; } if (t.lst.cnt >= k) t.lst = insert(t.lst, v, k); else t.rst = insert(t.rst, v, k - t.lst.cnt - 1); t.Update(); return balance(t); } protected override T removeat(T t, int k) { t = t.Push(); var cnt = t.lst.cnt; if (cnt < k) t.rst = removeat(t.rst, k - cnt - 1); else if (cnt > k) t.lst = removeat(t.lst, k); else { if (cnt == 0) return t.rst; if (t.rst.cnt == 0) return t.lst; var next = Find(t.lst, k - 1); var st = removeat(t.lst, k - 1); next.rst = t.rst; next.lst = st; t = next; } t.Update(); return balance(t); } T balance(T t) { if (t.lst.rank - t.rst.rank == -2) { if (t.rst.lst.rank - t.rst.rst.rank > 0) t.rst = rotR(t.rst); t = rotL(t); } else if (t.lst.rank - t.rst.rank == 2) { if (t.lst.lst.rank - t.lst.rst.rank < 0) t.lst = rotL(t.lst); t = rotR(t); } return t; } } #endregion #region BinaryTree public interface IKey { K Key { get; set; } } public abstract class BinaryTreeNode where T : BinaryTreeNode { public int cnt; public T lst, rst; public abstract T Push(); /// /// 各ノードは必要に応じて Update を継承して使う /// public abstract void Update(); } public abstract class Tree where TNode : BinaryTreeNode, new() { public Tree() { NIL = new TNode(); NIL.lst = NIL; NIL.rst = NIL; root = NIL; } public readonly TNode NIL; public TNode root; public int Count { get { return root.cnt; } } protected TNode rotR(TNode t) { t = t.Push(); var l = t.lst.Push(); var lr = l.rst; l.rst = t; t.lst = lr; t.Update(); l.Update(); return l; } protected TNode rotL(TNode t) { t = t.Push(); var r = t.rst.Push(); var rl = r.lst; t.rst = rl; r.lst = t; t.Update(); r.Update(); return r; } public TNode Find(TNode t, int k) { t = t.Push(); if (k == t.lst.cnt) return t; else if (k < t.lst.cnt) return Find(t.lst, k); else return Find(t.rst, k - t.lst.cnt - 1); } public void Insert(TNode v, int k) { root = insert(root, v, k); NIL.cnt = 0; } public void RemoveAt(int k) { root = removeat(root, k); NIL.cnt = 0; } protected abstract TNode insert(TNode t, TNode v, int k); protected abstract TNode removeat(TNode t, int k); } public static class TreeOperation { static public int LowerBound (this T t, K k, IComparer cmp) where T : BinaryTreeNode, IKey { if (t.cnt == 0) return 0; if (cmp.Compare(k, t.Key) <= 0) return LowerBound(t.lst, k, cmp); else return 1 + t.lst.cnt + LowerBound(t.rst, k, cmp); } static public int UpperBound (this T t, K k, IComparer cmp) where T : BinaryTreeNode, IKey { if (t.cnt == 0) return 0; if (cmp.Compare(t.Key, k) <= 0) return 1 + t.lst.cnt + UpperBound(t.rst, k, cmp); else return UpperBound(t.lst, k, cmp); } } #endregion #region Set public class aSet where T : IComparable { Node root = Node.NIL; public int Count { get { return root.cnt; } } public void Add(T v) { Insert(v, LowerBound(v)); } public bool Remove(T v) { if (EqualRange(v) == 0) return false; RemoveAt(LowerBound(v)); return true; } #region Impl public void Insert(T v, int k) { root = insert(root, v, k); } public void RemoveAt(int k) { root = removeat(root, k); } public int EqualRange(T v) { return UpperBound(v) - LowerBound(v); } public int LowerBound(T v) { return lowerBound(root, v); } public int UpperBound(T v) { return upperBound(root, v); } public T this[int k] { get { return find(root, k); } } Node insert(Node t, T v, int k) { Debug.Assert(t.cnt >= k); if (t == Node.NIL) return new Node(v); if (t.lst.cnt >= k) t.lst = insert(t.lst, v, k); else t.rst = insert(t.rst, v, k - t.lst.cnt - 1); t.Update(); if (t.lst.h - t.rst.h == -2) { if (t.rst.lst.h - t.rst.rst.h > 0) t.rst = rotR(t.rst); t = rotL(t); } else if (t.lst.h - t.rst.h == 2) { if (t.lst.lst.h - t.lst.rst.h < 0) t.lst = rotL(t.lst); t = rotR(t); } t.Update(); return t; } Node removeat(Node t, int k) { Debug.Assert(t.cnt > k); var cnt = t.lst.cnt; if (cnt < k) t.rst = removeat(t.rst, k - cnt - 1); else if (cnt > k) t.lst = removeat(t.lst, k); else { if (cnt == 0) return t.rst; if (t.rst.cnt == 0) return t.lst; t.val = find(t, k - 1); t.lst = removeat(t.lst, k - 1); } t.Update(); if (t.lst.h - t.rst.h == -2) { if (t.rst.lst.h - t.rst.rst.h > 0) t.rst = rotR(t.rst); t = rotL(t); } else if (t.lst.h - t.rst.h == 2) { if (t.lst.lst.h - t.lst.rst.h < 0) t.lst = rotL(t.lst); t = rotR(t); } else t.Update(); return t; } int lowerBound(Node t, T v) { if (t.cnt == 0) return 0; if (v.CompareTo(t.val) <= 0) return lowerBound(t.lst, v); else return t.lst.cnt + 1 + lowerBound(t.rst, v); } int upperBound(Node t, T v) { if (t.cnt == 0) return 0; if (t.val.CompareTo(v) <= 0) return t.lst.cnt + 1 + upperBound(t.rst, v); else return upperBound(t.lst, v); } T find(Node t, int k) { Debug.Assert(k < t.cnt); if (k == t.lst.cnt) return t.val; else if (k < t.lst.cnt) return find(t.lst, k); else return find(t.rst, k - (t.lst.cnt + 1)); } Node rotR(Node t) { var l = t.lst; var lr = l.rst; l.rst = t; t.lst = lr; t.Update(); l.Update(); return l; } Node rotL(Node t) { var r = t.rst; var rl = r.lst; t.rst = rl; r.lst = t; t.Update(); r.Update(); return r; } #endregion class Node { static public readonly Node NIL = new Node(); public int h; public int cnt; internal T val; internal Node lst, rst; private Node() { } internal Node(T v) { h = 1; cnt = 1; val = v; lst = NIL; rst = NIL; } public void Update() { if (cnt == 0) return; h = 1 + Math.Max(lst.h, rst.h); cnt = 1 + lst.cnt + rst.cnt; } public override string ToString() { return string.Format("count:{0}, value:{1}", cnt, val); } public T[] Items { get { return items(this); } } static public T[] items(Node t) { var ret = new T[t.cnt]; var ptr = 0; dfs(t, ref ptr, ret); return ret; } static void dfs(Node t, ref int ptr, T[] ret) { if (t == Node.NIL) return; dfs(t.lst, ref ptr, ret); ret[ptr++] = t.val; dfs(t.rst, ref ptr, ret); } } public T[] Items { get { return root.Items; } } public override string ToString() { return string.Format("Count = {0}", Count); } } #endregion