Problem:
Score : 400 points

Problem Statement

You are going out for a walk, when you suddenly encounter N monsters. Each monster has a parameter called health, and the health of the i-th monster is h_i at the moment of encounter. A monster will vanish immediately when its health drops to 0 or below.

Fortunately, you are a skilled magician, capable of causing explosions that damage monsters. In one explosion, you can damage monsters as follows:

Select an alive monster, and cause an explosion centered at that monster. The health of the monster at the center of the explosion will decrease by A, and the health of each of the other monsters will decrease by B. Here, A and B are predetermined parameters, and A > B holds.

At least how many explosions do you need to cause in order to vanish all the monsters?

Constraints

All input values are integers.

1 ≤ N ≤ 10^5

1 ≤ B < A ≤ 10^9

1 ≤ h_i ≤ 10^9

Input

Input is given from Standard Input in the following format:

N A B
h_1
h_2
:
h_N

Output

Print the minimum number of explosions that needs to be caused in order to vanish all the monsters.

Sample Input 1

4 5 3
8
7
4
2

Sample Output 1

2

You can vanish all the monsters in two explosion, as follows:

First, cause an explosion centered at the monster with 8 health. The healths of the four monsters become 3, 4, 1 and -1, respectively, and the last monster vanishes.

Second, cause an explosion centered at the monster with 4 health remaining. The healths of the three remaining monsters become 0, -1 and -2, respectively, and all the monsters are now vanished.

Sample Input 2

2 10 4
20
20

Sample Output 2

4

You need to cause two explosions centered at each monster, for a total of four.

Sample Input 3

5 2 1
900000000
900000000
1000000000
1000000000
1000000000

Sample Output 3

800000000

Solution in C# (Mono 4.6.2.0) (judge verdict: Time Limit Exceeded)

using System;
using System.Collections;
using System.Collections.Generic;
//using System.Data.Odbc;
using System.Diagnostics;
using System.Globalization;
using System.IO;
using System.Linq;
using System.Linq.Expressions;
using System.Reflection.Emit;
using System.Runtime.CompilerServices;
using System.Runtime.InteropServices;
using System.Runtime.Remoting.Proxies;
using System.Security.Cryptography;
using System.Text;
using System.Xml.Schema;
namespace ConsoleApplication {
    class MainClass {
        ////////////////////////////////////////////////////////////////////////////////        
        private int N, A, B;
        private int[] h;
        void Solve() {
            io.i(out N,out A,out B);
            io.ini(out h,N);
            var que=new PQueue <int>(1);
            N.REP(i => que.Enqueue(h[i]));
            var plusOne = A - B;
            var boarder = 0;
            var ans = 0;
            while(que.Peek() > boarder) {
                boarder += B;
                var cur = que.Dequeue()-plusOne;
                que.Enqueue(cur);
                ans++;
            }
            io.o(ans);
        }        
        class PQueue<T> where T : struct, IComparable<T> {
            public List<T> heap; private Comparison<T> comp; private IComparer<T> comparer;
            private int size; private int type;//type=0->min
            public PQueue(int type = 0) : this(Comparer<T>.Default) { this.type = type; }
            public PQueue(IComparer<T> comparer) : this(16, comparer.Compare) { this.comparer = comparer; }
            public PQueue(Comparison<T> comparison) : this(16, comparison) { }
            public PQueue(int capacity, Comparison<T> comparison) { this.heap = new List<T>(capacity); this.comp = comparison; }
            public void Enqueue(T item) {
                this.heap.Add(item); var i = size++;
                while (i > 0) { var p = (i - 1) >> 1; if (Compare(this.heap[p], item) <= 0) break; this.heap[i] = heap[p]; i = p; }
                this.heap[i] = item;
            }
            public T Dequeue() {
                var ret = this.heap[0]; var x = this.heap[--size]; var i = 0;
                while ((i << 1) + 1 < size) {
                    var a = (i << 1) + 1; var b = (i << 1) + 2; if (b < size && Compare(heap[b], heap[a]) < 0) a = b;
                    if (Compare(heap[a], x) >= 0) break; heap[i] = heap[a]; i = a;
                }
                heap[i] = x; heap.RemoveAt(size);
                return ret;
            }
            public T Peek() { return heap[0]; }
            public int Count { get { return size; } }
            public bool Any() { return size > 0; }
            public bool Empty() { return !Any(); }
            public bool Contains(T v) { return heap.Contains(v); }
            private int Compare(T x, T y) { return type == 0 ? x.CompareTo(y) : y.CompareTo(x); }
        }
        ////////////////////////////////////////////////////////////////////////////////
        public static void Main() => new MainClass().Stream();
        IO io = new IO();
        Mat mat = new Mat();
        void Stream() {
            Solve();
            //Test();
            io.Flush();
        }
        void Test() { }
        void FOR(int a, int b, Action <int> act) {
            for(int i = a; i < b; ++i) act(i);
        }
        void FORR(int a, int b, Action <int> act) {
            for(int i = a - 1; i >= b; --i) act(i);
        }
    }
    #region Default
    class IO {
        #region INPUT
        int _buffCnt;
        string[] _nextBuff;
        private readonly char[] _splitCharacter = new char[] {' '};
        private readonly StreamWriter _sw = new StreamWriter(Console.OpenStandardOutput()) {
            AutoFlush = false
        };
        public IO() {
            _nextBuff = new string[0];
            _buffCnt = 0;
            Console.SetOut(_sw);
        }
        private string Next() {
            if(_buffCnt < _nextBuff.Length) return _nextBuff[_buffCnt++];
            var str = Scan;
            while(str == "") str = Scan;
            _nextBuff = str.Split(_splitCharacter, StringSplitOptions.RemoveEmptyEntries);
            _buffCnt = 0;
            return _nextBuff[_buffCnt++];
        }
        private string Scan => Console.ReadLine();
        private string[] Arr => Scan.Split(' ');
        private void Read <T>(out T v) => v = SuitType <T>(Next());
        private T ConvertType <T, TU>(TU v) => (T)Convert.ChangeType(v, typeof(T));
        private bool TypeEqual <T, TU>() => typeof(T) == typeof(TU);
        private T SuitType <T>(string s)
            =>
                TypeEqual <T, int>()
                    ? ConvertType <T, int>(int.Parse(s))
                    : TypeEqual <T, long>()
                        ? ConvertType <T, long>(long.Parse(s))
                        : TypeEqual <T, double>()
                            ? ConvertType <T, double>(double.Parse(s))
                            : TypeEqual <T, char>() ? ConvertType <T, char>(char.Parse(s)) : ConvertType <T, string>(s);
        public string String => Next();
        public char Char => char.Parse(Next());
        public int Int => int.Parse(Next());
        public long Long => long.Parse(Next());
        public double Double => double.Parse(Next());
        public string[] ArrString => Arr;
        public char[] ArrChar => Array.ConvertAll(Arr, char.Parse);
        public int[] ArrInt => Array.ConvertAll(Arr, int.Parse);
        public long[] ArrLong => Array.ConvertAll(Arr, long.Parse);
        public double[] ArrDouble => Array.ConvertAll(Arr, double.Parse);
        public void Flush() => Console.Out.Flush();
        private T i <T>() { return SuitType <T>(String); }
        public void i <T>(out T v) => Read(out v);
        public void i <T, TU>(out T t, out TU u) {
            i(out t);
            i(out u);
        }
        public void i <T, TU, TV>(out T t, out TU u, out TV v) {
            i(out t, out u);
            i(out v);
        }
        public void i <T, TU, TV, TW>(out T t, out TU u, out TV v, out TW w) {
            i(out t, out u, out v);
            i(out w);
        }
        public void i <T, TU, TV, TW, TX>(out T t, out TU u, out TV v, out TW w, out TX x) {
            i(out t, out u, out v, out w);
            i(out x);
        }
        public void ini <T>(out T[] a, int n) {
            a = new T[n];
            for(int i = 0; i < n; ++i) a[i] = i <T>();
        }
        public void ini <T, TU>(out T[] a, out TU[] b, int n) {
            a = new T[n];
            b = new TU[n];
            for(int i = 0; i < n; ++i) {
                a[i] = i <T>();
                b[i] = i <TU>();
            }
        }
        public void ini <T, TU, TV>(out T[] a, out TU[] b, out TV[] c, int n) {
            a = new T[n];
            b = new TU[n];
            c = new TV[n];
            for(int i = 0; i < n; ++i) {
                a[i] = i <T>();
                b[i] = i <TU>();
                c[i] = i <TV>();
            }
        }
        public void ini <T>(out T[,] a, int h, int w) {
            a = new T[h, w];
            for(int i = 0; i < h; ++i) for(int j = 0; j < w; ++j) a[i, j] = i <T>();
        }
        public void ini <T, TU>(out Tuple <T, TU>[] t, int n) {
            t = new Tuple <T, TU>[n];
            for(int j = 0; j < n; ++j) {
                T i1;
                TU i2;
                i(out i1, out i2);
                t[j] = Tuple.Create(i1, i2);
            }
        }
        public void ini <T, TU, TV>(out Tuple <T, TU, TV>[] t, int n) {
            t = new Tuple <T, TU, TV>[n];
            for(int j = 0; j < n; ++j) {
                T i1;
                TU i2;
                TV i3;
                i(out i1, out i2, out i3);
                t[j] = Tuple.Create(i1, i2, i3);
            }
        }
        #endregion
        #region OUTPUT
        private void Out <T>(T v) => Console.Write(v);
        private void OutLine <T>(T v) => Console.WriteLine(v);
        public void o <T>(T v) => OutLine(v);
        public void o <T>(params T[] a) => Array.ForEach(a, OutLine);
        public void o <T>(T[,] a) {
            int a0 = a.GetLength(0), a1 = a.GetLength(1);
            for(int i = 0; i < a0; ++i) {
                for(int j = 0; j < a1 - 1; ++j) Out(a[i, j] + " ");
                OutLine(a[i, a1 - 1]);
            }
        }
        public void ol <T>(params T[] a) => OutLine(string.Join(" ", a));
        public void YN(bool f) => OutLine(f ? "YES" : "NO");
        public void Yn(bool f) => OutLine(f ? "Yes" : "No");
        public void yn(bool f) => OutLine(f ? "yes" : "no");
        #endregion
    }
    class Mat {
        public long mod = 1000000007; //10^9+7
        public long Pow(long a, long b) {
            if(b == 0) return 1;
            if(b % 2 == 1) return (a % mod * Pow(a % mod, b - 1) % mod) % mod;
            else return Pow(a * a % mod, b / 2) % mod;
        }
        public long Fact(long n) {
            long ret = 1;
            for(long i = 1; i <= n; i++) ret = (ret * i) % mod;
            return ret;
        }
        public long[,] C(int N) {
            long[,] Co = new long[N + 1, N + 1];
            (N + 1).REP(i => (i + 1).REP(j => Co[i, j] = (j == 0 || j == i) ? 1L : Co[i - 1, j - 1] + Co[i - 1, j]));
            return Co;
        }
        public long C(long n, long r) {
            if(r == 0 || n == r) return 1;
            if(n == 0) return 0;
            if(n < 0 || r < 0 || n < r) throw new ArgumentException("n or r invalid");
            else return (Fact(n) % mod * Pow((Fact(n - r) % mod * Fact(r) % mod) % mod, mod - 2) % mod) % mod;
        }
        public long NoModC(long n, long r) {
            var c = new long[r + 1];
            c[0] = 1;
            for(var i = 1; i <= n; ++i) for(var j = Math.Min(i, r); j > 0; j--) c[j] = c[j] + c[j - 1];
            return c[r];
        }
        public long H(long n, long r) => C(n + r - 1, r);
        public long P(long n, long r) => Fact(n) / Fact(n - r);
        public long Lcm(long a, long b) => a * (b / Gcd(a, b));
        public long Lcm(params long[] a) => a.Aggregate((v, n) => Lcm(v, n));
        public long Gcd(long a, long b) {
            if(a < b) Swap(ref a, ref b);
            return b == 0 ? a : Gcd(b, a % b);
        }
        public long Gcd(params long[] array) => array.Aggregate((v, n) => Gcd(v, n));
        public T Max <T>(params T[] a) => a.Max();
        public T Min <T>(params T[] a) => a.Min();
        public void Swap <T>(ref T a, ref T b) {
            T tmp = a;
            a = b;
            b = tmp;
        }
        public double Dis(int x1, int y1, int x2, int y2) => Math.Sqrt(Math.Pow((x2 - x1), 2) + Math.Pow((y2 - y1), 2));
        public int ManhattanDis(int x1, int y1, int x2, int y2) => Math.Abs(x1 - x2) + Math.Abs(y1 - y2);
        public int[] DigArr(int n) {
            int[] ret = new int[Digit(n)];
            ret.Length.REP(i => ret[i] = DigVal(n, i + 1));
            return ret;
        }
        public long DigArr2Num(IEnumerable <int> enu) { return enu.Aggregate((v, n) => v * 10 + n); }
        public int Digit(long n) { return (n == 0) ? 1 : (int)Math.Log10(n) + 1; }
        public int DigVal(int n, int dig) { return (n % (int)Pow(10, dig)) / (int)Pow(10, dig - 1); }
        public long Tousa(long a, long d, long n) { return a + (n - 1) * d; }
        public long TousaSum(long a, long d, long n) { return n * (2 * a + (n - 1) * d) / 2; }
        public long[] EnuDivsor(long N) {
            var ret = new SortedSet <long>();
            for(long i = 1; i * i <= N; i++)
                if(N % i == 0) {
                    ret.Add(i);
                    ret.Add(N / i);
                }
            return ret.ToArray();
        }
        public Dictionary <long, long> PrimeFactor(long n) {
            var ret = new Dictionary <long, long>();
            for(int i = 2; i * i <= n; ++i) {
                if(!ret.ContainsKey(i)) ret[i] = 0;
                while(n % i == 0) {
                    ++ret[i];
                    n /= i;
                }
            }
            return ret.Where(kp => kp.Value != 0).ToDictionary(kp => kp.Key, kp => kp.Value);
        }
    }
    public struct Edge : IComparable <Edge> {
        public int To;
        public long Cost;
        public Edge(int to, long cost) {
            To = to;
            Cost = cost;
        }
        public int CompareTo(Edge e) => Cost.CompareTo(e.Cost);
    }
    #endregion
    #region MyEx
    static class StringEX {
        public static string Reversed(this string s) => string.Join("", s.Reverse());
        public static string Repeated(this string s, int n) => string.Concat(Enumerable.Repeat(s, n).ToArray());
        public static string toString(this char[] a) => new string(a);
        public static int toInt(this string s) {
            int n;
            return (int.TryParse(s.TrimStart('0'), out n)) ? n : 0;
        }
        public static int toInt(this char c) => toInt(c.ToString());
        public static int toInt(this char[] c) => toInt(c.toString());
        public static long toLong(this string s) {
            long n;
            return (long.TryParse(s.TrimStart('0'), out n)) ? n : 0L;
        }
        public static long toLong(this char c) => toLong(c.ToString());
        public static long toLong(this char[] c) => toLong(c.toString());
    }
    static class NumericEX {
        public static string toString(this double d) => d.ToString("R", CultureInfo.InvariantCulture);
        public static string Pad0 <T>(this T s, int n) => s.ToString().PadLeft(n, '0');
        public static string RoundOff(this double v, int n)
            => Math.Round(v, n - 1, MidpointRounding.AwayFromZero).toString();
        public static string RoundUp(this double v) => Math.Ceiling(v).toString();
        public static string RoundDown(this double v) => Math.Floor(v).toString();
        public static bool Odd(this int v) => (v & 1) != 0;
        public static bool Odd(this long v) => (v & 1) != 0;
        public static void REP(this int v, Action <int> act) {
            for(int i = 0; i < v; ++i) act(i);
        }
        public static void REPR(this int v, Action <int> act) {
            for(int i = v - 1; i >= 0; --i) act(i);
        }
        public static void EREP(this int v, Action <int> act) => (v + 1).REP(act);
    }
    static class ArrayEX {
        public static T[] Sort <T>(this T[] a) {
            Array.Sort(a);
            return a;
        }
        public static T[] SortR <T>(this T[] a) {
            Array.Reverse(a.Sort());
            return a;
        }
        public static void Set <T>(this T[] a, T v) => a.Length.REP(i => a[i] = v);
        public static void Set <T>(this T[,] a, T v) => a.GetLength(0).REP(i => a.GetLength(1).REP(j => a[i, j] = v));
        public static void Set <T>(this T[,,] a, T v)
            => a.GetLength(0).REP(i => a.GetLength(1).REP(j => a.GetLength(2).REP(k => a[i, j, k] = v)));
        public static int LowerBound <T>(this T[] a, T x) where T : IComparable {
            int lb = -1, ub = a.Length;
            while(ub - lb > 1) {
                int mid = (ub + lb) >> 1;
                if(a[mid].CompareTo(x) >= 0) ub = mid;
                else lb = mid;
            }
            return ub;
        }
        public static int UpperBound <T>(this T[] a, T x) where T : IComparable {
            int lb = -1, ub = a.Length;
            while(ub - lb > 1) {
                int mid = (ub + lb) >> 1;
                if(a[mid].CompareTo(x) > 0) ub = mid;
                else lb = mid;
            }
            return ub;
        }
        public static int Range <T>(this T[] a, T from, T to) where T : IComparable
            => a.UpperBound(to) - a.LowerBound(from);
    }
    #endregion
}