Problem: 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.

Examples

Input

4 5 3
8
7
4
2


Output

2


Input

2 10 4
20
20


Output

4


Input

5 2 1
900000000
900000000
1000000000
1000000000
1000000000


Output

800000000

Solution (in JAVA):

Solution:
/**
 * Created at 04:22 on 2019-09-03
 */

import java.io.*;
import java.util.*;
import java.util.function.Predicate;

public class Main {

  static FastScanner sc = new FastScanner();
  static Output out = new Output(System.out);

  static final int[] dx = {0, 1, 0, -1};
  static final int[] dy = {-1, 0, 1, 0};

  static final long MOD = (long) (1e9 + 7);
  static final long INF = Long.MAX_VALUE / 2;

  static final int e5 = (int) 1e5;

  public static class Solver {
    public Solver() {

      //sc.load();

      int N = sc.nextInt();

      out.start();

      long A = sc.nextLong();
      long B = sc.nextLong();

      long[] H = sc.nextLongArray(N, false);

      long ans = BinarySearch.binarySearchLong(k -> {

        long count = 0;
        for (int i=0; i<N; i++) {
          count += Math.max(0, ceil(H[i] - B*k, A-B));
          if (count > k) return false;
        }

        return true;
      }, 1, Array.max(H), true);

      out.println(ans);
      //out.time("finish");

    }

    public long ceil(long a, long b) {
      if (b < 0) {
        a *= -1;
        b *= -1;
      }

      if (a > 0) {
        //よくある切り上げのテクニック
        return (a+b-1)/b;
      } else {
        //絶対値の小さい方に丸められる(負なら正の方向)
        return a/b;
      }
    }

    public static class BinarySearch {

      /*
       * [l, r)の区間でchecker.test()を実行する
       * rightOK ... 右側OK左側NGならtrue, 右側NG左側OKならfalse
       */
      public static long binarySearchLong(Predicate<Long> checker, long l, long r, boolean rightOK) {
        long ng, ok;

        if (rightOK) {
          ok = r-1;
          ng = l;
          if (!checker.test(ok)) {
            return r;
          }
          if (checker.test(ng)) {
            return l;
          }
        } else {
          ok = l;
          ng = r-1;
          if (!checker.test(ok)) {
            return l-1;
          }
          if (checker.test(ng)) {
            return r-1;
          }
        }

        /* ok と ng のどちらが大きいかわからないことを考慮 */
        while (Math.abs(ok - ng) > 1) {
          long mid = (ok + ng) / 2;

          if (checker.test(mid)) ok = mid;
          else ng = mid;
        }

        return ok;
      }

      /*
       * [l, r)の区間でchecker.test()を実行する
       */
      public static int binarySearch(Predicate<Integer> checker, int l, int r, boolean rightOK) {

        int ng, ok;

        if (rightOK) {
          ok = r-1;
          ng = l;
          if (!checker.test(ok)) {
            return r;
          }
          if (checker.test(ng)) {
            return l;
          }
        } else {
          ok = l;
          ng = r-1;
          if (!checker.test(ok)) {
            return l-1;
          }
          if (checker.test(ng)) {
            return r-1;
          }
        }

        while (Math.abs(ok - ng) > 1) {
          int mid = (ok + ng) / 2;

          if (checker.test(mid)) ok = mid;
          else ng = mid;
        }

        return ok;
      }

      public static int lowerBound(long[] a, long v) {

        if (a[0] >= v) return 0;

        int l = 0, r = a.length;
        int mid = (r + l) / 2;

        while (r - l > 1) {

          if (a[mid] >= v) r = mid;
          else l = mid;

          mid = (r + l) / 2;
        }

        return r;

      }

      public static int upperBound(long[] a, long v) {

        if (a[0] > v) return 0;

        int l = 0, r = a.length;
        int mid = (r + l) / 2;

        while (r - l > 1) {

          if (a[mid] > v) r = mid;
          else l = mid;

          mid = (r + l) / 2;
        }

        return r;

      }

      public static int count(long[] a, long v) {
        int lower = lowerBound(a, v);
        int upper = upperBound(a, v);
        return upper - lower;
      }

    }

    public static class Array {

      public static void sort(int[] a) {
        shuffle(a);
        Arrays.sort(a);
      }

      public static void sort(long[] a) {
        shuffle(a);
        Arrays.sort(a);
      }

      public static void shuffle(int[] arr){
        int n = arr.length;
        Random rnd = new Random();
        for(int i=0; i<n; ++i){
          int tmp = arr[i];
          int randomPos = i + rnd.nextInt(n-i);
          arr[i] = arr[randomPos];
          arr[randomPos] = tmp;
        }
      }

      public static void shuffle(long[] arr){
        int n = arr.length;
        Random rnd = new Random();
        for(int i=0; i<n; ++i){
          long tmp = arr[i];
          int randomPos = i + rnd.nextInt(n-i);
          arr[i] = arr[randomPos];
          arr[randomPos] = tmp;
        }
      }

      public static int[] reverse(int[] a) {
        int[] b = new int[a.length];
        for (int i=0; i<a.length; i++) {
          b[a.length-1-i] = a[i];
        }
        return b;
      }

      public static long[] reverse(long[] a) {
        long[] b = new long[a.length];
        for (int i=0; i<a.length; i++) {
          b[a.length-1-i] = a[i];
        }
        return b;
      }

      public static long[] toLong(int[] a) {
        long[] b = new long[a.length];
        for (int i=0; i<a.length; i++) {
          b[i] = a[i];
        }
        return b;
      }

      public static int[] toInt(long[] a) {
        int[] b = new int[a.length];
        for (int i=0; i<a.length; i++) {
          b[i] = (int)a[i];
        }
        return b;
      }

      public static long[] cumulativeSum(int[] a, long mod) {
        long[] b = new long[a.length+1];
        for(int i=1; i<=a.length; i++) {
          b[i] += (b[i-1] + a[i-1]) % mod;
        }
        return b;
      }

      public static long[] cumulativeSum(long[] a, long mod) {
        long[] b = new long[a.length+1];
        for(int i=1; i<=a.length; i++) {
          b[i] += (b[i-1] + a[i-1]) % mod;
        }
        return b;
      }

      public static long[] cumulativeSum(int[] a) {
        long[] b = new long[a.length+1];
        for(int i=1; i<=a.length; i++) {
          b[i] += b[i-1] + a[i-1];
        }
        return b;
      }

      public static long[] cumulativeSum(long[] a) {
        long[] b = new long[a.length+1];
        for(int i=1; i<=a.length; i++) {
          b[i] += b[i-1] + a[i-1];
        }
        return b;
      }

      /*
       * int配列の和を返す
       */
      public static long sum(int[] a) {
        long sum = 0;
        for (int i=0; i<a.length; i++) {
          sum += a[i];
        }
        return sum;
      }

      /*
       * long配列の和を返す
       */
      public static long sum(long[] a) {
        long sum = 0;
        for (int i=0; i<a.length; i++) {
          sum += a[i];
        }
        return sum;
      }

      public static void swap(int[] a, int i, int j) {
        int temp = a[i];
        a[i] = a[j];
        a[j] = temp;
      }

      public static void swap(long[] a, int i, int j) {
        long temp = a[i];
        a[i] = a[j];
        a[j] = temp;
      }

      public static int max(int... a) {
        int M = a[0];
        for (int i = 1; i < a.length; i++) {
          M = Math.max(M, a[i]);
        }
        return M;
      }

      public static int min(int... a) {
        int m = a[0];
        for (int i = 1; i < a.length; i++) {
          m = Math.min(m, a[i]);
        }
        return m;
      }

      public static long max(long... a) {
        long M = a[0];
        for (int i = 1; i < a.length; i++) {
          M = Math.max(M, a[i]);
        }
        return M;
      }

      public static long min(long... a) {
        long m = a[0];
        for (int i = 1; i < a.length; i++) {
          m = Math.min(m, a[i]);
        }
        return m;
      }

      public static int[] iota(int n) {
        int[] a = new int[n];
        for (int i=0; i<n; i++) {
          a[i] = i;
        }
        return a;
      }

      public static long[] iotaL(int n) {
        long[] a = new long[n];
        for (int i=0; i<n; i++) {
          a[i] = i;
        }
        return a;
      }

    }

  }

  public static void main(String[] args) {
    new Solver();
    out.flush();
  }

  static class FastScanner {
    private InputStream in = System.in;
    private final byte[] buffer = new byte[1024];
    private int ptr = 0;
    private int buflen = 0;


    public void load() {
      try {
        in = new FileInputStream(next());
      } catch (Exception e) {
        e.printStackTrace();
      }
    }

    private boolean hasNextByte() {
      if (ptr < buflen) {
        return true;
      } else {
        ptr = 0;
        try {
          buflen = in.read(buffer);
        } catch (IOException e) {
          e.printStackTrace();
        }
        if (buflen <= 0) {
          return false;
        }
      }
      return true;
    }

    private int readByte() {
      if (hasNextByte()) return buffer[ptr++];
      else return -1;
    }

    private static boolean isPrintableChar(int c) {
      return 33 <= c && c <= 126;
    }

    private void skipUnprintable() {
      while (hasNextByte() && !isPrintableChar(buffer[ptr])) ptr++;
    }

    public boolean hasNext() {
      skipUnprintable();
      return hasNextByte();
    }

    public String next() {
      if (!hasNext()) throw new NoSuchElementException();
      StringBuilder sb = new StringBuilder();
      int b = readByte();
      while (isPrintableChar(b)) {
        sb.appendCodePoint(b);
        b = readByte();
      }
      return sb.toString();
    }

    public long nextLong() {
      if (!hasNext()) throw new NoSuchElementException();
      long n = 0;
      boolean minus = false;
      int b = readByte();
      if (b == '-') {
        minus = true;
        b = readByte();
      }
      if (b < '0' || '9' < b) {
        throw new NumberFormatException();
      }
      while (true) {
        if ('0' <= b && b <= '9') {
          n *= 10;
          n += b - '0';
        } else if (b == -1 || !isPrintableChar(b)) {
          return minus ? -n : n;
        } else {
          throw new NumberFormatException();
        }
        b = readByte();
      }
    }

    public int nextInt() {
      return (int) nextLong();
    }

    public int[] nextIntArray(int N, boolean oneBased) {
      if (oneBased) {
        int[] array = new int[N + 1];
        for (int i = 1; i <= N; i++) {
          array[i] = sc.nextInt();
        }
        return array;
      } else {
        int[] array = new int[N];
        for (int i = 0; i < N; i++) {
          array[i] = sc.nextInt();
        }
        return array;
      }
    }

    public long[] nextLongArray(int N, boolean oneBased) {
      if (oneBased) {
        long[] array = new long[N + 1];
        for (int i = 1; i <= N; i++) {
          array[i] = sc.nextLong();
        }
        return array;
      } else {
        long[] array = new long[N];
        for (int i = 0; i < N; i++) {
          array[i] = sc.nextLong();
        }
        return array;
      }
    }
  }

  static class Output extends PrintWriter {

    private long startTime;

    public Output(PrintStream ps) {
      super(ps);
    }

    public void print(int[] a, String separator) {
      for (int i = 0; i < a.length; i++) {
        if (i == 0) print(a[i]);
        else print(separator + a[i]);
      }
      println();
    }

    public void print(long[] a, String separator) {
      for (int i = 0; i < a.length; i++) {
        if (i == 0) print(a[i]);
        else print(separator + a[i]);
      }
      println();
    }

    public void print(String[] a, String separator) {
      for (int i = 0; i < a.length; i++) {
        if (i == 0) print(a[i]);
        else print(separator + a[i]);
      }
      println();
    }

    public void print(ArrayList a, String separator) {
      for (int i = 0; i < a.size(); i++) {
        if (i == 0) print(a.get(i));
        else print(separator + a.get(i));
      }
      println();
    }

    public void start() {
      startTime = System.currentTimeMillis();
    }

    public void time(String s) {
      long time = System.currentTimeMillis() - startTime;
      println(s + "(" + time + ")");
    }

  }

}