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 Java8 (OpenJDK 1.8.0) (judge verdict: Wrong Answer)

import java.io.*;
import java.util.*;

class Main{

    void solve(){        
        int N = ni();
        int A = ni();
        int B = ni();
        int[] hp = new int[N];
        for(int i = 0; i < N; i++){
            hp[i] = ni();
        }

        int ans = lowerBound(INF / 2, 0, hp, A, B);
        System.out.println(ans);

    }

    boolean func(int K, int[] hp, int A, int B){
        int tmp = 0;
        for(int i = 0; i < hp.length; i++){
            int rem = hp[i] - B * K;
            if(rem > 0){
                tmp += (rem + (A - B - 1)) / (A - B);
            }
        }

        return tmp <= K;
    }
    int lowerBound(int ok, int ng, int[] hp, int A, int B){
        while(Math.abs(ok - ng) > 1){
            int mid = (ok + ng) / 2; 
            if(func(mid, hp, A, B)){
                ok = mid;
            } else {
                ng = mid;
            }
        }
        return ok;
    }
    public static void main(String[] args){
        new Main().solve();
    }

    private FastScanner scan = new FastScanner();
    private final int MOD = 1_000_000_007;
    private final int INF = 2147483647;
    private final long LINF = 9223372036854775807L;
    private long[] fac;
    private long[] finv;
    private long[] inv;

    // Scanner
    int ni(){ return scan.nextInt();}
    int[] ni(int n){int[] a = new int[n]; for(int i = 0; i < n; i++){a[i] = ni();} return a;}
    int[][] ni(int y, int x){int[][] a = new int[y][x];
        for(int i = 0; i < y; i++){for(int j = 0; j < x; j++){a[i][j] = ni();}} return a;}
    long nl(){return scan.nextLong();}
    long[] nl(int n){long[] a = new long[n]; for(int i = 0; i < n; i++){a[i] = nl();} return a;}
    long[][] nl(int y, int x){long[][] a = new long[y][x];
        for(int i = 0; i < y; i++){for(int j = 0; j < x; j++){a[i][j] = nl();}} return a;}
    String ns(){return scan.next();}
    String[] ns(int n){String[] a = new String[n]; for(int i = 0; i < n; i++){a[i] = ns();} return a;}
    String[][] ns(int y, int x){String[][] a = new String[y][x];
        for(int i = 0; i < y; i++){for(int j = 0; j < x; j++){a[i][j] = ns();}} return a;}

    // Mathematics
    int max(int a, int b){return Math.max(a, b);}
    long max(long a, long b){return Math.max(a, b);}
    double max(double a, double b){return Math.max(a, b);}
    int max(int[] a){int max = a[0]; for(int value:a){max = max(max,value);} return max;}
    long max(long[] a){long max = a[0]; for(long value:a){max = max(max,value);} return max;}
    double max(double[] a){double max = a[0]; for(double value:a){max = max(max,value);} return max;}
    int min(int a, int b){return Math.min(a, b);}
    long min(long a, long b){return Math.min(a, b);}
    double min(double a, double b){return Math.min(a, b);}
    int min(int[] a){int min = a[0]; for(int value:a){min = min(min,value);} return min;}
    long min(long[] a){long min = a[0]; for(long value:a){min = min(min,value);} return min;}
    double min(double[] a){double min = a[0]; for(double value:a){min = min(min,value);} return min;}
    long sum(int[] a){long sum = 0; for(int value:a){sum += value;} return sum;}
    long sum(long[] a){long sum = 0; for(long value:a){sum += value;} return sum;}
    double sum(double[] a){double sum = 0; for(double value:a){sum += value;} return sum;}
    int gcd(int a, int b){return b == 0 ? a : gcd(b, a % b);}
    long gcd(long a, long b){return b == 0 ? a : gcd(b, a % b);}
    int lcm(int a, int b){return a / gcd(a, b) * b;}
    long lcm(long a, long b){return a / gcd(a, b) * b;}
    long fact(int n){ if(n == 0){ return 1; } long a = n; for(long i = n - 1; i >= 2; i--){ a = a % MOD * i; } return a; }
    long fact(long n){ if(n == 0){ return 1; } long a = n; for(long i = n - 1; i >= 2; i--){ a = a % MOD * i; } return a; }
    // nPr(int)
    long npr(int n, int r){
        long a = 1;
        for(int i = n; i > n - r; i--){
            a *= i;
        }
        return a;
    }
    // nPr(long)
    long npr(long n, long r){
        long a = 1;
        for(long i = n; i > n - r; i--){
            a *= i;
        }
        return a;
    }
    // 素数判定(int)
    boolean checkPrime(int n){
        for(int i = 2; i * i <= n; i++){
            if(n % i == 0){
                return false;
            }
        }
        return true;
    }
    // 素数判定(long)
    boolean checkPrime(long n){
        for(long i = 2; i * i <= n; i++){
            if(n % i == 0){
                return false;
            }
        }
        return true;
    }
    // mod pにおける累乗 a^n
    long modpow(long a, long n, long p){
        long res = 1;
        while(n > 0){
            if((n & 1) == 1){
                res = res * a % p;
            }
            a = a * a % p;
            n = n >> 1;
        }
        return res;
    }
    // mod pにおけるaの逆元a^-1
    long modinv(long a, long p){
        return modpow(a, p - 2, p);
    }
    // fac,finv,invの初期化
    void comInit(int max){
        fac = new long[max];
        finv = new long[max];
        inv = new long[max];
        fac[0] = fac[1] = 1;
        finv[0] = finv[1] = 1;
        inv[1] = 1;
        for(int i = 2; i < max; i++){
            fac[i] = fac[i - 1] * i % MOD;
            inv[i] = MOD - inv[MOD % i] * (MOD / i) % MOD;
            finv[i] = finv[i - 1] * inv[i] % MOD;
        }
    }
    // 二項係数nCr
    long com(int n, int r){
        if(n < r || (n < 0 || r < 0)){
            return 0;
        }
        return fac[n] * (finv[r] * finv[n - r] % MOD) % MOD;
    }
    // 二項係数nCr（nが10^9など巨大なとき用）
    long ncr(long n, long k){
        long a = 1;
        long b = 1;
        for(int i = 1; i <= k; i++){
            a = a * (n + 1 - i) % MOD;
            b = b * i % MOD;
        }
        
        return modinv(b, MOD) * a % MOD;
    }
    // 二次元上の二点間の距離
    double distance(double x1, double y1, double x2, double y2){
        double dist = Math.sqrt((x1 - x2) * (x1 - x2) + (y1 - y2) * (y1 - y2));
        return dist;
    }
    // 三次元上の二点間の距離
    double distance(double x1, double y1, double z1, double x2, double y2, double z2){
        double dist = Math.sqrt((x1 - x2) * (x1 - x2) + (y1 - y2) * (y1 - y2) + (z1 - z2) * (z1 - z2));
        return dist;
    }


    // Array
    void sort(int[] a){ Arrays.sort(a);}
    void sort(long[] a){ Arrays.sort(a);}
    void sort(double[] a){ Arrays.sort(a);}
    void sort(String[] a){ Arrays.sort(a);}
    int[] reverse(int[] a){
        int[] reversed = new int[a.length];
        for(int i = 0; i < a.length; i++){
            reversed[a.length - i - 1] = a[i];
        }
        return reversed;
    }
    long[] reverse(long[] a){
        long[] reversed = new long[a.length];
        for(int i = 0; i < a.length; i++){
            reversed[a.length - i - 1] = a[i];
        }
        return reversed;
    }
    double[] reverse(double[] a){
        double[] reversed = new double[a.length];
        for(int i = 0; i < a.length; i++){
            reversed[a.length - i - 1] = a[i];
        }
        return reversed;
    }
    char[] reverse(char[] a){
        char[] reversed = new char[a.length];
        for(int i = 0; i < a.length; i++){
            reversed[a.length - i - 1] = a[i];
        }
        return reversed;
    }
    String[] reverse(String[] a){
        String[] reversed = new String[a.length];
        for(int i = 0; i < a.length; i++){
            reversed[a.length - i - 1] = a[i];
        }
        return reversed;
    }
    boolean[] reverse(boolean[] a){
        boolean[] reversed = new boolean[a.length];
        for(int i = 0; i < a.length; i++){
            reversed[a.length - i - 1] = a[i];
        }
        return reversed;
    }
    void fill(int[] array, int x) { Arrays.fill(array, x); }
    void fill(long[] array, long x) { Arrays.fill(array, x); }
    void fill(double[] array, double x) { Arrays.fill(array, x); }
    void fill(boolean[] array, boolean x) { Arrays.fill(array, x); }
    void fill(int[][] array, int x) { for(int a[] : array) { fill(a, x); } }
    void fill(long[][] array, long x) { for(long a[] : array) { fill(a, x); } }
    void fill(double[][] array, double x) { for(double a[] : array) { fill(a, x); } }
    void fill(boolean[][] array, boolean x) { for(boolean a[] : array) { fill(a, x); } }
    void fill(int[][][] array, int x) { for(int[][] ary : array) { for(int[] a : ary){ fill(a, x); } } }
    void fill(long[][][] array, long x) { for(long[][] ary : array) { for(long[] a : ary){ fill(a, x); } } }

    // Algorithm
    // 深さ優先探索
    /*
        HashMap<Integer, List<Integer>> graph = new HashMap<>();
        List<Integer> list;
    */
    int minCost = INF;
    void dfs(HashMap<Integer, List<Integer>> graph, int v, boolean[] seen, long[] x){
        seen[v] = true;
        if(!graph.containsKey(v) || graph.get(v).size() == 0) return;
        List<Integer> todo = graph.get(v);
        for(int next : todo){
            if(seen[next]) continue;
            x[next] += x[v];
            dfs(graph, next, seen, x);
        }
    }
    // 幅優先探索
    /*
        HashMap<Integer, List<Integer>> graph = new HashMap<>();
        List<Integer> list;
    */
    void bfs(HashMap<Integer, List<Integer>> graph, int v, int[] dist){
        Queue<Integer> que = new ArrayDeque<>();
        que.add(v);

        while(que.size() > 0){
            v = que.poll();
            if(!graph.containsKey(v)) continue;
            for(int next : graph.get(v)){
                if(dist[next] != -1) continue;
                dist[next] = dist[v] + 1;
                que.add(next);
            }
        }
    }
    // ダイクストラ法
    Node[] dijkstra(HashMap<Integer, List<Integer>> graph, int size, int v, boolean[] flag, int[][] cost, int[] temp, int X){
        Queue<Node> queue = new PriorityQueue<>(new MyComparator());
        Node[] nodes = new Node[size];
        int[] hot = new int[size]; // 最後に暑すぎる部屋を出た時刻
        int[] cold = new int[size]; // 最後に寒すぎる部屋を出た時刻
        for(int i = 0; i < size; i++){
            nodes[i] = new Node(i, INF, -1);            // id, dist, pastを指定して初期化
        }
        /* for(int key : graph.keySet()){
            nodes[key] = new Node(key, INF, -1);    // id, dist, pastを指定して初期化
        } */
       
        nodes[v].dist = 0;  // 始点のコストを0に
        try{
            queue.add(nodes[v].clone());
        } catch(CloneNotSupportedException e){
            e.printStackTrace();
        }

        while(queue.size() > 0){
            Node now = queue.poll();        // 未確定の中で最もコストの低いノードを取り出す
            //flag[now.id] = true;                // 確定
            if(temp[now.id] != 1) flag[now.id] = true;
            if(!graph.containsKey(now.id)) continue;
            for(int next : graph.get(now.id)){      // 辺で繋がっているノードを順にチェック
                if(flag[next] || nodes[next].dist < nodes[now.id].dist + cost[now.id][next]) continue;
                if(Math.abs(temp[now.id] - temp[next]) == 2 && cost[now.id][next] < X) continue;//
                int lastTime = 0;   //
                if(temp[next] == 0){
                    lastTime = hot[now.id];
                } else if(temp[next] == 2){
                    lastTime = cold[now.id];
                }
                if(cost[now.id][next] < X - lastTime){ //
                    int min = INF;
                    for(int next2 : graph.get(now.id)){
                        if(next2 == next || Math.abs(temp[next2] - temp[next]) == 2) continue;
                        min = min(min, cost[now.id][next2]);
                    }
                    if(min == INF) continue;
                    min *= 2;
                    while(nodes[now.id].dist + cost[now.id][next] + min < X + lastTime){
                        min += min;
                    }
                    if(nodes[next].dist < nodes[now.id].dist + cost[now.id][next] + min) continue;
                    nodes[next].dist = nodes[now.id].dist + cost[now.id][next] + min;     // distを更新
                    nodes[next].past = now.id;                                                    // pastを現在のノードに
                    hot[next] = hot[now.id] + cost[now.id][next] + min;
                    cold[next] = cold[now.id] + cost[now.id][next] + min;
                    if(temp[next] == 2) hot[next] = 0;
                    if(temp[next] == 0) cold[next] = 0;
                    try{
                        queue.add(nodes[next].clone());
                    } catch (CloneNotSupportedException e){
                        e.printStackTrace();
                    }
                    continue;
                }//
                nodes[next].dist = nodes[now.id].dist + cost[now.id][next];     // distを更新
                nodes[next].past = now.id;                                                    // pastを現在のノードに
                hot[next] = hot[now.id] + cost[now.id][next]; //
                cold[next] = cold[now.id] + cost[now.id][next];
                if(temp[next] == 2) hot[next] = 0;
                if(temp[next] == 0) cold[next] = 0; //
                try{
                    queue.add(nodes[next].clone());
                } catch (CloneNotSupportedException e){
                    e.printStackTrace();
                }
            }
        }

        return nodes;
    }
    
    // ソート済みint型配列でkey以上の値の最小indexを返す
 /*    int lowerBound(int[] a, int key){
        int ng = -1;
        int ok = a.length;
        while(Math.abs(ok - ng) > 1){
            int mid = (ok + ng) / 2; 
            if(a[mid] >= key){
                ok = mid;
            } else {
                ng = mid;
            }
        }
        return ok;
    } */
    // ソート済みlong型配列でkey以上の値の最小indexを返す
    int lowerBound(long[] a, long key){
        int ng = -1;
        int ok = a.length;
        while(Math.abs(ok - ng) > 1){
            int mid = (ok + ng) / 2; 
            if(a[mid] >= key){
                ok = mid;
            } else {
                ng = mid;
            }
        }
        return ok;
    }
    // 文字列sとtの最長共通部分列の長さを返す
    int lcs(String s , String t){
        int[][] dp = new int[s.length() + 1][t.length() + 1];

        for(int i = 0; i < s.length(); i++){
            for(int j = 0; j < t.length(); j++){
                if(s.charAt(i) == t.charAt(j)){
                    dp[i + 1][j + 1] = max(dp[i][j] + 1, dp[i + 1][j + 1]);
                }
                dp[i + 1][j + 1] = max(dp[i + 1][j + 1], dp[i + 1][j]);
                dp[i + 1][j + 1] = max(dp[i + 1][j + 1], dp[i][j + 1]);
            }
        }

        return dp[s.length()][t.length()];
    }

}
// ダイクストラ法におけるノード
class Node implements Cloneable{
    int id;             // ノード番号
    int dist;           // 最低必要コスト
    int past;           // 直前の頂点

    Node(int id, int dist, int past){
        this.id = id;
        this.dist = dist;
        this.past = past;
    }
    @Override
    protected Node clone() throws CloneNotSupportedException{
        Node node = (Node)super.clone();
        return node;
    }
    public String toString(){
        return "[" + id + ", " + dist + " ," + past + "]";
    }
}
// ダイクストラ法における重み比較のComparator
class MyComparator implements Comparator<Node>{
    @Override
    public int compare(Node n1, Node n2){
        int dist1 = n1.dist;
        int dist2 = n2.dist;
        if(dist1 < dist2){
            return -1;
        } else if(dist1 > dist2){
            return 1;
        } else {
            return 0;
        }
    }
}
// 辺の情報を持つクラス
class Edge implements Cloneable{
    int from;       // どの頂点から
    int to;          //  どの頂点へ
    double cost;       // 辺の重み

    Edge(int from, int to, double cost){
        this.from = from;
        this.to = to;
        this.cost = cost;
    }
    @Override
    protected Edge clone() throws CloneNotSupportedException{
        Edge edge = (Edge)super.clone();
        return edge;
    }
    public String toString(){
        return "[" + from + " to " + to + "," + cost + "]";
    }
}
// 辺の重み比較のComparator
class EdgeComparator implements Comparator<Edge>{
    @Override
    public int compare(Edge e1, Edge e2){
        double cost1 = e1.cost;
        double cost2 = e2.cost;
        if(cost1 < cost2){
            return -1;
        } else if(cost1 > cost2){
            return 1;
        } else {
            return 0;
        }
    }
}
// Union-Find
class UnionFind{
    int[] par;
    int[] size;
    UnionFind(int N){
        par = new int[N];
        size = new int[N];
        for(int i = 0; i < N; i++){
            par[i] = i;
            size[i] = 1;
        }
    }

    void init(int N){
        for(int i = 0; i < N; i++){
            par[i] = i;
            size[i] = 1;
        }
    }

    int root(int x){
        if(par[x] == x){
            return x;
        } else {
            return par[x] = root(par[x]);
        }
    }

    boolean same(int x, int y){
        return root(x) == root(y);
    }

    void unite(int x, int y){
        x = root(x);
        y = root(y);
        if(x == y) return;
        if(size[x] < size[y]){
            int tmp = x;
            x = y;
            y = tmp;
        }
        size[x] += size[y];
        par[y] = x;
    }

    int size(int x){
        return size[root(x)];
    }

}

// 順列を管理する
class Permutation {
    private int number;
    private int listSize;
    private int searched;
    private int nextIndex;
    private int[][] permList;

    Permutation(int num) {
        this.number = num;
        this.listSize  = this.fact(this.number);
        this.searched   = 0;
        this.nextIndex = 0;
        this.permList  = new int[this.listSize][this.number];

        this.create(0, new int[this.number], new boolean[this.number]);
    }

    int[] nextPerm() {
        return permList[this.nextIndex++];
    }

    boolean isNext() {
        if(this.nextIndex < this.listSize) {
            return true;
        } else {
            this.nextIndex = 0;
            return false;
        }
    }

    int fact(int n){
        return n == 0 ? 1 : n * fact(n-1);
    }

    void create(int num, int[] list, boolean[] flag) {
        if(num == this.number) {
            copyArray(list, permList[this.searched]);
            this.searched++;
        }
        for(int i = 0; i < this.number; i++){
            if(flag[i]) continue;
            list[num] = i;
            flag[i] = true;
            this.create(num+1, list, flag);
            flag[i] = false;

        }
    }

    void copyArray(int[] from, int[] to) {
        for(int i=0; i<from.length; i++) to[i] = from[i];
    }

    void printNum(int[] nums) {
        for(int n : nums) System.out.print(n);
        System.out.println();
    }
}

// Binary Indexed Tree
class BIT{
    int[] tree;

    BIT(int N){
        this.tree = new int[N + 1];
    }

    int sum(int i){
        int sum = 0;
        while(i > 0){
            sum += this.tree[i];
            i -= i & -i;
        }
        return sum;
    }

    void add(int i, int x){
        while(i <= tree.length){
            this.tree[i] += x;
            i += i & -i;
        }
    }
    
}

// 標準のScannerより高速に標準入力する
class FastScanner {
    private final InputStream in = System.in;
    private final byte[] buffer = new byte[1024];
    private int ptr = 0;
    private int buflen = 0;
    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;}
    public boolean hasNext() { while(hasNextByte() && !isPrintableChar(buffer[ptr])) ptr++; 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() {
        long nl = nextLong();
        if (nl < Integer.MIN_VALUE || nl > Integer.MAX_VALUE) throw new NumberFormatException();
        return (int) nl;
    }
    public double nextDouble() { return Double.parseDouble(next());}
}