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 Kotlin (1.0.0) (judge verdict: Accepted)

import java.io.PrintWriter
import java.util.*
import java.math.*
import java.lang.*
import kotlin.comparisons.*

val pw = PrintWriter(System.out)
val MOD: Long = (1e+9 + 7).toLong()

fun enough(t: Int, hArr: Array<Int>, a: Int, b: Int, n: Int): Boolean {
	var cnt = 0L
	for(i in 0 until n) {
		val h = hArr[i]
		val bt = b * t
		if(bt < h) {
			val restH = (h - bt)
			val numAppendDamege = restH / (a - b) + if(restH % (a - b) > 0) 1 else 0
			cnt += numAppendDamege.toLong()
		}
	}
	return cnt <= t.toLong()
}

fun main(args: Array<String>) {
	val (n, a, b) = readListOfInt()
	val hArr = Array(n) { 0 }
	for(i in 0 until n) {
		val h = readInt()
		hArr[i] = h
	}
	val hmax = hArr.max()!!
	var l = 0
	var r = hmax / b + 1
	while(l < r) {
		val mid = (l + r) / 2
		val isEnough = enough(mid, hArr, a, b, n)
		if(isEnough) {
			r = mid
		} else {
			l = mid + 1
		}
	}
	println(l)

	pw.flush()
}

/****** Declared Functions and Data Structures ******/
// IO
fun read() = readLine()!!
fun readInt() = read().toInt()
fun readLong() = read().toLong()
fun readDouble() = read().toDouble()
fun readListOfString() = read().split(" ")
fun readListOfInt() = readListOfString().map { it.toInt() }
fun readListOfLong() = readListOfString().map { it.toLong() }
fun readListOfDouble() = readListOfString().map { it.toDouble() }

fun Double.format(digits: Int) = String.format("%.${digits}f", this)
fun Float.format(digits: Int) = String.format("%.${digits}f", this)

fun print(value: Any) { pw.print(value) }
fun println(value : Any) { pw.println(value) }

// Extensions
fun<T> List<T>.toBuckets(): Map<T, Int>
	= this.groupBy { it }.mapValues { it.value.size }

fun<T: Comparable<T>> List<T>.upperBound(element: T, fromIndex: Int=0, toIndex: Int=this.size): Int {
	var l = fromIndex
	var r = toIndex
	while(l < r) {
		val mid = (l+r) / 2
		if(element >= this[mid]) { 
			l = mid + 1
		} else {
			r = mid
		}
	}
	return l
}

fun<T: Comparable<T>> List<T>.lowerBound(element: T, fromIndex: Int=0, toIndex: Int=this.size): Int {
	var l = fromIndex
	var r = toIndex
	while(l < r) {
		val mid = (l+r) / 2
		if(element <= this[mid]) { 
			r = mid
		} else {
			l = mid + 1
		}
	}
	return r 
}

fun <K, V> Map<K, V>.toMutableMap(): MutableMap<K, V> = HashMap(this)

// Util Functions
fun Long.makeDivisors(): List<Long> {
	val divisors = mutableListOf<Long>()
	for(i in 1L .. Math.sqrt(this.toDouble()).toLong()+1L) {
		if(this % i == 0L) {
			divisors.add(i)
			if(i != this/i) {
				divisors.add(this/i)
			}
		}
	}
	return divisors.distinct().sorted()
}

fun Long.isPrime(): Boolean {
	if(this==1L) return false
	for(i in 2L .. Math.sqrt(this.toDouble()).toLong() + 1L) {
		if(this % i == 0L && this != i) {
			return false
		}
	}
	return true
}


fun<T> permutations(src: List<T>): List<List<T>> {
	if(src.size == 1) return listOf(src)
	val perms = mutableListOf<List<T>>()
	val insertElement = src[0]
	permutations(src.drop(1)).forEach { perm ->
		for(i in 0..perm.size) {
			val newPerm = perm.toMutableList()
			newPerm.add(i, insertElement)
			perms.add(newPerm.toList())
		}
	}
	return perms
}

// return nCr, if you want nCr, please access v[n][r]
fun combinations(n: Long): List<List<Long>> {
	val v = (0..n).map { (0..n).map{0L}.toMutableList() }.toMutableList()
	for(i in 0 until v.size) {
		v[i][0] = 1L
		v[i][i] = 1L
	}
	for(i in 0 until v.size) {
		for(j in 1 until i) {
			v[i][j] = (v[i-1][j-1] + v[i-1][j]) % MOD
		}
	}
	return v.map { it.toList() }.toList()
}

fun repeatedModPow(a: Long, n: Long, mod: Long): Long = 
	when {
		n == 1L -> a % mod
		n % 2L == 1L -> (a * repeatedModPow(a, n-1L, mod)) % mod
		else -> {
			val tmp = repeatedModPow(a, n / 2L, mod)
			(tmp * tmp) % mod
		}
	}

// return nCr % MOD
fun modnCkWithoutArray(n: Long, k: Long, mod: Long): Long {
	var ret = 1L
	val min = Math.min(k, n-k)
	// まず分母の計算
	for(i in n downTo (n - min + 1)) {
		ret = ret * i % mod
	}
	for(i in min downTo 1) {
		ret = ret * repeatedModPow(i, (mod - 2L), mod) % mod
	}
	return ret
}

// return nCr % MOD
fun modnCk(n: Int, k: Int, mod: Long): Long {
	val factorials = Array(n+1) { 0L }.apply {
		this[0] = 1L
		if(this.size > 1) this[1] = 1L
	}
	val inverses = Array(n+1) { 0L }.apply {
		this[0] = 1L
		if(this.size > 1) this[1] = 1L
	}
	val factorialInverses = Array(n+1) { 0L }.apply {
		this[0] = 1L
		if(this.size > 1) this[1] = 1L
	}
	for(i in 2 .. n) {
		factorials[i] = (factorials[i-1] * i.toLong() % mod)
		inverses[i] = (mod - inverses[mod.toInt() % i] * (mod / i.toLong()) % mod)
		factorialInverses[i] = (factorialInverses[i-1] * inverses[i] % mod)
	}

	return factorials[n] % mod * (factorialInverses[k] * factorialInverses[n-k] % mod) % mod
}

// should be a >= b
fun gcd(a: Long, b: Long): Long = 
	if(b == 0L) a else gcd(b, a % b)

// shoud be a >= b
fun lcm(a: Long, b: Long): Long = 
	a / gcd(a, b) * b

fun sumDigits(num_: Long): Long {
	var num = num_
	var rtn: Long = 0
	while(num != 0.toLong()) {
		val tmp = num % 10
		rtn += tmp
		num /= 10
	}
	return rtn
}

fun Double.isDecimal(): Boolean = ((this - Math.floor(this)) != 0.0)

// Data Structures

class UnionFind(private val n: Int) {
	private val parent: Array<Int> = Array(n) { 0 }
	private val rank: Array<Int> = Array(n) { 0 }
	private val size: Array<Int> = Array(n) { 0 }

	init {
		for(i in 0 until n) {
			parent[i] = i
			rank[i] = 1
			size[i] = 1
		}
	}

	fun union(u: Int, v: Int) {
		var x = root(u)
		var y = root(v)
		if(x != y) {
			if(rank[y] < rank[x]) {
				val tmp = y 
				y = x
				x = tmp 
			}
			parent[x] = y
			rank[y] += rank[x]
			rank[x] = -1
			val totalSize = size[x] + size[y]
			size[x] = totalSize
			size[y] = totalSize
		}
	}

	fun root(u: Int): Int {
		var x = u
		while(parent[x] != x) {
			x = parent[x]
		}
		return x 
	}

	fun size(u: Int): Int = size[root(u)]
}