Chef is playing a video game, and is now fighting the final boss.

The boss has H health points. Each attack of Chef reduces the health of the boss by X.  
Chef also has a special attack that can be used at most once, and will decrease the health of the boss by Y.

Chef wins when the health of the boss is ≤ 0.  
What is the minimum number of attacks needed by Chef to win?

------ Input Format ------ 

- The first line of input will contain a single integer T, denoting the number of test cases.
- The first and only line of each test case will contain three space-separated integers H, X, Y — the parameters described in the statement.

------ Output Format ------ 

For each test case, output on a new line the minimum number of attacks needed by Chef to win.

------ Constraints ------ 

$1 ≤ T ≤ 1000$
$1 ≤ X < Y ≤ H ≤ 100$

----- Sample Input 1 ------ 
4
100 25 40
100 29 45
46 1 2
78 15 78

----- Sample Output 1 ------ 
4
3
45
1

----- explanation 1 ------ 
Test case $1$: Chef can attack the boss $4$ times normally. This results in $25 + 25 + 25 + 25 = 100$ damage, which is enough to defeat the boss.

Test case $2$: Chef can attack the boss $2$ times normally, then use the special attack. This results in $29 + 29 + 45 = 103$ damage, which is enough to defeat the boss.

Test case $3$: Chef can proceed as follows:
- First, use the special attack. This leaves the boss with $46 - 2 = 44$ health.
- Then, use $44$ normal attacks to defeat the boss, since each one does $1$ damage.

This takes a total of $44 + 1 = 45$ attacks.

Test case $4$: Chef can use the special attack to immediately bring the health of the boss to zero, hence only needing one attack.

Difficulty: EASY
Tags: Mathematics

Starter code:

Solutions:
T = int(input())
for i in range(T):
	(x, y, z) = input().split()
	(x, y, z) = (int(x), int(y), int(z))
	x -= z
	u = 1
	while x > 0:
		x -= y
		u += 1
	print(u)


t = int(input())
for i in range(0, t):
	(a, b, c) = input().split()
	a = int(a)
	b = int(b)
	c = int(c)
	ans1 = a // b if a % b == 0 else a // b + 1
	rem = a - c
	ans2 = rem // b if rem % b == 0 else rem // b + 1
	ans2 = ans2 + 1
	print(min(ans1, ans2))


for _ in range(int(input())):
	(h, x, y) = map(int, input().split())
	a = h - y
	b = a % x
	c = a // x
	if b == 0:
		print(c + 1)
	else:
		print(c + 1 + 1)


for _ in range(int(input())):
	(h, x, y) = map(int, input().split())
	if h == y:
		print(1)
	elif (h - y) % x == 0:
		print((h - y) // x + 1)
	else:
		print((h - y) // x + 2)


import math
a = int(input())
for i in range(0, a):
	(h, x, y) = map(int, input().split())
	count = 1
	h = h - y
	temp = math.ceil(h / x)
	count = count + temp
	print(count)


from math import ceil
t = int(input())
for _ in range(t):
	attacks = 0
	(health, attack, special_attack) = map(int, input().split())
	health -= special_attack
	if health <= 0:
		print(1)
	else:
		print(1 + ceil(health / attack))


for _ in range(int(input())):
	(boss, normal, special) = map(int, input().split())
	att = 0
	boss = boss - special
	if boss <= 0:
		print(1)
	else:
		att = 1
		while boss > 0:
			boss = boss - normal
			att += 1
		print(att)


for _ in range(int(input())):
	(h, x, y) = map(int, input().split())
	ans = 0
	if y > x:
		h = h - y
		ans = ans + 1
	if h <= 0:
		print(ans)
		continue
	else:
		ans = ans + h // x
		if h % x > 0:
			ans = ans + 1
		print(ans)


import math
for i in range(int(input())):
	(h, x, y) = map(int, input().split())
	if x >= y:
		print(math.ceil(h / x))
	else:
		print(math.ceil((h - y) / x) + 1)


for j in range(int(input())):
	(h, x, y) = map(int, input().split())
	h = h - y
	a = 1
	while h > 0:
		a += 1
		h -= x
	print(a)


t = int(input())
while t > 0:
	(a, b, c) = map(int, input().split())
	count = 1
	a = a - c
	while a > 0:
		a -= b
		count += 1
	print(count)
	t -= 1


for _ in range(int(input())):
	(h, x, y) = map(int, input().split())
	after_special = h - y
	moves = after_special // x
	if moves < after_special / x:
		moves += 1
	moves += 1
	print(moves)


for _ in range(int(input(''))):
	(h, x, y) = map(int, input('').split(' '))
	l = 0
	if x < y:
		h -= y
		l += 1
	while h > 0:
		h -= x
		l += 1
	print(l)


t = int(input())
for i in range(t):
	(h, x, y) = map(int, input().split())
	minhealth = h - y
	cnt = 0
	if y >= h:
		print('1')
	else:
		while minhealth > 0:
			cnt += 1
			minhealth = minhealth - x
		print(cnt + 1)


t = int(input())
for i in range(t):
	(h, x, y) = map(int, input().split())
	if (h - y) % x == 0:
		print((h - y) // x + 1)
	else:
		print((h - y) // x + 2)


import math
for i in range(int(input())):
	(h, x, y) = map(int, input().split())
	res = h - y
	print(math.ceil(res / x) + 1)


import math
t = int(input())
while t > 0:
	(h, x, y) = map(int, input().split())
	cnt = 1
	rem = h - y
	cnt += rem // x
	if rem % x != 0:
		cnt += 1
	print(cnt)
	t -= 1


for i in range(int(input())):
	(a, b, c) = map(int, input().split())
	if a == c:
		print('1')
	elif (a - c) % b == 0:
		print((a - c) // b + 1)
	else:
		print((a - c) // b + 2)


for i in range(int(input())):
	(health, attack, special) = map(int, input().split(' '))
	remain = health - special
	if remain == 0:
		print(1)
	elif remain % attack == 0:
		print(remain // attack + 1)
	else:
		print(remain // attack + 2)


for i in range(int(input())):
	(health, attack, special) = map(int, input().split(' '))
	count = 1
	remain = health - special
	while remain > 0:
		remain -= attack
		count += 1
	print(count)


t = int(input())
for _ in range(t):
	(h, x, y) = list(map(int, input().split()))
	h = h - y
	c = 1
	while h > 0:
		h = h - x
		c = c + 1
	print(c)


import math
t = int(input())
for i in range(t):
	(a, b, c) = map(int, input().split())
	if a - c == 0:
		print('1')
	else:
		d = a - c
		print(int(math.ceil(d / b)) + 1)


t = int(input())
for i in range(t):
	(h, x, y) = map(int, input().split())
	h = h - y
	c = 1
	while h > 0:
		c = c + 1
		h = h - x
	print(c)


for j in range(int(input())):
	(h, x, y) = map(int, input().split())
	if h > y:
		result = (h - y) / x
		if (h - y) % x == 0:
			print(int(result + 1))
		else:
			print(int(result + 2))
	else:
		print(1)


t = int(input())
for h in range(t):
	(a, b, c) = map(int, input().split())
	x = a - c
	if x % b == 0:
		print(x // b + 1)
	elif x % b != 0:
		print(x // b + 2)


for _ in range(int(input())):
	(h, x, y) = map(int, input().split())
	h -= y
	counter = 1
	if h % x == 0:
		counter += h // x
	else:
		counter += h // x + 1
	print(counter)


import math as m
for _ in range(int(input())):
	(a, b, c) = map(int, input().split())
	print(m.ceil((a - c) / b) + 1)


for i in range(int(input())):
	x = [int(x) for x in input().split()]
	if (x[0] - x[2]) % x[1] == 0:
		print(1 + (x[0] - x[2]) // x[1])
	else:
		print(2 + (x[0] - x[2]) // x[1])


import math
n = int(input())
for i in range(n):
	(a, b, c) = list(map(int, input().split()))
	a -= c
	if a >= 0:
		print(math.ceil(a / b) + 1)
	else:
		print(1)


import math
for i in range(int(input())):
	(h, a, b) = map(int, input().split())
	h -= b
	if h > 0:
		print(math.ceil(h / a) + 1)
	else:
		print(1)


import math
T = int(input())
for _ in range(T):
	(H, X, Y) = map(int, input().split())
	if Y >= H:
		print(1)
	else:
		print(min(math.ceil(H / X), math.ceil((H - Y) / X) + 1))


import math
for t in range(int(input())):
	(h, x, y) = map(int, input().split())
	print(math.ceil((h - y) / x) + 1)


for i in range(int(input())):
	(x, y, z) = map(int, input().split())
	if x - z <= 0:
		print(1)
	elif (x - z) % y == 0:
		print((x - z) // y + 1)
	else:
		print((x - z) // y + 2)


t = int(input())
import math
for i in range(t):
	(n, k, s) = map(int, input().split())
	print(math.ceil((n - s) / k) + 1)


t = int(input())
for i in range(t):
	(x, y, k) = map(int, input().split())
	count = 0
	while x > 0:
		if x - k <= 0:
			x -= k
		else:
			x -= y
		count += 1
	print(count)


t = int(input())
for i in range(t):
	(h, x, y) = map(int, input().split(' '))
	ans = 1 + (h - y) // x
	if (h - y) % x > 0:
		ans = ans + 1
	print(ans)


for _ in range(int(input())):
	(h, x, y) = map(int, input().split())
	spl = h - y
	count = 1
	while spl > 0:
		spl = spl - x
		count += 1
	print(count)


import math
for _ in range(int(input())):
	(a, b, c) = map(int, input().split())
	if b <= c:
		d = math.ceil((a - c) / b) + 1
	else:
		d = math.ceil(a / b)
	print(d)


t = int(input())
for i in range(t):
	(h, x, y) = [int(x) for x in input().split()]
	d = 0
	f = 0
	while h > 0:
		if f == 0:
			h -= max(x, y)
		else:
			h -= x
		f += 1
	print(f)


T = int(input())
for i in range(0, T):
	(H, X, Y) = map(int, input().split())
	if H == Y:
		print('1')
	elif (H - Y) % X == 0:
		print((H - Y) // X + 1)
	else:
		print((H - Y) // X + 2)


import math as m
for t in range(int(input())):
	(h, x, y) = map(int, input().split())
	if h == y:
		print('1')
	elif (h - y) % x == 0:
		print((h - y) // x + 1)
	else:
		print((h - y) // x + 2)


t = int(input())
for i in range(t):
	(h, n, s) = map(int, input().split())
	a = 1
	h = h - s
	if h <= 0:
		print(a)
	else:
		while h > 0:
			h = h - n
			a = a + 1
		print(a)


from math import *
for _ in range(int(input())):
	(h, x, y) = map(int, input().split())
	k = ceil((h - y) / x)
	print(1 + k)


from math import ceil
t = int(input())
for _ in range(t):
	(h, x, y) = map(int, input().split())
	a = ceil(h / x)
	b = ceil((h - y) / x) + 1
	print(min(a, b))


goals = int(input())
for distractions in range(goals):
	(aim, life, stress) = map(int, input().split())
	aim -= stress
	wife = 1
	while aim > 0:
		aim -= life
		wife += 1
	print(wife)


for i in range(int(input())):
	(a, b, c) = map(int, input().split())
	a -= c
	d = 1
	while a > 0:
		a -= b
		d += 1
	print(d)


import math
for i in range(int(input())):
	(h, x, y) = map(int, input().split())
	c1 = 1
	c1 += math.ceil((h - y) / x)
	c2 = math.ceil(h / x)
	print(min(c1, c2))


t = int(input())
for i in range(t):
	(h, x, y) = map(int, input().split())
	for j in range(h):
		if j * x + y >= h:
			print(j + 1)
			break


import sys
sys.setrecursionlimit(10 ** 7)
mod = 10 ** 9 + 7

def readInt():
	return int(input())

def readIntList():
	return list(map(int, input().split()))

def readStringList():
	return list(input())

def readStringListWithSpace():
	return list(input().split())

def readString():
	return input()
import math

def execute():
	for _ in range(readInt()):
		(h, x, y) = readIntList()
		count = int(math.ceil((h - y) / x)) + 1
		print(count)
execute()


from math import ceil
t = int(input())
for _ in range(t):
	(h, x, y) = map(int, input().split())
	ans = h - y
	if ans > 0:
		print(ceil(ans / x) + 1)
	else:
		print(1)


for i in range(int(input())):
	(h, x, y) = map(int, input().split())
	t = 100
	s = y
	for j in range(t + 1):
		if s >= h:
			if j == 0:
				print(j + 1)
				break
			elif j > 1:
				print(j)
				break
			else:
				pass
		elif s <= h:
			if j == 0:
				s = x * j + s
			elif j >= 1:
				s += x
			else:
				pass
		else:
			pass


import math
for i in range(int(input())):
	(a, b, c) = map(int, input().split())
	if a <= c:
		print('1')
	else:
		k = math.ceil((a - c) / b)
		print(k + 1)


import math
n = int(input())
for i in range(n):
	(h, x, y) = map(int, input().split())
	a = h - y
	b = a / x
	print(math.ceil(b) + 1)


t = int(input())
for i in range(t):
	(h, x, y) = input().split()
	x = int(x)
	y = int(y)
	h = int(h)
	l = h - y
	count = 1
	while l > 0:
		l = l - x
		count = count + 1
	print(count)


t = int(input())
while t != 0:
	(h, x, y) = map(int, input().split(' '))
	attacks = 0
	i = 0
	while h > 0:
		if i == 0:
			h -= y
			attacks += 1
			i += 1
		else:
			h -= x
			attacks += 1
	print(attacks)
	t -= 1


import math
t = int(input())
for i in range(t):
	l = list(map(int, input().strip().split()))
	if l[0] <= l[2]:
		print('1')
	elif l[0] > l[2]:
		if (l[0] - l[2]) // l[1] < (l[0] - l[2]) / l[1]:
			print(2 + (l[0] - l[2]) // l[1])
		else:
			p = (l[0] - l[2]) // l[1] == (l[0] - l[2]) / l[1]
			print(int(1 + (l[0] - l[2]) / l[1]))


n = int(input())
for i in range(n):
	(x, y, z) = map(int, input().split())
	a = x - z
	b = a // y
	if x <= z or z <= y:
		print(1)
	elif a % y == 0:
		print(b + 1)
	else:
		print(b + 2)


import math
testcases = int(input())
for eachcase in range(testcases):
	(health, atk, s_atk) = map(int, input().split())
	count = 1
	health = health - s_atk
	if health > 0:
		count += math.ceil(health / atk)
	print(count)


q = int(input())
for i in range(q):
	(h, x, y) = map(int, input().split())
	count = 1
	a = h - y
	if a % x == 0:
		count += a // x
	else:
		count += a // x + 1
	print(count)