Chef wants to host some Division-3 contests. Chef has $N$ setters who are busy creating new problems for him. The $i^{th}$ setter has made $A_i$ problems where $1 \leq i \leq N$.    
A Division-3 contest should have exactly $K$ problems. Chef wants to plan for the next $D$ days using the problems that they have currently. But Chef cannot host more than one Division-3 contest in a day.
Given these constraints, can you help Chef find the maximum number of Division-3 contests that can be hosted in these $D$ days?

-----Input:-----
- The first line of input contains a single integer $T$ denoting the number of test cases. The description of $T$ test cases follows.
- The first line of each test case contains three space-separated integers - $N$, $K$ and $D$ respectively.
- The second line of each test case contains $N$ space-separated integers $A_1, A_2, \ldots, A_N$ respectively. 

-----Output:-----
For each test case, print a single line containing one integer ― the maximum number of Division-3 contests Chef can host in these $D$ days.

-----Constraints-----
- $1 \leq T \leq 10^3$
- $1 \leq N \leq 10^2$
- $1 \le K \le 10^9$ 
- $1 \le D \le 10^9$
- $1 \le A_i \le 10^7$ for each valid $i$

-----Subtasks-----
Subtask #1 (40 points):
- $N = 1$
- $1 \le A_1 \le 10^5$
Subtask #2 (60 points): Original constraints

-----Sample Input:-----
5
1 5 31
4
1 10 3
23
2 5 7
20 36
2 5 10
19 2
3 3 300
1 1 1

-----Sample Output:-----
0
2
7
4
1

-----Explanation:-----
- 
Example case 1: Chef only has $A_1 = 4$ problems and he needs $K = 5$ problems for a Division-3 contest. So Chef won't be able to host any Division-3 contest in these 31 days. Hence the first output is $0$.
- 
Example case 2: Chef has $A_1 = 23$ problems and he needs $K = 10$ problems for a Division-3 contest. Chef can choose any $10+10 = 20$ problems and host $2$ Division-3 contests in these 3 days. Hence the second output is $2$.
- 
Example case 3: Chef has $A_1 = 20$ problems from setter-1 and $A_2 = 36$ problems from setter-2, and so has a total of $56$ problems. Chef needs $K = 5$ problems for each Division-3 contest. Hence Chef can prepare $11$ Division-3 contests. But since we are planning only for the next $D = 7$ days and Chef cannot host more than $1$ contest in a day, Chef cannot host more than $7$ contests. Hence the third output is $7$.

Difficulty: UNKNOWN_DIFFICULTY

Starter code:

Solutions:
for T in range(int(eval(input()))):
	(N, K, D) = list(map(int, input().split()))
	A = list(map(int, input().split()))
	P = sum(A) // K
	print(min(P, D))


r = int(input())
while r > 0:
	(n, k, d) = map(int, input().split())
	l = list(map(int, input().split()))[0:n]
	sum = 0
	for x in range(n):
		sum = sum + l[x]
	c = sum // k
	if c >= d:
		print(d)
	else:
		print(c)
	r -= 1


test = int(input())
while test != 0:
	(n, k, d) = list(map(int, input().split()))
	li = list(map(int, input().split()))
	days = sum(li) // k
	print(min(days, d))
	test = test - 1


t = int(input())
for x in range(0, t):
	(n, k, d) = list(map(int, input().split()))
	noofq = list(map(int, input().split()))
	sum1 = 0
	poss = 0
	for j in range(n):
		sum1 = sum1 + noofq[j]
	if sum1 >= k:
		poss = sum1 // k
	else:
		poss = 0
	if poss > d:
		poss = d
	print(poss)


for i in range(int(input())):
	(n, k, d) = map(int, input().split())
	l = list(map(int, input().split()))
	t = sum(l)
	if t < k:
		print('0')
	elif t == k:
		print('1')
	elif t > k:
		a = t // k
		if a >= d:
			print(str(d))
		else:
			print(str(a))


t = int(input())
for _ in range(t):
	nkd = list(map(int, input().split()))
	k = nkd[1]
	d = nkd[2]
	an = list(map(int, input().split()))
	sum1 = sum(an)
	if sum1 < k:
		print('0')
	else:
		a = sum1 // k
		if a > d:
			print(d)
		else:
			print(a)


T = int(input())
for i in range(T):
	(n, k, d) = [int(x) for x in input().split()]
	A = [int(x) for x in input().split()]
	s = sum(A)
	if s // k < d:
		print(s // k)
	else:
		print(d)


for _ in range(int(input())):
	l = list(map(int, input().split()))
	a = list(map(int, input().split()))
	s = sum(a)
	d = s // l[1]
	if d > l[2]:
		print(l[2])
	else:
		print(d)


for _ in range(int(input())):
	(n, k, d) = list(map(int, input().split()))
	a = sum(map(int, input().split()[:n]))
	da = a // k
	if da >= d:
		print(d)
	else:
		print(da)


xx = int(input(''))
for j in range(xx):
	(a, b, c) = list(map(int, input('').split()))
	x = list(map(int, input('').split()))
	t = 0
	k = 0
	z = 0
	for i in x:
		t = t + (i + k) // b
		k = (i + k) % b
		if t > c:
			z = 1
			print(c)
			break
	if z == 0:
		print(t)


k = int(input())
for j in range(k):
	(a, b, c) = list(map(int, input().split()))
	l = []
	l = list(map(int, input().split()))
	s = sum(l)
	if s < b:
		print('0')
	else:
		d = int(s / b)
		if d < c:
			print(d)
		else:
			print(c)


t = int(input())
while t > 0:
	a = list(map(int, input().rstrip().split()))
	n = a[0]
	k = a[1]
	d = a[2]
	a1 = list(map(int, input().rstrip().split()))
	x = sum(a1) // k
	if x <= d:
		print(x)
	else:
		print(d)
	t = t - 1


for t in range(int(input())):
	(n, k, d) = list(map(int, input().split()))
	problems = list(map(int, input().split()))
	sum = day = 0
	for i in problems:
		sum += i
	contest = sum // k
	if contest == 0:
		print(0)
	elif contest > d:
		print(d)
	else:
		print(contest)


t = int(input())
for _ in range(t):
	(n, k, d) = map(int, input().split())
	a = list(map(int, input().split()))
	total = sum(a)
	contests = total // k
	if contests <= d:
		ans = contests
	else:
		ans = d
	print(ans)


for a in range(int(input())):
	(n, k, d) = map(int, input().split())
	q = map(int, input().split())
	problem = sum(q)
	days = problem // k
	if problem < k:
		print(0)
	elif days <= d:
		print(days)
	else:
		print(d)


for _ in range(int(input())):
	(n, k, d) = [int(x) for x in input().split()]
	A = [int(x) for x in input().split()]
	t = sum(A)
	if t < k:
		print(0)
	else:
		res = t // k
		print(min(res, d))


t = int(input())
for i in range(t):
	(n, k, d) = map(int, input().split())
	arr = list(map(int, input().split()))
	s = sum(arr)
	c = s // k
	if c >= d:
		print(d)
	else:
		print(c)


testc = int(input())
for i in range(testc):
	(a, b, c) = input().split()
	A = int(a)
	B = int(b)
	C = int(c)
	lis = list(map(int, input().split()))
	s = sum(lis)
	ans = s // B
	if ans > C:
		print(C)
	else:
		print(ans)


import math
t = int(input())
for _ in range(t):
	(n, k, d) = list(map(int, input().split()))
	total_prob = sum(list(map(int, input().split())))
	nd = math.floor(total_prob / k)
	if total_prob < k:
		print(0)
	elif nd < d:
		print(nd)
	else:
		print(d)


t = int(input())
for i in range(t):
	(n, k, d) = map(int, input().split())
	if n == 1:
		summ = int(input())
	else:
		a = []
		a = list(map(int, input().strip().split()))[:n]
		summ = sum(a)
	tot = summ // k
	print(min(d, tot))