Alice and Bob love playing one-dimensional battle ships. They play on the field in the form of a line consisting of n square cells (that is, on a 1 × n table).

At the beginning of the game Alice puts k ships on the field without telling their positions to Bob. Each ship looks as a 1 × a rectangle (that is, it occupies a sequence of a consecutive squares of the field). The ships cannot intersect and even touch each other.

After that Bob makes a sequence of "shots". He names cells of the field and Alice either says that the cell is empty ("miss"), or that the cell belongs to some ship ("hit").

But here's the problem! Alice like to cheat. May be that is why she responds to each Bob's move with a "miss". 

Help Bob catch Alice cheating — find Bob's first move, such that after it you can be sure that Alice cheated.


-----Input-----

The first line of the input contains three integers: n, k and a (1 ≤ n, k, a ≤ 2·10^5) — the size of the field, the number of the ships and the size of each ship. It is guaranteed that the n, k and a are such that you can put k ships of size a on the field, so that no two ships intersect or touch each other.

The second line contains integer m (1 ≤ m ≤ n) — the number of Bob's moves.

The third line contains m distinct integers x_1, x_2, ..., x_{m}, where x_{i} is the number of the cell where Bob made the i-th shot. The cells are numbered from left to right from 1 to n.


-----Output-----

Print a single integer — the number of such Bob's first move, after which you can be sure that Alice lied. Bob's moves are numbered from 1 to m in the order the were made. If the sought move doesn't exist, then print "-1".


-----Examples-----
Input
11 3 3
5
4 8 6 1 11

Output
3

Input
5 1 3
2
1 5

Output
-1

Input
5 1 3
1
3

Output
1

Difficulty: MEDIUM_HARD
Tags: Sorting

Data structures

Greedy algorithms
Skill types: Sorting

Data structures

Greedy algorithms

Starter code:

Solutions:
(n, k, a) = list(map(int, input().split()))
m = int(input()) + 1
x = list(map(int, input().split())) + [0]
(l, r) = (0, m)
while r - l > 1:
	d = (l + r) // 2
	y = sorted(x[:d])
	if sum(((q - p) // (a + 1) for (p, q) in zip([0] + y, y + [n + 1]))) >= k:
		l = d
	else:
		r = d
print(r % m - (r == m))


import sys

def minp():
	return sys.stdin.readline().strip()

def mint():
	return int(minp())

def mints():
	return map(int, minp().split())

def solve():
	(n, k, a) = mints()
	a += 1
	m = mint()
	x = list(mints())
	l = 0
	r = m + 1
	while r - l > 1:
		c = (l + r) // 2
		b = x[:c]
		b.sort()
		last = 0
		cnt = 0
		for i in b:
			if i != last:
				cnt += (i - last) // a
			last = i
		cnt += (n + 1 - last) // a
		if cnt < k:
			r = c
		else:
			l = c
	if r == m + 1:
		r = -1
	print(r)
solve()


import math
import heapq, bisect
import sys
from collections import deque
from fractions import Fraction
import os
import sys
from io import BytesIO, IOBase
BUFSIZE = 8192

class FastIO(IOBase):
	newlines = 0

	def __init__(self, file):
		self._fd = file.fileno()
		self.buffer = BytesIO()
		self.writable = 'x' in file.mode or 'r' not in file.mode
		self.write = self.buffer.write if self.writable else None

	def read(self):
		while True:
			b = os.read(self._fd, max(os.fstat(self._fd).st_size, BUFSIZE))
			if not b:
				break
			ptr = self.buffer.tell()
			(self.buffer.seek(0, 2), self.buffer.write(b), self.buffer.seek(ptr))
		self.newlines = 0
		return self.buffer.read()

	def readline(self):
		while self.newlines == 0:
			b = os.read(self._fd, max(os.fstat(self._fd).st_size, BUFSIZE))
			self.newlines = b.count(b'\n') + (not b)
			ptr = self.buffer.tell()
			(self.buffer.seek(0, 2), self.buffer.write(b), self.buffer.seek(ptr))
		self.newlines -= 1
		return self.buffer.readline()

	def flush(self):
		if self.writable:
			os.write(self._fd, self.buffer.getvalue())
			(self.buffer.truncate(0), self.buffer.seek(0))

class IOWrapper(IOBase):

	def __init__(self, file):
		self.buffer = FastIO(file)
		self.flush = self.buffer.flush
		self.writable = self.buffer.writable
		self.write = lambda s: self.buffer.write(s.encode('ascii'))
		self.read = lambda : self.buffer.read().decode('ascii')
		self.readline = lambda : self.buffer.readline().decode('ascii')
(sys.stdin, sys.stdout) = (IOWrapper(sys.stdin), IOWrapper(sys.stdout))
input = lambda : sys.stdin.readline().rstrip('\r\n')

class SegmentTree:

	def __init__(self, data, default=0, func=lambda a, b: a + b):
		self._default = default
		self._func = func
		self._len = len(data)
		self._size = _size = 1 << (self._len - 1).bit_length()
		self.data = [default] * (2 * _size)
		self.data[_size:_size + self._len] = data
		for i in reversed(range(_size)):
			self.data[i] = func(self.data[i + i], self.data[i + i + 1])

	def __delitem__(self, idx):
		self[idx] = self._default

	def __getitem__(self, idx):
		return self.data[idx + self._size]

	def __setitem__(self, idx, value):
		idx += self._size
		self.data[idx] = value
		idx >>= 1
		while idx:
			self.data[idx] = self._func(self.data[2 * idx], self.data[2 * idx + 1])
			idx >>= 1

	def __len__(self):
		return self._len

	def query(self, start, stop):
		if start == stop:
			return self.__getitem__(start)
		stop += 1
		start += self._size
		stop += self._size
		res = self._default
		while start < stop:
			if start & 1:
				res = self._func(res, self.data[start])
				start += 1
			if stop & 1:
				stop -= 1
				res = self._func(res, self.data[stop])
			start >>= 1
			stop >>= 1
		return res

	def __repr__(self):
		return 'SegmentTree({0})'.format(self.data)

class Factorial:

	def __init__(self, MOD):
		self.MOD = MOD
		self.factorials = [1, 1]
		self.invModulos = [0, 1]
		self.invFactorial_ = [1, 1]

	def calc(self, n):
		if n <= -1:
			print('Invalid argument to calculate n!')
			print('n must be non-negative value. But the argument was ' + str(n))
			exit()
		if n < len(self.factorials):
			return self.factorials[n]
		nextArr = [0] * (n + 1 - len(self.factorials))
		initialI = len(self.factorials)
		prev = self.factorials[-1]
		m = self.MOD
		for i in range(initialI, n + 1):
			prev = nextArr[i - initialI] = prev * i % m
		self.factorials += nextArr
		return self.factorials[n]

	def inv(self, n):
		if n <= -1:
			print('Invalid argument to calculate n^(-1)')
			print('n must be non-negative value. But the argument was ' + str(n))
			exit()
		p = self.MOD
		pi = n % p
		if pi < len(self.invModulos):
			return self.invModulos[pi]
		nextArr = [0] * (n + 1 - len(self.invModulos))
		initialI = len(self.invModulos)
		for i in range(initialI, min(p, n + 1)):
			next = -self.invModulos[p % i] * (p // i) % p
			self.invModulos.append(next)
		return self.invModulos[pi]

	def invFactorial(self, n):
		if n <= -1:
			print('Invalid argument to calculate (n^(-1))!')
			print('n must be non-negative value. But the argument was ' + str(n))
			exit()
		if n < len(self.invFactorial_):
			return self.invFactorial_[n]
		self.inv(n)
		nextArr = [0] * (n + 1 - len(self.invFactorial_))
		initialI = len(self.invFactorial_)
		prev = self.invFactorial_[-1]
		p = self.MOD
		for i in range(initialI, n + 1):
			prev = nextArr[i - initialI] = prev * self.invModulos[i % p] % p
		self.invFactorial_ += nextArr
		return self.invFactorial_[n]

class Combination:

	def __init__(self, MOD):
		self.MOD = MOD
		self.factorial = Factorial(MOD)

	def ncr(self, n, k):
		if k < 0 or n < k:
			return 0
		k = min(k, n - k)
		f = self.factorial
		return f.calc(n) * f.invFactorial(max(n - k, k)) * f.invFactorial(min(k, n - k)) % self.MOD

def powm(a, n, m):
	if a == 1 or n == 0:
		return 1
	if n % 2 == 0:
		s = powm(a, n // 2, m)
		return s * s % m
	else:
		return a * powm(a, n - 1, m) % m

def sort_list(list1, list2):
	zipped_pairs = zip(list2, list1)
	z = [x for (_, x) in sorted(zipped_pairs)]
	return z

def product(l):
	por = 1
	for i in range(len(l)):
		por *= l[i]
	return por

def binarySearchCount(arr, n, key):
	left = 0
	right = n - 1
	count = 0
	while left <= right:
		mid = int((right + left) / 2)
		if arr[mid] <= key:
			count = mid + 1
			left = mid + 1
		else:
			right = mid - 1
	return count

def countGreater(arr, n, k):
	l = 0
	r = n - 1
	leftGreater = n
	while l <= r:
		m = int(l + (r - l) / 2)
		if arr[m] > k:
			leftGreater = m
			r = m - 1
		else:
			l = m + 1
	return n - leftGreater
(n, m, k) = map(int, input().split())
r = int(input())
l = list(map(int, input().split()))
st = 1
end = r
cout = -1
while st <= end:
	mid = (st + end) // 2
	y = sorted(l[:mid])
	stw = 1
	cur = 0
	for i in range(mid):
		cur += (y[i] - 1 - stw + 2) // (k + 1)
		stw = y[i] + 1
	cur += (n - stw + 2) // (k + 1)
	if cur < m:
		cout = mid
		end = mid - 1
	else:
		st = mid + 1
print(cout)


import math
from bisect import bisect_right, bisect_left
from collections import Counter, defaultdict
from heapq import heappop, heappush
from itertools import accumulate
R = lambda : map(int, input().split())
(mm, k, a) = R()
junk = int(input())
arr = list(R())
(l, r) = (0, len(arr))
while l < r:
	m = (l + r) // 2
	tarr = [0] + sorted(arr[:m + 1]) + [mm + 1]
	cnt = 0
	for i in range(1, len(tarr)):
		cnt += (tarr[i] - tarr[i - 1]) // (a + 1)
	if cnt < k:
		r = m
	else:
		l = m + 1
print(l + 1 if l < len(arr) else -1)


(n, k, a) = map(int, input().split())
m = int(input())
x = [int(y) for y in input().split()]

def check(K):
	used = [0] * (n + 1)
	for i in range(K):
		used[x[i]] = 1
	for i in range(1, n + 1):
		used[i] += used[i - 1]
	have = 0
	i = a
	while i < n + 1:
		if used[i] - used[i - a] == 0:
			have += 1
			i += a
		i += 1
	return have >= k
if check(m):
	print(-1)
else:
	low = -1
	high = m
	while high - low > 1:
		if check((low + high + 1) // 2):
			low = (low + high + 1) // 2
		else:
			high = (low + high + 1) // 2
	print(high)