Evlampiy has found one more cool application to process photos. However the application has certain limitations.

Each photo i has a contrast v_{i}. In order for the processing to be truly of high quality, the application must receive at least k photos with contrasts which differ as little as possible.

Evlampiy already knows the contrast v_{i} for each of his n photos. Now he wants to split the photos into groups, so that each group contains at least k photos. As a result, each photo must belong to exactly one group.

He considers a processing time of the j-th group to be the difference between the maximum and minimum values of v_{i} in the group. Because of multithreading the processing time of a division into groups is the maximum processing time among all groups.

Split n photos into groups in a such way that the processing time of the division is the minimum possible, i.e. that the the maximum processing time over all groups as least as possible.


-----Input-----

The first line contains two integers n and k (1 ≤ k ≤ n ≤ 3·10^5) — number of photos and minimum size of a group.

The second line contains n integers v_1, v_2, ..., v_{n} (1 ≤ v_{i} ≤ 10^9), where v_{i} is the contrast of the i-th photo.


-----Output-----

Print the minimal processing time of the division into groups.


-----Examples-----
Input
5 2
50 110 130 40 120

Output
20

Input
4 1
2 3 4 1

Output
0



-----Note-----

In the first example the photos should be split into 2 groups: [40, 50] and [110, 120, 130]. The processing time of the first group is 10, and the processing time of the second group is 20. Maximum among 10 and 20 is 20. It is impossible to split the photos into groups in a such way that the processing time of division is less than 20.

In the second example the photos should be split into four groups, each containing one photo. So the minimal possible processing time of a division is 0.

Difficulty: HARD
Tags: Dynamic programming

Sorting
Skill types: Dynamic programming

Sorting

Starter code:

Solutions:
def f(m):
	nonlocal dp, sdp
	l = 0
	for i in range(n):
		while l < n and v[l] < v[i] - m:
			l += 1
		if l - 1 > i - k:
			dp[i] = False
		else:
			dp[i] = sdp[i - k + 1] != sdp[l - 1]
		sdp[i + 1] = sdp[i] + (1 if dp[i] else 0)
	return dp[n - 1]
(n, k) = map(int, input().split())
dp = [False for i in range(n + 2)]
sdp = [0 for i in range(n + 2)]
dp[-1] = True
sdp[0] = 1
v = list(map(int, input().split()))
v.sort()
le = -1
r = v[-1] - v[0]
while r - le > 1:
	m = (r + le) // 2
	if f(m):
		r = m
	else:
		le = m
print(r)


from bisect import bisect_left, bisect_right

class Result:

	def __init__(self, index, value):
		self.index = index
		self.value = value

class BinarySearch:

	def __init__(self):
		pass

	@staticmethod
	def greater_than(num: int, func, size: int=1):
		if isinstance(func, list):
			index = bisect_right(func, num)
			if index == len(func):
				return Result(None, None)
			else:
				return Result(index, func[index])
		else:
			(alpha, omega) = (0, size - 1)
			if func(omega) <= num:
				return Result(None, None)
			while alpha < omega:
				if func(alpha) > num:
					return Result(alpha, func(alpha))
				if omega == alpha + 1:
					return Result(omega, func(omega))
				mid = (alpha + omega) // 2
				if func(mid) > num:
					omega = mid
				else:
					alpha = mid

	@staticmethod
	def less_than(num: int, func, size: int=1):
		if isinstance(func, list):
			index = bisect_left(func, num) - 1
			if index == -1:
				return Result(None, None)
			else:
				return Result(index, func[index])
		else:
			(alpha, omega) = (0, size - 1)
			if func(alpha) >= num:
				return Result(None, None)
			while alpha < omega:
				if func(omega) < num:
					return Result(omega, func(omega))
				if omega == alpha + 1:
					return Result(alpha, func(alpha))
				mid = (alpha + omega) // 2
				if func(mid) < num:
					alpha = mid
				else:
					omega = mid
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')
from math import gcd, ceil

def pre(s):
	n = len(s)
	pi = [0] * n
	for i in range(1, n):
		j = pi[i - 1]
		while j and s[i] != s[j]:
			j = pi[j - 1]
		if s[i] == s[j]:
			j += 1
		pi[i] = j
	return pi

def prod(a):
	ans = 1
	for each in a:
		ans = ans * each
	return ans

def lcm(a, b):
	return a * b // gcd(a, b)

def binary(x, length=16):
	y = bin(x)[2:]
	return y if len(y) >= length else '0' * (length - len(y)) + y
for _ in range(int(input()) if not True else 1):
	(n, k) = map(int, input().split())
	a = sorted(list(map(int, input().split())))
	if k == 1:
		print(0)
		continue
	bs = BinarySearch()
	a = [0] + a
	d = [False] * (n + 1)

	def check(x):
		dp = list(d)
		dp[0] = True
		if a[k] - a[1] <= x:
			dp[k] = True
		else:
			return 0
		cur = 1
		for i in range(k + 1, n + 1):
			while cur <= n and a[i] - a[cur] > x:
				cur += 1
			while cur <= n and (not dp[cur - 1]):
				cur += 1
			if cur <= i - k + 1:
				dp[i] = True
		return dp[-1]
	(alpha, omega) = (0, 10 ** 9)
	ans = omega
	while alpha < omega:
		mid = (alpha + omega) // 2
		x = mid
		if check(x):
			omega = mid
			ans = omega
		else:
			alpha = mid + 1
	print(ans)