Problem: Twilight Sparkle was playing Ludo with her friends Rainbow Dash, Apple Jack and Flutter Shy. But she kept losing. Having returned to the castle, Twilight Sparkle became interested in the dice that were used in the game.

The dice has m faces: the first face of the dice contains a dot, the second one contains two dots, and so on, the m-th face contains m dots. Twilight Sparkle is sure that when the dice is tossed, each face appears with probability <image>. Also she knows that each toss is independent from others. Help her to calculate the expected maximum number of dots she could get after tossing the dice n times.

Input

A single line contains two integers m and n (1 ≤ m, n ≤ 105).

Output

Output a single real number corresponding to the expected maximum. The answer will be considered correct if its relative or absolute error doesn't exceed 10  - 4.

Examples

Input

6 1


Output

3.500000000000


Input

6 3


Output

4.958333333333


Input

2 2


Output

1.750000000000

Note

Consider the third test example. If you've made two tosses:

  1. You can get 1 in the first toss, and 2 in the second. Maximum equals to 2. 
  2. You can get 1 in the first toss, and 1 in the second. Maximum equals to 1. 
  3. You can get 2 in the first toss, and 1 in the second. Maximum equals to 2. 
  4. You can get 2 in the first toss, and 2 in the second. Maximum equals to 2. 



The probability of each outcome is 0.25, that is expectation equals to: 

<image>

You can read about expectation using the following link: http://en.wikipedia.org/wiki/Expected_value

Solution (in PYTHON3):

Solution:
from math import ceil, floor, sqrt, log
	
def mod_expo(n, p, m):
	"""find (n^p)%m"""
	result = 1
	while p != 0:
		if p%2 == 1:
			result = (result * n)%m
		p //= 2
		n = (n * n)%m
	return result
	
def dec_pow(a, n):
	res = 1
	while n > 0:
		if n%2 == 1:
			res *= a
		a *= a
		n //= 2
	return res 
	
def is_prime(n):
	for i in range(2, floor(sqrt(n)+1)):
		if n%i == 0:
			return False
	return True 
	
def find_k(n):
	for k in range(0, ceil(n/2)+1):
		if is_prime(k + n):
			return k
			
def get_expect(n, m):
	e = 0
	for i in range(1, m+1):
		e += i*(dec_pow(i/m, n) - dec_pow((i-1)/m, n))
	return e

def get_graph(n):
	k = find_k(n)
	m = n+k
	print(m)
	for i in range(1, n):
		print(i, i+1)
	print(n, 1)
	for i in range(1, k+1):
		print(i, i+floor(n/2))
	
def alice_wins(n, k):
	if n < k:
		if n%3 != 0:
			return True
		return False
	if alice_wins(k-1, k):
		if (n - (k+1))%3 != 0:
			return True
	else:
		if (n - (k+2))%3 != 0:
			return True
	return False
	
def prime_factorization(x):
	answer = []
	i = 2
	while i*i <= x:
		if x%i == 0:
			answer.append(i)
			while x%i == 0: 
				x //= i
		i += 1
	if x > 1: 
		answer.append(x)
	return answer
	
def pf(X, N):
	answer = 1
	m = pow(10, 9) + 7
	x_primes = prime_factorization(X)
	for prime in x_primes:
		power = 0
		factor = prime
		while factor <= N:
			power += N // factor
			factor *= prime
		answer *= pow(prime, power, m)
		answer %= m
	return answer
	
def find_ops(n):
	c = floor(n/3)
	n -= 3 * floor(n/3)
	b = floor(n/2)
	n -= 2 * floor(n/2)
	return n + b + c
		
def count_operations(a, b):
	if a < b:
		val = int(log(b/a, 2))
		if pow(2, val) * a == b:
			return find_ops(val)
	else:
		val = int(log(a/b, 2))
		if pow(2, val) * b == a:
			return find_ops(val)
	return -1
	
def find_m(n, x):
	return 1 + max(0, (n - pow(2,x-1) + 1)//pow(2, x))
		
def find_total_diff(n):
	n -= 1
	total = n//2  + 1
	x = 1
	while pow(2, x) - 1 <= n:
		total += (x+1)*find_m(n, x+1)
		x += 1
	return total

t = 1 
#t = int(input())
while t:
	t = t - 1
	#n = int(input())
	#s = input()
	#x1, y1, x2, y2 = map(int, input().split())
	#
	m, n = map(int, input().split())
	#l = list(map(int, input().strip().split()))[:n]
	#str1 = input()
	#find_massive_x(n)
	#result = find_min(n, l)
	print(get_expect(n, m))
	#if alice_wins(n, k):
	#	print("Alice")
	#else:
	#	print("Bob")
	# find_arr(u, v)