problem

AOR Ika likes rooted trees with a fractal (self-similar) structure. Consider using the weighted rooted tree $ T $ consisting of $ N $ vertices to represent the rooted tree $ T'$ with the following fractal structure.

* $ T'$ is the addition of a tree rooted at $ x $ and having a tree structure similar to $ T $ (same cost) for each vertex $ x $ of $ T $.
* The root of $ T'$ is the same as that of $ T $.



The tree represented in this way is, for example, as shown in the figure below.

<image>

AOR Ika is trying to do a depth-first search for $ T'$, but finds that it takes a lot of time to trace all the vertices. Therefore, we decided to skip some node visits by performing a depth-first search with a policy of transitioning with a probability of $ p $ and not transitioning with a probability of $ 1-p $ at the time of transition during a depth-first search. Given $ T $ and the probability $ p $, find the expected value of the sum of the costs of all edges to follow when performing a depth-first search for $ T'$. The information of $ T $ is given by the number of vertices $ N $ and the information of the edges of $ N-1 $, and the vertex $ 1 $ is the root. Each vertex is labeled $ 1,2, \ dots, N $, and the $ i \ (1 \ le i \ le N-1) $ th edge costs the vertices $ x_i $ and $ y_i $ $ c_i $ It is tied with. The non-deterministic algorithm of the depth-first search that transitions to a child with a probability of $ p $, which is dealt with in this problem, is expressed as follows. The sum of the costs of the edges that the output $ \ mathrm {answer} $ follows.

1. Prepare an empty stack $ S $.
2. Set $ ​​\ mathrm {answer} = 0 $
3. Push the root vertex of $ T'$ to $ S $.
4. Extract the first element of $ S $ and make it $ x $.
5. For each child $ c $ of $ x $, do the following with probability $ p $ and do nothing with probability $ 1-p $.
* Add vertex $ c $ to $ S $. Then add the weight of the edge connecting $ x $ to $ c $ to $ \ mathrm {answer} $.
6. If S is not empty, transition to 3.
7. Output $ \ mathrm {answer} $.



output

Print the answer in one line. If the relative or absolute error is less than $ 10 ^ {-6} $, then AC. Also, output a line break at the end.

Example

Input

0.75
4
1 2 1
2 3 3
3 4 10


Output

24.8569335938

Source: aizu | Difficulty: UNKNOWN_DIFFICULTY


Solutions:
import math, string, itertools, fractions, heapq, collections, re, array, bisect, sys, random, time
sys.setrecursionlimit(10 ** 7)
inf = 10 ** 20
mod = 10 ** 9 + 7

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

def LF():
	return list(map(float, input().split()))

def LS():
	return input().split()

def I():
	return int(input())

def F():
	return float(input())

def S():
	return input()

def main():
	p = F()
	n = I()
	d = collections.defaultdict(list)
	for _ in range(n - 1):
		(x, y, c) = LI()
		d[x - 1].append((y - 1, c))
		d[y - 1].append((x - 1, c))
	f = [None] * n
	f[0] = (0, 0)
	q = [(0, 0)]
	while q:
		(x, b) = q[0]
		q = q[1:]
		for (y, c) in d[x]:
			if f[y]:
				continue
			q.append((y, b + 1))
			f[y] = (b + 1, c)
	s = 0
	for (b, c) in f:
		s += p ** b * c
	r = s
	for (b, c) in f:
		r += p ** b * s
	return r
print(main())