It is the easy version of the problem. The only difference is that in this version $k = 3$.

You are given a positive integer $n$. Find $k$ positive integers $a_1, a_2, \ldots, a_k$, such that:

$a_1 + a_2 + \ldots + a_k = n$

$LCM(a_1, a_2, \ldots, a_k) \le \frac{n}{2}$

Here $LCM$ is the least common multiple of numbers $a_1, a_2, \ldots, a_k$.

We can show that for given constraints the answer always exists.


-----Input-----

The first line contains a single integer $t$ $(1 \le t \le 10^4)$  — the number of test cases.

The only line of each test case contains two integers $n$, $k$ ($3 \le n \le 10^9$, $k = 3$).


-----Output-----

For each test case print $k$ positive integers $a_1, a_2, \ldots, a_k$, for which all conditions are satisfied.


-----Examples-----

Input
3
3 3
8 3
14 3
Output
1 1 1
4 2 2
2 6 6


-----Note-----

None

Difficulty: EASY

Solutions:
import sys

def get_ints():
	return list(map(int, sys.stdin.readline().strip().split()))
testcases = int(input())
for testcase in range(testcases):
	temparr = get_ints()
	a = temparr[0]
	b = temparr[1]
	ans = []
	if a == 4:
		print('2 1 1')
	elif a & 1:
		ans.append(str(1))
		a -= 1
		diff = a >> 1
		ans.append(str(diff))
		ans.append(str(diff))
		print(' '.join(ans))
	else:
		diff = a >> 1
		ans = []
		if diff & 1:
			ans.append(str(2))
			ans.append(str(diff - 1))
			ans.append(str(diff - 1))
			print(' '.join(ans))
		else:
			halfhalf = diff >> 1
			ans.append(str(diff))
			ans.append(str(halfhalf))
			ans.append(str(halfhalf))
			print(' '.join(ans))


import sys
input = sys.stdin.readline
ins = lambda : input().rstrip()
ini = lambda : int(input().rstrip())
inm = lambda : map(int, input().rstrip().split())
inl = lambda : list(map(int, input().split()))
out = lambda x, s='\n': print(s.join(map(str, x)))
t = ini()
for _ in range(t):
	(n, k) = inm()
	if n % 2:
		print(1, n // 2, n // 2)
	else:
		x = n // 2
		if x % 2:
			print(2, x - 1, x - 1)
		else:
			print(x, x // 2, x // 2)


from collections import defaultdict
from sys import stdin
input = lambda : stdin.readline().strip()
for _ in range(int(input())):
	(n, k) = [int(i) for i in input().split()]
	if n % 2 == 0:
		if n % 3 == 0:
			print(n // 3, n // 3, n // 3)
		elif n % 4 == 0:
			print(n // 2, n // 2 // 2, n // 2 // 2)
		else:
			print(2, (n - 2) // 2, (n - 2) // 2)
	else:
		print(1, n // 2, n // 2)


import sys
import math as mt
import collections as cc
input = sys.stdin.readline
I = lambda : list(map(int, input().split()))
for tc in range(int(input())):
	(n, k) = I()
	if n % 2:
		print(n // 2, n // 2, 1)
	elif n % 4 == 0:
		print(n // 2, n // 4, n // 4)
	else:
		print(2, n // 2 - 1, n // 2 - 1)


import sys
from math import log

def solve(n, k):
	if 2 ** int(log(n, 2)) == n:
		return ' '.join([str(n // 2), str(n // 4), str(n // 4)])
	else:
		if n % 2 == 1:
			c = 1
			a = (n - 1) // 2
			b = a
			return ' '.join([str(a), str(b), str(c)])
		counter = 2
		while counter < n:
			if n % counter == 0:
				if n // counter % 2 == 1:
					a = counter
					b = counter * (n // counter - 1) // 2
					c = b
					return ' '.join([str(a), str(b), str(c)])
			counter += 2
	return None
t = int(sys.stdin.readline().strip())
ans = 0
for _ in range(t):
	line = sys.stdin.readline().strip()
	(n, k) = list(map(int, line.split()))
	print(solve(n, k))


import math
answers = []

def solve(n, k):
	if n % 3 == 0:
		res = n // 3
		answers.append([res, res, res])
		return
	if n % 4 == 0:
		a1 = n // 4
		a2 = n // 2
		answers.append([a2, a1, a1])
		return
	if n % 2 == 1:
		res = n // 2
		answers.append([1, res, res])
		return
	if n % 2 == 0 and n % 4 == 2:
		rem = (n - 2) // 2
		answers.append([2, rem, rem])
		return
T = int(input())
while T:
	(n, k) = [int(x) for x in input().split()]
	solve(n, k)
	T -= 1
for ans in answers:
	print(*ans)


import sys

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

def iinput():
	return int(input())

def rinput():
	return map(int, sys.stdin.readline().strip().split())

def get_list():
	return list(map(int, sys.stdin.readline().strip().split()))
t = iinput()
for _ in range(t):
	(n, k) = rinput()
	if n % 2 == 0:
		a = (n - 2) / 2
		if a % 2 == 0:
			a = 2
			b = (n - 2) / 2
		else:
			a = n / 2
			b = n / 4
	else:
		a = 1
		b = (n - 1) / 2
	print(int(a), int(b), int(b))


for _ in range(int(input())):
	(a, b) = map(int, input().split())
	if a & 1:
		print(1, a // 2, a // 2)
	elif a % 4 == 0:
		print(a // 2, a // 4, a // 4)
	else:
		print(2, a // 2 - 1, a // 2 - 1)


t = int(input().strip())
for i in range(t):
	(n, _) = list(map(int, input().strip().split()))
	if n % 2 == 1:
		print('{} {} {}'.format(1, (n - 1) // 2, (n - 1) // 2))
	elif n % 4 == 0:
		print('{} {} {}'.format(n // 2, n // 4, n // 4))
	else:
		print('{} {} {}'.format(2, n // 2 - 1, n // 2 - 1))


import math as m
i = input()
inp = []
for a in range(0, int(i)):
	inp += [input()]
for i in inp:
	n = int(i.split()[0])
	x = 1
	a = n
	while a % 2 == 0:
		x *= 2
		a = a // 2
	if a == 1:
		print(x // 2, x // 4, x // 4)
	else:
		print(x, x * (a - 1) // 2, x * (a - 1) // 2)


k = int(input())
sp = []
for i in range(k):
	(n, m) = list(map(int, input().split()))
	if n % 2 == 0:
		if n // 2 % 2 == 0:
			sp.append([n // 2, n // 2 // 2, n // 2 // 2])
		else:
			sp.append([2, (n - 2) // 2, (n - 2) // 2])
	else:
		sp.append([1, (n - 1) // 2, (n - 1) // 2])
for i in sp:
	print(*i, end='\n')


cases = int(input())
for _ in range(0, cases):
	input1 = input().split()
	(n, k) = (int(input1[0]), int(input1[1]))
	if n % 2 == 1:
		print(n // 2, n // 2, 1)
	else:
		temp = int(n / 2)
		if temp % 2 == 0:
			print(temp, int(temp / 2), int(temp / 2))
		else:
			print(2, int(temp) - 1, int(temp) - 1)


def ss(n):
	for i in range(1, 1 + n ** 0.5):
		if n % i == 0:
			return n // i
	return 1
for _ in range(int(input())):
	(n, k) = map(int, input().split())
	if n % 2 == 0:
		if n % 4 == 0:
			print(*[n // 2, n // 4, n // 4])
		else:
			print(*[2, n // 2 - 1, n // 2 - 1])
	else:
		print(*[1, n // 2, n // 2])


t = int(input())
while t:
	(n, k) = map(int, input().split())
	if n & 1 == 0:
		if n // 2 & 1 == 0:
			print(n // 2, n // 4, n // 4)
		else:
			print(2, n // 2 - 1, n // 2 - 1)
	else:
		print(n // 2, n // 2, 1)
	t -= 1


for _ in range(int(input())):
	(a, b) = map(int, input().split(' '))
	if a % 2 == 1:
		print(a // 2, a // 2, 1)
	else:
		c = a // 2
		if c % 2 == 0:
			print(c, c // 2, c // 2)
		else:
			a = a - 2
			print(2, a // 2, a // 2)


import sys, time
from math import ceil, floor
fun = lambda : map(int, input().split())
for _ in range(int(input())):
	(n, k) = fun()
	ans = [[n // 2, n // 4, n // 4], [1, (n - 1) // 2, (n - 1) // 2], [2, (n - 2) // 2, (n - 2) // 2], [1, (n - 1) // 2, (n - 1) // 2]]
	print(*ans[n % 4])


for _ in range(int(input())):
	(n, k) = map(int, input().split())
	if n % 3 == 0:
		print(n // 3, n // 3, n // 3)
	elif n % 2 == 1:
		print(1, (n - 1) // 2, (n - 1) // 2)
	elif n % 8 == 0:
		print(n // 2, n // 4, n // 4)
	elif n == 4:
		print(1, 1, 2)
	elif n // 2 % 2 == 1:
		print(2, (n - 2) // 2, (n - 2) // 2)
	else:
		print(4, (n - 4) // 2, (n - 4) // 2)


for x in range(int(input())):
	(n, k) = map(int, input().split())
	if n % 2 == 0:
		n = n // 2
		if n % 2 == 1:
			print(2, n - 1, n - 1)
		else:
			print(n, n // 2, n // 2)
	elif n % 2 == 1:
		print(n // 2, n // 2, 1)


from math import floor
t = int(input())
for i in range(t):
	(n, k) = map(int, input().split())
	k = 3
	x = []
	if n % 2 == 0:
		if n / 2 % 2 == 0:
			x.append(int(n / 2))
			x.append(int(n / 2 / 2))
			x.append(int(n / 2 / 2))
		else:
			x.append(2)
			x.append(int(n / 2 - 1))
			x.append(int(n / 2 - 1))
	else:
		x.append(1)
		x.append(floor(n / 2))
		x.append(floor(n / 2))
	print(' '.join(map(str, x)))


def processing():
	(n, k) = [int(x) for x in input().split()]
	if n % 2 == 1:
		print(1, n // 2, n // 2, sep=' ', end='\n')
	elif n % 4 == 0:
		print(n // 2, n // 2 // 2, n // 2 // 2, sep=' ', end='\n')
	else:
		print(2, (n - 2) // 2, (n - 2) // 2, sep=' ', end='\n')
t = int(input())
for i in range(t):
	processing()


n = int(input())
for i in range(n):
	(num, k) = map(int, input().split())
	if num % 2 == 0:
		if num % 4 == 0:
			print(num // 2, num // 4, num // 4)
		else:
			print(2, (num - 2) // 2, (num - 2) // 2)
	else:
		print(1, (num - 1) // 2, (num - 1) // 2)