Problem: Consider a [billiard table](https://en.wikipedia.org/wiki/Billiard_table) of rectangular size n × m with four pockets. Let's introduce a coordinate system with the origin at the lower left corner (see the picture). 

<image>

There is one ball at the point (x, y) currently. Max comes to the table and strikes the ball. The ball starts moving along a line that is parallel to one of the axes or that makes a 45^{\circ} angle with them. We will assume that: 

  1. the angles between the directions of the ball before and after a collision with a side are equal, 
  2. the ball moves indefinitely long, it only stops when it falls into a pocket, 
  3. the ball can be considered as a point, it falls into a pocket if and only if its coordinates coincide with one of the pockets, 
  4. initially the ball is not in a pocket. 



Note that the ball can move along some side, in this case the ball will just fall into the pocket at the end of the side.

Your task is to determine whether the ball will fall into a pocket eventually, and if yes, which of the four pockets it will be.

Input

The only line contains 6 integers n, m, x, y, v_x, v_y (1 ≤ n, m ≤ 10^9, 0 ≤ x ≤ n; 0 ≤ y ≤ m; -1 ≤ v_x, v_y ≤ 1; (v_x, v_y) ≠ (0, 0)) — the width of the table, the length of the table, the x-coordinate of the initial position of the ball, the y-coordinate of the initial position of the ball, the x-component of its initial speed and the y-component of its initial speed, respectively. It is guaranteed that the ball is not initially in a pocket.

Output

Print the coordinates of the pocket the ball will fall into, or -1 if the ball will move indefinitely.

Examples

Input

4 3 2 2 -1 1


Output

0 0

Input

4 4 2 0 1 1


Output

-1

Input

10 10 10 1 -1 0


Output

-1

Note

The first sample: 

<image>

The second sample: 

<image>

In the third sample the ball will never change its y coordinate, so the ball will never fall into a pocket.

Solution (in PYTHON3):

Solution:
import math

# USAREMOS UNA IMPLEMENTACION EFICIENTE DE TEOREMA DEL RESTO CHINO
# BASADA EN https://www.geeksforgeeks.org/chinese-remainder-theorem-set-2-implementation/
def inv(a, m) : 
	m0 = m 
	x0 = 0
	x1 = 1
	if (m == 1) : 
		return 0
	while (a > 1) : 
		if m == 0:
			return -1
		q = a // m 
		t = m 
		m = a % m 
		a = t 
		t = x0 
		x0 = x1 - q * x0 
		x1 = t 
	if (x1 < 0) : 
		x1 = x1 + m0 
	return x1 


def CRT(num, rem):
	k = 2
	prod = 1
	for i in range(0, k):
		prod = prod * num[i]
	result = 0
	for i in range(0,k): 
		pp = prod // num[i]
		is_zero = inv(pp, num[i])
		if is_zero == -1:
			return -1
		result = result + rem[i] * inv(pp, num[i]) * pp 
	return result % prod 

# https://www.geeksforgeeks.org/python-program-for-basic-and-extended-euclidean-algorithms-2/
def gcdExtended(a, b):  
	if a == 0 :   
		return b,0,1 
	gcd,x1,y1 = gcdExtended(b%a, a)  
	x = y1 - (b//a) * x1  
	y = x1  
	return gcd,x,y 


def main():
	n,m,x,y,vx,vy = [int(x) for x in input().split(' ')]

	if vx == 0 and x != 0 and x != n:
		# Si la velocidad horizontal es 0, y no esta en un borde  es imposible que entre
		return -1
	elif vx == 0:
		# Si la velocidad horizontal es 0, pero esta en un borde
		# Entra SSI la vy es != 0
		if vy == 0:
			return -1
		elif vy == 1:
			return str(x) + " " + str(m)
		elif vy == -1:
			return str(x) + " " + str(0) 



	if vy == 0 and y != 0 and y != m:
		return -1
	elif vy == 0:
		if vx == 0:
			return -1
		elif vx == 1:
			return str(n) + " " + str(y)
		elif vx == -1:
			return str(0) + " " + str(y)


	if vx == 1:
		rest1 = n-x
	else:
		rest1 = x


	if vy == 1:
		rest2 = m-y
	else:
		rest2 = y


	nk = [n,m]
	rest = [rest1,rest2]
	g = math.gcd(n,m)
	if g == 1:
		t = CRT(nk,rest)
	elif rest1 % g != rest2 %g :
		return -1
	else:
		# SI NO SON COPRIMOS CALCULAR CON EXTENDED
		# https://forthright48.com/chinese-remainder-theorem-part-2-non-coprime-moduli/
		g, p, q = gcdExtended(n,m)
		mod = m // g
		lcm = n * mod
		t = ((rest1 % lcm)+n*((p % mod)*(((rest2-rest1)//g) % mod) % mod) % lcm)
		
	if t == -1:
		return -1
	else:
		kx = (t-rest1) / n
		ky = (t-rest2)/m
		izq = False
		up = False
		if vx == 1:
			if kx % 2 == 1:
				izq = True
			else:
				izq = False
		elif vx == -1:
			if kx % 2 == 1:
				izq = False
			else:
				izq = True
		
		if vy == 1:
			if ky % 2 == 1:
				up = False
			else:
				up = True
		elif vy == -1:
			if ky % 2 == 1:
				up = True
			else:
				up = False
				
		if up and izq:
			return str(0) + " " + str(m)
		elif not up and not izq:
			return str(n) + " 0"
		elif up and not izq:
			return str(n) + " " + str(m)
		else:
			return "0 0"

print(main())