Consider a linear function f(x) = Ax + B. Let's define g(0)(x) = x and g(n)(x) = f(g(n - 1)(x)) for n > 0. For the given integer values A, B, n and x find the value of g(n)(x) modulo 109 + 7.

Input

The only line contains four integers A, B, n and x (1 ≤ A, B, x ≤ 109, 1 ≤ n ≤ 1018) — the parameters from the problem statement.

Note that the given value n can be too large, so you should use 64-bit integer type to store it. In C++ you can use the long long integer type and in Java you can use long integer type.

Output

Print the only integer s — the value g(n)(x) modulo 109 + 7.

Examples

Input

3 4 1 1


Output

7


Input

3 4 2 1


Output

25


Input

3 4 3 1


Output

79
data1 = raw_input().split(' ')

def egcd(a, b):
	if a == 0:
		return (b, 0, 1)
	else:
		g, y, x = egcd(b % a, a)
		return (g, x - (b // a) * y, y)

def modinv(a, m):
	g, x, y = egcd(a, m)
	return x % m

data = []
for i in data1:
	data.append(int(i))
A = data[0]
B = data[1]
n = data[2]
x = data[3]
mod = 1000000007
sh1 = (pow(A,n,mod) * x) % mod
sh3 = B * ((pow(A, n, mod) - 1) * modinv(A - 1, mod)) % mod
if A != 1:
	print (sh1 + sh3) % mod
else:
	print (n * B + x) % mod

#A^n * x + B * ((A^(n-1) - 1)/(A - 1)) mod 10^9 + 7