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
import string
import sys
import copy

def my_product(ma, mb, mod):
	res = [[0, 0], [0, 0]]
	for i in range(0, 2):
		for j in range(0, 2):
			for k in range(0, 2):
				res[i][j] += ( ( ma[i][k] % mod ) * ( mb[k][j] % mod ) ) % mod
	return res


def main_work():
	cts = sys.stdin.readline().split(' ')
	a = int(cts[0])
	b = int(cts[1])
	n = int(cts[2])
	x = int(cts[3])
	mod = 1000000007
	slist = []
	t = n
	while t > 0:
		slist.append(t%2)
		t = t / 2
	slist.reverse()
	m_ori = [ [a, 0], [b, 1] ]
	m_cur = copy.copy(m_ori)
	for i in range(1, len(slist)):
		if slist[i] == 0:
			m_cur = my_product(m_cur, m_cur, mod)
		else:
			m_cur = my_product(m_cur, m_cur, mod)
			m_cur = my_product(m_cur, m_ori, mod)
	print ( x * m_cur[0][0] + m_cur[1][0] ) % mod


if __name__ == "__main__":
	main_work()
 		 	  		 		  						 	  		 			