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
from sys import stdin


# 2**0 + 2**1 + 2**2 +..
def sum_pow(r, n, m=None):
    if r > 1:
        return div(add(1, -pow(r, n + 1, mod)), (1 - r))
    else:
        return n + 1


rints = lambda: [int(x) for x in stdin.readline().split()]
add = lambda a, b: (a % mod + b % mod) % mod
mult = lambda a, b: ((a % mod) * (b % mod)) % mod
div = lambda a, b: mult(a, inv(b))
inv = lambda a: pow(a, mod - 2, mod)
mod = 10 ** 9 + 7

a, b, n, x = rints()
g = [x]
for i in range(2):
    g.append(a * g[-1] + b)

fac = g[1] - g[0]
po = (g[-1] - g[1]) // fac

print(add(x, mult(fac, sum_pow(po, n - 1))))
