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
def our_sum(a, n):
    if n == 1:
        return 1
    elif n % 2 == 0:
        q = our_sum(a, n // 2)
        return (q + q * pow(a, n // 2, mod)) % mod
    else:
        return (our_sum(a, n - 1) + pow(a, n - 1, mod)) % mod


a, b, n, x = map(int, input().split())
mod = 10 ** 9 + 7
#n %= mod
res = pow(a, n, mod) * x
res %= mod
if a != 1:
    res += our_sum(a, n) * b % mod
else:
    res += b * n % mod
res %= mod
print(res)