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 mod_exp(x, y, p):
    res = 1
    x %= p
    while y:
        if y&1:
            res = (res * x) % p
        y >>= 1
        x = (x * x) % p
    return res


def power(a, b, m):
    x, y = 1, a
    while b:
        if b&1:
            x = (x * y) % m
        y = (y * y) % m
        b //= 2
    return x


def mod_inverse(a, m):
    return power(a, m - 2, m)


def solve(a, b, n, x):
    m = 10**9 + 7
    if a == 1:
        return (b * n * a + x) % m
    p = mod_exp(a, n, m)
    return (b * (p - 1) * mod_inverse(a - 1, m) + p * x) % m

a, b, n, x = map(int, input().split())

print(solve(a, b, n, x))
