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 poll(a, k):
    if k == 1:
        return a
    if k % 2 == 1:
        return poll(a * a % 1000000007, k // 2) * a % 1000000007
    return poll(a * a % 1000000007, k // 2)

a, b, n, x = [int(i) for i in input().split()]
if a != 1:
    r = poll(a, n)
    rr = r - 1
    rr *= poll((a - 1), 1000000005)
    rr *= b
    r *= x
    print((r + rr) % 1000000007)
else:
    r = x + b * n
    print(r % 1000000007)