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 modPow(base, pow, mod):
    ret = 1
    while pow > 0:
        if (pow % 2) == 0:
            base = (base * base) % mod
            pow >>= 1
        else:
            ret = (ret * base) % mod
            pow = pow - 1
    return ret;

a, b, n, x = map(int, raw_input().split())
modulo = 1000000007

first = modPow(a,n,modulo)
second = x % modulo
third = 0
if a != 1:
    third = modPow(a, n, modulo * (a - 1))
    third = modulo * (a - 1) - 1 if third == 0 else third - 1
    third = third / (a - 1) * b
else:
    third = (b * n) % modulo
ans = (((first * second) % modulo) + third % modulo) % modulo
print ans