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
A,B,n,x = list(map(int, input().strip().split()))

def f(a, n, p):
    # calculate A ** n % p
    power = []
    while n > 0:
        power.append(n % 2)
        n = n // 2
    st = a
    c = 1
    for i in power:
        if i != 0:
            c *= st
            c = c % p
        st = st * st
        st = st % p
    return c
    

p = 1000000000 + 7
if A == 1:
    print ((x + ((n%p) * B) % p) % p)
else:
    expA = f(A, n, p) # calculate A ** n % p
    invA = f(A-1, p-2, p) #calculate 1/(A-1)
    res = ((expA * x)%p + ((B * (expA-1))%p*invA)%p)%p
    print(res)