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
import math

def modInverse(b,m):
    g = math.gcd(b, m)
    if (g != 1):
        return -1
    return pow(b, m - 2, m)
 
def modDivide(a,b,m):
    a = a % m
    inv = modInverse(b,m)
    if(inv == -1):
        return -1
    return (inv*a) % m

a,b,n,x = [int(k) for k in input().split()]

m = 1000000007

if a==1:
    print( (x%m + ((b%m)*(n%m))%m)%m )
else:
    a_n = pow(a, n, m)

    ter = ((a%m * x%m)%m + b%m - x%m + m)%m

    num = ( (a_n * ter)%m - b%m + m)%m
    den = a-1

    print(modDivide(num, den, m))