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
s = raw_input()
a , b , n , x = s.split(' ')
a= int(a)
b = int(b)
n = int(n)
x = int(x)
ans = 0
mod = 10**9 + 7 
if( n == 0  ):
    ans = x
elif( n == 1):
    ans = a*x + b
else:
    tmp  = ( pow(a , n , mod ) * x ) % mod 
    tmp2 = 0
    if a != 1:
        tmp2 = (  pow(a,n,mod) - 1 + mod ) % mod
        tmp2 *= pow(a-1, mod - 2 , mod)
        tmp2 *= b
        tmp2 %= mod
    else:
        tmp2 = n*b
        tmp2 %= mod
    ans = tmp + tmp2
print ( (ans % mod) + mod ) % mod
