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

mod = 1000000007
def power(x, n):

   if(n==0):
      return 1

   tmp = power(x,n/2)

   if(n%2):
     return (((tmp*tmp)%mod)*x)%mod

   return (tmp*tmp)%mod


def divide(a , b):
    return (a * power(b,1000000005))%mod



ans=0;
a,b,n,x = raw_input().split(" ")
a,b,n,x = int(a) , int(b) , int(n) , int(x)
if(a>1): ans = (ans + (b* divide(power(a,n) - 1 , a-1))%mod)%mod
else : ans = (ans + (n*b)%mod)%mod
ans = (ans + (power(a,n)*x)%mod)%mod
if(ans<0):
    ans += mod
print ans
