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 java.util.*;
 
 public class Solution
{
static long pow(long a , long b)
{
       if(b == 0)
       return 1;
       
       long mod = 1000000007;
       long ans = pow(a,b/2);
       if(b%2 == 0)
       return ans*ans%mod;
       
       return ans*ans%mod*a%mod;
}

static long modInverse(long x)
{
       return pow(x , 1000000005);
}
       public static void main(String []args)
       {
              Scanner sc = new Scanner(System.in);
              long a = sc.nextLong();
              long b = sc.nextLong();
              long n = sc.nextLong();
              long x = sc.nextLong();
              long mod = 1000000007;
              long t1 = pow(a , n)*x%mod;
              long t2 = 0;
              if(a != 1)
              {
               t2 = pow(a,n)-1;
              t2 = (t2 + mod)%mod;
              t2 = t2*b%mod;
              t2 = t2*(modInverse(a-1))%mod;
              }
              
              else
              {
                     t2 = n%mod*b%mod;
              }
              t1 = (t1 + t2)%mod;
              System.out.println(t1);
       }
}
