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.*;
import java.io.*;
public class A
{
      public static void main(String ar[]) throws Exception
      {
            BufferedReader br=new BufferedReader(new InputStreamReader(System.in));
            String s1[]=br.readLine().split(" ");
            long a=Long.parseLong(s1[0]);
            long b=Long.parseLong(s1[1]);
            long n=Long.parseLong(s1[2]);
            long x=Long.parseLong(s1[3]);
            
            long mod=1000000007;
            
            long g1=(pow(a,n)*x)%mod;
            long g2=(b*((pow(a,n)-1+mod)%mod))%mod;
            
            g2=g2*pow(a-1,mod-2);
            
            if(a==1)
             System.out.println((((n%mod)*(b*a)%mod)%mod+x)%mod);
            else
             System.out.println((g1+g2)%mod);
      }
      
      public static long pow(long x,long n)
      {
            long res=1;
            long mod=1000000007;
            while(n>0)
            {
                  if(n%2==1)
                  {
                        res=(res*x)%mod;
                  }
                  
                  x=(x*x)%mod;
                  n=n/2;
            }
            return res;
      }
}