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.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
public class EducationalCodeforces13D
{
	public static long f(long a,long n,long mod)
	{
		long res=1;
		for(long p=a;n>0;n>>=1,p=(p*p)%mod)
			if((n&1)!=0)
				res=(long)(res*p %mod);
		return res;
	}
	public static void main(String[] args)throws IOException
	{
		BufferedReader br=new BufferedReader(new InputStreamReader(System.in));
		String input[]=br.readLine().split(" ");
		long a=Long.parseLong(input[0]);
		long b=Long.parseLong(input[1]);
		long n=Long.parseLong(input[2]);
		long x=Long.parseLong(input[3]);
		long ans=0;
		long mod = (int)1e9 + 7;
		if(a==1)
		{
			ans=(x+((b%mod)*(n%mod))%mod)%mod;
		}
		else
		{
			
			long p=f(a,n,mod);
			ans= (p*x)%mod + (((b*(p-1))%mod)*f(a-1,mod-2,mod))%mod;
			ans%=mod;
		}
		System.out.println(ans);
	}
}