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.BufferedInputStream;
import java.text.DecimalFormat;
import java.util.Scanner;

public class Main {
	static long mod =1000000007;
	//static DecimalFormat ff=new DecimalFormat("0");
public static void main(String []args){
	
	Scanner in=new Scanner(new BufferedInputStream(System.in));
	long a=in.nextLong()%mod;
	long b=in.nextLong()%mod;
	long n=in.nextLong();
	long x=in.nextLong();
//System.out.println(0.1%mod);
	long ans;
	if(a==1)ans=(x+n%mod*b%mod)%mod;
	else{  long kk=pow(a,n);
		ans=x*kk%mod+b*(kk-1)%mod*pow((a-1),mod-2)%mod;
	
	}
	System.out.println(ans%mod);
}
static long pow(long a,long b){
	long ans=1;
	while(b!=0){
	if((b&1)!=0)	ans=ans*a%mod;
		a=a*a%mod;
		b>>=1;
	}
	//System.out.println(ans);
	return ans;
}
}