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 Tests{
	public static void main (String []args) {
		Scanner in = new Scanner (System.in);
		int a = in.nextInt();
		int b = in.nextInt();
		long n = in.nextLong();
		int x = in.nextInt();
		int mod = 1000000000+7;
		long w =f(a,n,mod);
		long t = f(a-1,mod-2,mod);
		long ans = t*(w-1)%mod * b%mod ;
		ans = (ans + w*x)%mod;
		if(a==1) {long T =(f(n,1,mod)*b%mod+x%mod)%mod ; 
		System.out.println(T);}
		else System.out.println(ans);

		
		
		
		
	}
	static long   f(long  a , long b, int c){
		
		long x =1 ; 
		long y =a ; 
		while (b!=0){
			if(b%2==1){
				x=(x*y)%c;
			}
			y=(y*y)%c;
			b/=2;
		}
		return x%c;
		
	}
		
	}