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.math.BigInteger;
import java.util.Arrays;
import java.util.Scanner;

public class q1 {
	static int n;
	static long h[],r[],w,l;
	static int mod=1000000007;
	public static void main(String cd[]){
		Scanner in=new Scanner(System.in);
		long a=in.nextLong();
		long b=in.nextLong();
		long n=in.nextLong();
		long x=in.nextLong();
		if(n==0){
			System.out.println(x);
			return;
		}
		if(n==1){
			System.out.println(((a*x)%mod+b)%mod);
			return;
		}
		if(a==1){
			n%=mod;
			System.out.println(((n*b)%mod+x)%mod);
			return;
		}
		
		
			long an=pow(a,n);
		long xx=(an*x)%mod;
		long yx=(((an-1)%mod)*b)%mod;
		long zx=giveModInverse(a-1);
		
		System.out.println((xx+(yx*zx)%mod)%mod);
	}
	public static long giveModInverse(long x){
		BigInteger big=new BigInteger(x+"");
		return big.modInverse(new BigInteger(mod+"")).longValue();
	}
	public static long pow(long a,long n){
		if(n==0){
			return 1;
		}
		if(n==1){
			return a%mod;
		}
		long temp=pow(a,n/2);
		if(n%2==0){
			
			return (temp*temp)%mod;
		}
		else{
			return (((temp*temp)%mod)*a)%mod;
		}
	}
	public static boolean check(long x){
		long ans=0;
		for(int i=0;i<n;i++){
			long y=(h[i]+r[i]*x);
			if(y>=l)
			ans+=y;
			
			if(ans>=w){
				return true;
			}
		}
		
		return ans>=w;
	}
	public static long gcd(long a,long b){
		if(b==0){
			return a;
		}
		return gcd(b,a%b);
	}
}
