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.Scanner;

public class Main {
	public static long getModInverse(long a, long m){
		return pow(a, m - 2, m);
	}
	public static long pow(long base, long exp, long mod){
		long rem = 1;
		while(exp > 1){
			if(exp % 2 == 1){
				rem = (rem * base) % mod;
			}
			base = (base * base) % mod;
			exp /= 2;
		}
		return (base * rem) % mod;
	}
	public static void main(String[] args){
		Scanner sc = new Scanner(System.in);
		long A = sc.nextLong();
		long B = sc.nextLong();
		long n = sc.nextLong();
		long x = sc.nextLong();
		long mod = 1000000007;
		if(A == 1){
			System.out.println(((x + ((n%mod) * B))) % mod);
		}
		else{
			long s = (B * getModInverse(A - 1, mod)) % mod;
			long ans = ((pow(A, n, mod) * (x + s)) - s) % mod;
			System.out.println(ans);
		}
	}
}
