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;
import java.math.BigInteger;
import java.util.Arrays;
public class ZZZ{
    
    public static long mod = 1000000007;
    public static long Big_mod(long A,long B)
    {
        long ret = 1;
        while(B > 0){
            if(B % 2 == 1) ret = (ret * A) % mod;
            A = (A * A) % mod;
            B = B >> 1;
        }
        return ret;
    }
    public static void main (String[] args){
        Scanner cin = new Scanner(System.in);
        long a,b,n,x;
        a = cin.nextLong();
        b = cin.nextLong();
        n = cin.nextLong();
        x = cin.nextLong();
        a = a % mod;
        b = b % mod;
        x = x % mod;
        long ans;
        if(a == 1){
            n = n % mod;
            ans = x + (b * n) % mod;
            ans = ans % mod;
        }
        else {
            long tp = Big_mod(a,n);
            long tt = (tp - 1) * Big_mod(a - 1,mod - 2);
            tt = (tt % mod) * b;
            tt = tt % mod;
            ans = (tp * x) % mod + tt;
            ans = ans % mod;
        }
        System.out.println(ans);
        
    }
}