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.*;
import java.util.*;
public final class iterated_linear_func
{
    static BufferedReader br=new BufferedReader(new InputStreamReader(System.in));
	static FastScanner sc=new FastScanner(br);
    static PrintWriter out=new PrintWriter(System.out);
	static long[][] base,val;
	static long mod=(long)(1e9+7);
	
	static long[][] matrix_mul(long[][] a,long[][] b,int r1,int c1,int r2,int c2)
	{
		long[][] c=new long[r1][c2];
		for(int i=0;i<r1;i++)
		{
			for(int j=0;j<c2;j++)
			{
				for(int k=0;k<c1;k++)
				{
					c[i][j]=(c[i][j]+(a[i][k]*b[k][j]))%mod;
				}
			}
		}
		return c;
	}
	
	static long[][] matrix_pow(long[][] base,long b)
	{
		long[][] res=new long[][]{{1,0},{0,1}};
		while(b>0)
		{
			if(b%2==1)
			{
				res=matrix_mul(res,base,2,2,2,2);
			}
			base=matrix_mul(base,base,2,2,2,2);
			b=b/2;
		}
		return res;
	}
	
	public static void main(String args[]) throws Exception
	{
		long a=sc.nextLong(),b=sc.nextLong(),n=sc.nextLong(),x=sc.nextLong();base=new long[][]{{a,0},{b,1}};val=new long[][]{{x,1}};
		base=matrix_pow(base,n);long[][] res=matrix_mul(val,base,1,2,2,2);out.println(res[0][0]);out.close();
	}
}
class FastScanner
{
    BufferedReader in;
    StringTokenizer st;

    public FastScanner(BufferedReader in) {
        this.in = in;
    }
	
    public String nextToken() throws Exception {
        while (st == null || !st.hasMoreTokens()) {
            st = new StringTokenizer(in.readLine());
        }
        return st.nextToken();
    }
	
	public String next() throws Exception {
		return nextToken().toString();
	}
	
    public int nextInt() throws Exception {
        return Integer.parseInt(nextToken());
    }

    public long nextLong() throws Exception {
        return Long.parseLong(nextToken());
    }

    public double nextDouble() throws Exception {
        return Double.parseDouble(nextToken());
    }
}