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.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.PrintWriter;

public class Main {

    public static long MOD = (long) 1e9 + 7;
    
    public static void main(String[] args) throws Exception {
        BufferedReader in = new BufferedReader(new InputStreamReader(System.in));
        InputReader inputReader = new InputReader(in);
        PrintWriter out = new PrintWriter(System.out);

        long a = inputReader.getNextLong();
        long b = inputReader.getNextLong();
        long n = inputReader.getNextLong();
        long x = inputReader.getNextLong();

        long aAtN = getAtPowMod(a, n, MOD);
        long secondPart = a == 1 ? n % MOD : (((aAtN + MOD - 1) * getAtPowMod(a-1, MOD - 2, MOD)) % MOD);
        long res = ((x * aAtN) % MOD) + ((b * secondPart) % MOD);

        out.println(res % MOD);

        in.close();
        out.close();
    }

    public static long getAtPowMod(long b, long e, long mod) {
        long res = 1;

        while(e > 0) {
            if((e & 1) != 0) {
                res = (res * b) % mod;
            }

            b = (b * b) % mod;
            e >>= 1;
        }

        return res;
    }

    public static class InputReader {

        static final String SEPARATOR = " ";

        String[] split;
        int head = 0;
        BufferedReader in;

        public InputReader(BufferedReader in) {
            this.in = in;
        }

        private void fillBuffer() throws IOException {
            if(split == null || head >= split.length) {
                head = 0;
                split = in.readLine().split(SEPARATOR);
            }
        }

        public String getNextToken() throws IOException {
            fillBuffer();
            return split[head++];

        }

        public int getNextInt() throws IOException {
            return Integer.parseInt(getNextToken());
        }

        public long getNextLong() throws IOException {
            return Long.parseLong(getNextToken());
        }
    }

    public static <T> String arrayToString(T[] arr) {
        StringBuilder stringBuilder = new StringBuilder();
        for(T x: arr) {
            stringBuilder.append(x + " ");
        }
        return stringBuilder.toString();
    }

}