[THE SxPLAY & KIVΛ - 漂流](https://soundcloud.com/kivawu/hyouryu)

[KIVΛ & Nikki Simmons - Perspectives](https://soundcloud.com/kivawu/perspectives)

With a new body, our idol Aroma White (or should we call her Kaori Minamiya?) begins to uncover her lost past through the OS space.

The space can be considered a 2D plane, with an infinite number of data nodes, indexed from 0, with their coordinates defined as follows:

  * The coordinates of the 0-th node is (x_0, y_0) 
  * For i > 0, the coordinates of i-th node is (a_x ⋅ x_{i-1} + b_x, a_y ⋅ y_{i-1} + b_y) 



Initially Aroma stands at the point (x_s, y_s). She can stay in OS space for at most t seconds, because after this time she has to warp back to the real world. She doesn't need to return to the entry point (x_s, y_s) to warp home.

While within the OS space, Aroma can do the following actions:

  * From the point (x, y), Aroma can move to one of the following points: (x-1, y), (x+1, y), (x, y-1) or (x, y+1). This action requires 1 second. 
  * If there is a data node at where Aroma is staying, she can collect it. We can assume this action costs 0 seconds. Of course, each data node can be collected at most once. 



Aroma wants to collect as many data as possible before warping back. Can you help her in calculating the maximum number of data nodes she could collect within t seconds?

Input

The first line contains integers x_0, y_0, a_x, a_y, b_x, b_y (1 ≤ x_0, y_0 ≤ 10^{16}, 2 ≤ a_x, a_y ≤ 100, 0 ≤ b_x, b_y ≤ 10^{16}), which define the coordinates of the data nodes.

The second line contains integers x_s, y_s, t (1 ≤ x_s, y_s, t ≤ 10^{16}) – the initial Aroma's coordinates and the amount of time available.

Output

Print a single integer — the maximum number of data nodes Aroma can collect within t seconds.

Examples

Input


1 1 2 3 1 0
2 4 20


Output


3

Input


1 1 2 3 1 0
15 27 26


Output


2

Input


1 1 2 3 1 0
2 2 1


Output


0

Note

In all three examples, the coordinates of the first 5 data nodes are (1, 1), (3, 3), (7, 9), (15, 27) and (31, 81) (remember that nodes are numbered from 0).

In the first example, the optimal route to collect 3 nodes is as follows: 

  * Go to the coordinates (3, 3) and collect the 1-st node. This takes |3 - 2| + |3 - 4| = 2 seconds. 
  * Go to the coordinates (1, 1) and collect the 0-th node. This takes |1 - 3| + |1 - 3| = 4 seconds. 
  * Go to the coordinates (7, 9) and collect the 2-nd node. This takes |7 - 1| + |9 - 1| = 14 seconds. 



In the second example, the optimal route to collect 2 nodes is as follows: 

  * Collect the 3-rd node. This requires no seconds. 
  * Go to the coordinates (7, 9) and collect the 2-th node. This takes |15 - 7| + |27 - 9| = 26 seconds. 



In the third example, Aroma can't collect any nodes. She should have taken proper rest instead of rushing into the OS space like that.
import java.io.OutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.OutputStream;
import java.io.PrintWriter;
import java.io.BufferedWriter;
import java.io.Writer;
import java.io.OutputStreamWriter;
import java.util.InputMismatchException;
import java.io.IOException;
import java.util.ArrayList;
import java.io.InputStream;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 *
 * @author Mufaddal Naya
 */
public class Main {
    public static void main(String[] args) {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        InputReader in = new InputReader(inputStream);
        OutputWriter out = new OutputWriter(outputStream);
        DAromasSearch solver = new DAromasSearch();
        solver.solve(1, in, out);
        out.close();
    }

    static class DAromasSearch {
        long xx;
        long yy;
        long t;

        public void solve(int testNumber, InputReader c, OutputWriter w) {
            long x = c.readLong(), y = c.readLong(), ax = c.readLong(), ay = c.readLong(), bx = c.readLong(), by =
                    c.readLong();
            xx = c.readLong();
            yy = c.readLong();
            t = c.readLong();
            long prevx = x, prevy = y;
            ArrayList<set> ss = new ArrayList<>();
            ss.add(new set(prevx, prevy));
            for (int i = 0; i < 100; i++) {
                if (prevx < (1e18 + 10 - bx) / ax && prevy < (1e18 + 10 - by) / ay) {
                    prevx = prevx * ax + bx;
                    prevy = prevy * ay + by;
                    ss.add(new set(prevx, prevy));
                }
            }

//        w.printLine(ss);
            long max1 = 0;
            for (int op = 0; op < ss.size(); op++) {
                long max = 0;
                for (int i = op; i < ss.size(); i++) {
                    long mm = 0;
                    for (int k = op; k <= i; k++) {
                        long tt = t;
                        long px = xx, py = yy;
                        int cnt = 0;
                        for (int j = op; j <= k; j++) {
                            set str = ss.get(j);
                            long dd = Math.abs(px - str.x) + Math.abs(py - str.y);
//                if(i == op) w.printLine(dd);
                            if (dd <= tt) {
                                cnt++;
                                tt -= dd;
                                px = str.x;
                                py = str.y;
                            } else {
                                break;
                            }
                        }
                        for (int j = op - 1; j >= 0; j--) {
                            set str = ss.get(j);
                            long dd = Math.abs(px - str.x) + Math.abs(py - str.y);
                            if (dd <= tt) {
                                cnt++;
                                tt -= dd;
                                px = str.x;
                                py = str.y;
                            }
                        }
                        mm = Math.max(mm, cnt);
                    }
                    max = Math.max(max, mm);
//            w.printLine(ss.get(i),max,cnt);

                    mm = 0;
                    for (int k = op; k >= 0; k--) {
                        long tt = t;
                        long px = xx;
                        long py = yy;
                        long cnt = 0;

                        for (int j = op; j >= k; j--) {
                            set str = ss.get(j);
                            long dd = Math.abs(px - str.x) + Math.abs(py - str.y);
                            if (dd <= tt) {
                                cnt++;
                                tt -= dd;
                                px = str.x;
                                py = str.y;
                            } else {
                                break;
                            }
                        }
                        for (int j = op + 1; j <= i; j++) {
                            set str = ss.get(j);
                            long dd = Math.abs(px - str.x) + Math.abs(py - str.y);
//                if(i == op) w.printLine(dd);
                            if (dd <= tt) {
                                cnt++;
                                tt -= dd;
                                px = str.x;
                                py = str.y;
                            } else {
                                break;
                            }
                        }
                        mm = Math.max(mm, cnt);
                    }
                    max = Math.max(max, mm);
                }
                max1 = Math.max(max, max1);
            }
            w.printLine(max1);

        }

    }

    static class set {
        long x;
        long y;

        public String toString() {
            return "set{" +
                    "x=" + x +
                    ", y=" + y +
                    '}';
        }

        public set(long x, long y) {
            this.x = x;
            this.y = y;
        }

    }

    static class OutputWriter {
        private final PrintWriter writer;

        public OutputWriter(OutputStream outputStream) {
            writer = new PrintWriter(new BufferedWriter(new OutputStreamWriter(outputStream)));
        }

        public OutputWriter(Writer writer) {
            this.writer = new PrintWriter(writer);
        }

        public void close() {
            writer.close();
        }

        public void printLine(long i) {
            writer.println(i);
        }

    }

    static class InputReader {
        private InputStream stream;
        private byte[] buf = new byte[1024];
        private int curChar;
        private int numChars;
        private InputReader.SpaceCharFilter filter;

        public InputReader(InputStream stream) {
            this.stream = stream;
        }

        public int read() {
            if (numChars == -1) {
                throw new InputMismatchException();
            }
            if (curChar >= numChars) {
                curChar = 0;
                try {
                    numChars = stream.read(buf);
                } catch (IOException e) {
                    throw new InputMismatchException();
                }
                if (numChars <= 0) {
                    return -1;
                }
            }
            return buf[curChar++];
        }

        public long readLong() {
            int c = read();
            while (isSpaceChar(c)) {
                c = read();
            }
            int sgn = 1;
            if (c == '-') {
                sgn = -1;
                c = read();
            }
            long res = 0;
            do {
                if (c < '0' || c > '9') {
                    throw new InputMismatchException();
                }
                res *= 10;
                res += c - '0';
                c = read();
            } while (!isSpaceChar(c));
            return res * sgn;
        }

        public boolean isSpaceChar(int c) {
            if (filter != null) {
                return filter.isSpaceChar(c);
            }
            return isWhitespace(c);
        }

        public static boolean isWhitespace(int c) {
            return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
        }

        public interface SpaceCharFilter {
            public boolean isSpaceChar(int ch);

        }

    }
}

