[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.*;
import java.util.*;

import static java.lang.Math.*;
import static java.util.Arrays.*;

public class cf1292b {

    public static void main(String[] args) throws IOException {
        long x0 = rnl(), y0 = nl(), ax = nl(), ay = nl(), bx = nl(), by = nl(), xs = rnl(), ys = nl(), t = nl();
        long data[][] = new long[64][2];
        data[0][0] = x0;
        data[0][1] = y0;
        int ind = 0;
        while(data[ind][0] < LMAX / ax && data[ind][1] < LMAX / ay) {
            ++ind;
            data[ind][0] = data[ind - 1][0] * ax + bx;
            data[ind][1] = data[ind - 1][1] * ay + by;
        }
        int ans = 0;
        for(int i = 0; i < ind; ++i) {
            for(int j = i; j < ind; ++j) {
                long treq = dist(data[i][0], data[i][1], data[j][0], data[j][1]);
                long dist = min(dist(xs, ys, data[i][0], data[i][1]), dist(xs, ys, data[j][0], data[j][1]));
                treq += dist;
                if(t >= treq) {
                    ans = max(ans, j - i + 1);
                }
            }
        }
        prln(ans);
        close();
    }

    static long dist(long x0, long y0, long x1, long y1) {
        return abs(y1 - y0) + abs(x1 - x0);
    }

    static BufferedReader __in = new BufferedReader(new InputStreamReader(System.in));
    static PrintWriter __out = new PrintWriter(new OutputStreamWriter(System.out));
    static StringTokenizer input;
    static Random __rand = new Random();

    // references
    // IBIG = 1e9 + 7
    // IMAX ~= 2e10
    // LMAX ~= 9e18
    
    // constants
    static final int IBIG = 1000000007;
    static final int IMAX = 2147483647;
    static final int IMIN = -2147483648;
    static final long LMAX = 9223372036854775807L;
    static final long LMIN = -9223372036854775808L;
    // math util
    static int minof(int a, int b, int c) {return min(a, min(b, c));}
    static int minof(int... x) {if(x.length == 1) return x[0]; if(x.length == 2) return min(x[0], x[1]); if(x.length == 3) return min(x[0], min(x[1], x[2])); int min = x[0]; for(int i = 1; i < x.length; ++i) if(x[i] < min) min = x[i]; return min;}
    static long minof(long a, long b, long c) {return min(a, min(b, c));}
    static long minof(long... x) {if(x.length == 1) return x[0]; if(x.length == 2) return min(x[0], x[1]); if(x.length == 3) return min(x[0], min(x[1], x[2])); long min = x[0]; for(int i = 1; i < x.length; ++i) if(x[i] < min) min = x[i]; return min;}
    static int maxof(int a, int b, int c) {return max(a, max(b, c));}
    static int maxof(int... x) {if(x.length == 1) return x[0]; if(x.length == 2) return max(x[0], x[1]); if(x.length == 3) return max(x[0], max(x[1], x[2])); int max = x[0]; for(int i = 1; i < x.length; ++i) if(x[i] > max) max = x[i]; return max;}
    static long maxof(long a, long b, long c) {return max(a, max(b, c));}
    static long maxof(long... x) {if(x.length == 1) return x[0]; if(x.length == 2) return max(x[0], x[1]); if(x.length == 3) return max(x[0], max(x[1], x[2])); long max = x[0]; for(int i = 1; i < x.length; ++i) if(x[i] > max) max = x[i]; return max;}
    static int powi(int a, int b) {if(a == 0) return 0; int ans = 1; while(b > 0) {if((b & 1) > 0) ans *= a; a *= a; b >>= 1;} return ans;}
    static long powl(long a, int b) {if(a == 0) return 0; long ans = 1; while(b > 0) {if((b & 1) > 0) ans *= a; a *= a; b >>= 1;} return ans;}
    static int fli(double d) {return (int)d;}
    static int cei(double d) {return (int)ceil(d);}
    static long fll(double d) {return (long)d;}
    static long cel(double d) {return (long)ceil(d);}
    static int gcf(int a, int b) {return b == 0 ? a : gcf(b, a % b);}
    static long gcf(long a, long b) {return b == 0 ? a : gcf(b, a % b);}
    static int randInt(int min, int max) {return __rand.nextInt(max - min + 1) + min;}
    static long hash(long x) {x += 0x9e3779b97f4a7c15L; x = (x ^ (x >> 30)) * 0xbf58476d1ce4e5b9L; x = (x ^ (x >> 27)) * 0x94d049bb133111ebL; return x ^ (x >> 31);}
    // array util
    static void reverse(int[] a) {for(int i = 0, n = a.length, half = n / 2; i < half; ++i) {int swap = a[i]; a[i] = a[n - i - 1]; a[n - i - 1] = swap;}}
    static void reverse(long[] a) {for(int i = 0, n = a.length, half = n / 2; i < half; ++i) {long swap = a[i]; a[i] = a[n - i - 1]; a[n - i - 1] = swap;}}
    static void reverse(char[] a) {for(int i = 0, n = a.length, half = n / 2; i < half; ++i) {char swap = a[i]; a[i] = a[n - i - 1]; a[n - i - 1] = swap;}}
    static void shuffle(int[] a) {int n = a.length - 1; for(int i = 0; i < n; ++i) {int ind = randInt(i, n); int swap = a[i]; a[i] = a[ind]; a[ind] = swap;}}
    static void shuffle(long[] a) {int n = a.length - 1; for(int i = 0; i < n; ++i) {int ind = randInt(i, n); long swap = a[i]; a[i] = a[ind]; a[ind] = swap;}}
    static void rsort(int[] a) {shuffle(a); sort(a);}
    static void rsort(long[] a) {shuffle(a); sort(a);}
    static int[] copy(int[] a) {int[] ans = new int[a.length]; for(int i = 0; i < a.length; ++i) ans[i] = a[i]; return ans;}
    static long[] copy(long[] a) {long[] ans = new long[a.length]; for(int i = 0; i < a.length; ++i) ans[i] = a[i]; return ans;}
    static char[] copy(char[] a) {char[] ans = new char[a.length]; for(int i = 0; i < a.length; ++i) ans[i] = a[i]; return ans;}
    static int[] sorted(int[] a) {int[] ans = copy(a); sort(ans); return ans;}
    static long[] sorted(long[] a) {long[] ans = copy(a); sort(ans); return ans;}
    static int[] rsorted(int[] a) {int[] ans = copy(a); rsort(ans); return ans;}
    static long[] rsorted(long[] a) {long[] ans = copy(a); rsort(ans); return ans;}
    // graph util
    static List<List<Integer>> graph(int n) {List<List<Integer>> g = new ArrayList<>(); for(int i = 0; i < n; ++i) g.add(new ArrayList<>()); return g;}
    static List<List<Integer>> graph(List<List<Integer>> g, int m) throws IOException {for(int i = 0; i < m; ++i) connect(g, rni() - 1, ni() - 1); return g;}
    static List<List<Integer>> graph(int n, int m) throws IOException {return graph(graph(n), m);}
    static List<List<Integer>> dgraph(List<List<Integer>> g, int m) throws IOException {for(int i = 0; i < m; ++i) connecto(g, rni() - 1, ni() - 1); return g;}
    static List<List<Integer>> dgraph(List<List<Integer>> g, int n, int m) throws IOException {return dgraph(graph(n), m);}
    static List<Set<Integer>> sgraph(int n) {List<Set<Integer>> g = new ArrayList<>(); for(int i = 0; i < n; ++i) g.add(new HashSet<>()); return g;}
    static List<Set<Integer>> sgraph(List<Set<Integer>> g, int m) throws IOException {for(int i = 0; i < m; ++i) connect(g, rni() - 1, ni() - 1); return g;}
    static List<Set<Integer>> sgraph(int n, int m) throws IOException {return sgraph(sgraph(n), m);}
    static List<Set<Integer>> dsgraph(List<Set<Integer>> g, int m) throws IOException {for(int i = 0; i < m; ++i) connecto(g, rni() - 1, ni() - 1); return g;}
    static List<Set<Integer>> dsgraph(List<Set<Integer>> g, int n, int m) throws IOException {return dsgraph(sgraph(n), m);}
    static void connect(List<? extends Collection<Integer>> g, int u, int v) {g.get(u).add(v); g.get(v).add(u);}
    static void connecto(List<? extends Collection<Integer>> g, int u, int v) {g.get(u).add(v);}
    static void dconnect(List<? extends Collection<Integer>> g, int u, int v) {g.get(u).remove(v); g.get(v).remove(u);}
    static void dconnecto(List<? extends Collection<Integer>> g, int u, int v) {g.get(u).remove(v);}
    // input
    static void r() throws IOException {input = new StringTokenizer(__in.readLine());}
    static int ri() throws IOException {return Integer.parseInt(__in.readLine());}
    static long rl() throws IOException {return Long.parseLong(__in.readLine());}
    static int[] ria(int n) throws IOException {int[] a = new int[n]; input = new StringTokenizer(__in.readLine()); for(int i = 0; i < n; ++i) a[i] = Integer.parseInt(input.nextToken()); return a;}
    static int[] riam1(int n) throws IOException {int[] a = new int[n]; input = new StringTokenizer(__in.readLine()); for(int i = 0; i < n; ++i) a[i] = Integer.parseInt(input.nextToken()) - 1; return a;}
    static long[] rla(int n) throws IOException {long[] a = new long[n]; input = new StringTokenizer(__in.readLine()); for(int i = 0; i < n; ++i) a[i] = Long.parseLong(input.nextToken()); return a;}
    static char[] rcha() throws IOException {return __in.readLine().toCharArray();}
    static String rline() throws IOException {return __in.readLine();}
    static int rni() throws IOException {input = new StringTokenizer(__in.readLine()); return Integer.parseInt(input.nextToken());}
    static int ni() {return Integer.parseInt(input.nextToken());}
    static long rnl() throws IOException {input = new StringTokenizer(__in.readLine()); return Long.parseLong(input.nextToken());}
    static long nl() {return Long.parseLong(input.nextToken());}
    // output
    static void pr(int i) {__out.print(i);}
    static void prln(int i) {__out.println(i);}
    static void pr(long l) {__out.print(l);}
    static void prln(long l) {__out.println(l);}
    static void pr(double d) {__out.print(d);}
    static void prln(double d) {__out.println(d);}
    static void pr(char c) {__out.print(c);}
    static void prln(char c) {__out.println(c);}
    static void pr(char[] s) {__out.print(new String(s));}
    static void prln(char[] s) {__out.println(new String(s));}
    static void pr(String s) {__out.print(s);}
    static void prln(String s) {__out.println(s);}
    static void pr(Object o) {__out.print(o);}
    static void prln(Object o) {__out.println(o);}
    static void prln() {__out.println();}
    static void pryes() {__out.println("yes");}
    static void pry() {__out.println("Yes");}
    static void prY() {__out.println("YES");}
    static void prno() {__out.println("no");}
    static void prn() {__out.println("No");}
    static void prN() {__out.println("NO");}
    static void pryesno(boolean b) {__out.println(b ? "yes" : "no");};
    static void pryn(boolean b) {__out.println(b ? "Yes" : "No");}
    static void prYN(boolean b) {__out.println(b ? "YES" : "NO");}
    static void prln(int... a) {for(int i = 0, len = a.length - 1; i < len; __out.print(a[i]), __out.print(' '), ++i); __out.println(a[a.length - 1]);}
    static void prln(long... a) {for(int i = 0, len = a.length - 1; i < len; __out.print(a[i]), __out.print(' '), ++i); __out.println(a[a.length - 1]);}
    static <T> void prln(Collection<T> c) {int n = c.size() - 1; Iterator<T> iter = c.iterator(); for(int i = 0; i < n; __out.print(iter.next()), __out.print(' '), ++i); if(n >= 0) __out.println(iter.next()); else __out.println();}
    static void h() {__out.println("hlfd");}
    static void flush() {__out.flush();}
    static void close() {__out.close();}
}