[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 java.text.*;
import java.lang.*;
import java.math.*;
 
public class Main{
    //static ArrayList[] a = new ArrayList[200001];
    static boolean [][] a = new boolean [3][100000 + 1];

   static long f(long x , long y , long xx , long yy) {
	   long x1 = Math.abs(xx - x); 
	   long y1 = Math.abs(yy - y);
	   if(x1 > 1e17 || y1 > 1e17) return Long.MAX_VALUE;
	   return x1+y1;
   }
    public void solve () throws IOException  {
       
    	InputReader in = new InputReader(System.in);
        PrintWriter pw = new PrintWriter(System.out);
        long x = in.nextLong();
        long y = in.nextLong();
        long a[] = new long [2];
        long b[] = new long [2];
        for(int i = 0 ; i < 2 ; i++)
        	a[i] = in.nextLong();
        for(int j = 0 ; j < 2; j++) {
        	b[j] = in.nextLong();
        }
        long s = in.nextLong();
        long e = in.nextLong();
        long t = in.nextLong();
        long xx = x;
        long yy = y;
        long p[][] = new long[10000][2];
        int idx = 0;
        long maxi = Long.MAX_VALUE;
        while(true) {
        	p[idx][0] = xx;
        	p[idx][1] = yy;
        	idx ++;
        	if((1e17 - b[0]) / a[0] >= xx && (1e17 - b[1]) / a[1] >= yy  ) {
        		xx = a[0] * xx + b[0] ;
        		yy = a[1] * yy + b[1];
        	}
        	else
        		break;
        }
        long ans  = 0;
        for(int i = 0 ; i < idx ; i++ ) {
        	long tot = 0L;
        	tot = f(p[i][0] , p[i][1] , s , e);
        	long got = 0L;
        	if(tot > t) continue;
        	int can = 1;
        	for(int j =  i + 1 ; j < idx ; j++) {
        		got += f(p[j][0] , p[j][1] , p[j - 1][0] , p[j - 1][1]);
        		if(t - got - tot >= 0)
            		ans = Math.max(ans, can + 1);
        		else
        			break;
        		if(maxi / 2L < got) continue;
        		can ++;
        		
        		int can1 = 0;
        		long rem = t - got * 2L - tot;
        		
        		for(int k = i - 1 ; k >= 0 && rem >= 0 ; k--) {
        			rem -= f(p[k][0] , p[k][1] , p[k + 1][0] , p[k + 1][1]);
        			if(rem >= 0L) can1 ++;
        			ans = Math.max(ans, can + can1);
        		}
        			
        	}
        	got = 0L;
        	can = 1;
    		ans = Math.max(ans, can );
        	for(int j =  i - 1 ; j >= 0 ; j--) {
        		got += f(p[j][0] , p[j][1] , p[j + 1][0] , p[j + 1][1]);
        		if(t - got - tot >= 0)
            		ans = Math.max(ans, can + 1 );
        		else
        			break;
        		if(maxi / 2L < got)  continue;
        		can ++;
        		int can1 = 0;
        		long rem = t - got * 2L - tot;
        		
        		for(int k = i + 1 ; k < idx && rem >= 0 ; k++) {
        			rem -= f(p[k][0] , p[k][1] , p[k - 1][0] , p[k - 1][1]);
        			if(rem >= 0L) can1 ++;
        			ans = Math.max(ans, can + can1);
        		}
        			
        	}
        	
        }
        pw.println(ans);
        pw.flush();
        pw.close();
    }
    public static void main(String[] args) throws Exception {
        
        
        new Thread(null,new Runnable() {
            public void run() {
                    try {
                        new Main().solve();
                    } catch (FileNotFoundException e) {
                        // TODO Auto-generated catch block
                        e.printStackTrace();
                    } catch (IOException e) {
						// TODO Auto-generated catch block
						e.printStackTrace();
					}
            } 
        },"1",1<<26).start();
        
        
    }
   
    static void debug(Object... o) {
        System.out.println(Arrays.deepToString(o));
        }
        
        static class InputReader 
        {
        private final InputStream stream;
        private final byte[] buf = new byte[8192];
        private int curChar, snumChars;
        private SpaceCharFilter filter;
 
        public InputReader(InputStream stream) 
        {
            this.stream = stream;
        }
        public int snext() 
        {
            if (snumChars == -1)
                throw new InputMismatchException();
            if (curChar >= snumChars) 
            {
                curChar = 0;
                try 
                {
                    snumChars = stream.read(buf);
                } 
                catch (IOException e) 
                {
                    throw new InputMismatchException();
                }
                if (snumChars <= 0)
                    return -1;
            }
            return buf[curChar++];
        }
 
        public int nextInt() 
        {
            int c = snext();
            while (isSpaceChar(c)) 
            {
                c = snext();
            }
            int sgn = 1;
            if (c == '-')
            {
                sgn = -1;
                c = snext();
            }
            int res = 0;
            do 
            {
                if (c < '0' || c > '9')
                    throw new InputMismatchException();
                res *= 10;
                res += c - '0';
                c = snext();
            } while (!isSpaceChar(c));
            return res * sgn;
        }
 
        public long nextLong()
        {
            int c = snext();
            while (isSpaceChar(c)) 
            {
                c = snext();
            }
            int sgn = 1;
            if (c == '-') 
            {
                sgn = -1;
                c = snext();
            }
            long res = 0;
            do 
            {
                if (c < '0' || c > '9')
                    throw new InputMismatchException();
                res *= 10;
                res += c - '0';
                c = snext();
            } while (!isSpaceChar(c));
            return res * sgn;
        }
 
        public int[] nextIntArray(int n) 
        {
            int a[] = new int[n];
            for (int i = 0; i < n; i++) 
            {
                a[i] = nextInt();
            }
            return a;
        }
 
        public String readString()
        {
            int c = snext();
            while (isSpaceChar(c)) 
            {
                c = snext();
            }
            StringBuilder res = new StringBuilder();
            do 
            {
                res.appendCodePoint(c);
                c = snext();
            } while (!isSpaceChar(c));
            return res.toString();
        }
 
        public String nextLine() 
        {
            int c = snext();
            while (isSpaceChar(c))
                c = snext();
            StringBuilder res = new StringBuilder();
            do 
            {
                res.appendCodePoint(c);
                c = snext();
            } while (!isEndOfLine(c));
            return res.toString();
        }
 
        public boolean isSpaceChar(int c) 
        {
            if (filter != null)
                return filter.isSpaceChar(c);
            return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
        }
 
        private boolean isEndOfLine(int c) 
        {
            return c == '\n' || c == '\r' || c == -1;
        }
 
        public interface SpaceCharFilter
        {
            public boolean isSpaceChar(int ch);
        }
    }
        public static long mod = 1000000007;
        public static int d;
        public static int p;
        public static int q;
        public void extended(int a,int b) {
            if(b==0) {
                d=a;
                p=1;
                q=0;
            }
            else
            {
                extended(b,a%b);
                int temp=p;
                p=q;
                q=temp-(a/b)*q;
            }
        }
       
        
        public static long binaryExponentiation(long x,long n)
        {
            long result=1;
            while(n>0)
            {
                if(n % 2 ==1)
                    result=result * x;
                x=x*x;
                n=n/2;
            }
            return result;
        }
        
        public static long[] shuffle(long[] a,Random gen)
        {
            int n = a.length;
            for(int i=0;i<n;i++)
            {
                int ind = gen.nextInt(n-i)+i;
                long temp = a[ind];
                a[ind] = a[i];
                a[i] = temp;
            }
            return a;
        }
        
        public static void swap(int a, int b){
            int temp = a;
            a = b;
            b = temp;
        }
        
        public static HashSet<Integer> primeFactorization(int n)
        {
            HashSet<Integer> a =new HashSet<Integer>();
            for(int i=2;i*i<=n;i++)
            {
                while(n%i==0)
                {
                    a.add(i);
                    n/=i;
                }
            }
            if(n!=1)
                a.add(n);
            return a;
        }
        
        public static void sieve(boolean[] isPrime,int n)
        {
            for(int i=1;i<n;i++)
                isPrime[i] = true;
            
            isPrime[0] = false;
            isPrime[1] = false;
            
            for(int i=2;i*i<n;i++)
            {
                if(isPrime[i] == true)
                {
                    for(int j=(2*i);j<n;j+=i)
                        isPrime[j] = false;
                }
            }
        }
        
        public static long GCD(long n,long m)
        {
            if(m==0)
                return n;
            else
                return GCD(m,n%m);
        }
        public static long LCM (long a,long b) {
            return ((a*b)/(GCD(a,b)));
        }
        
        static class pair implements Comparable<pair>
        {
            Integer y , x ;
            
            pair(int l,Integer y)
            {
                this.x=l;
                this.y=y;
            }

           
            public int compareTo(pair o) {
                int result = x.compareTo(o.x);
                if(result==0)
                    result = y.compareTo(o.y);
                
                return result;
            }  
            
            public String toString()
            {
                return x+" "+y;
            }
            
            public boolean equals(Object o)
            {
                if (o instanceof pair)
                {
                    pair p = (pair)o;
                    return p.x == x && p.y == y ;
                }
                return false;
            }
            public int hashCode()
            {
                return new Long(x).hashCode()*3 + new Long(y).hashCode();
                
            }
        }
        public static int binaryExponentiation(int x,int n)
        {
            int result=1;
            while(n>0)
            {
                if(n % 2 ==1)
                    result=result * x;
                x=x*x;
                n=n/2;
            }
            return result;
        }
        
       
        
        public static int modularExponentiation(int x,int n,int M)
        {
            int result=1;
            while(n>0)
            {
                if(n % 2 ==1)
                    result=(result * x)%M;
                x=(x%M*x)%M;
                n=n/2;
            }
            return result;
        }
        
        public static long modularExponentiation(long x,long n,long M)
        {
            long result=1;
            while(n>0)
            {
                if(n % 2 ==1)
                    result=(result%M * x%M)%M;
                x=(x%M * x%M)%M;
                n=n/2;
            }
            return result;
        }
        
        public static long modInverse(int A,int M)
        {
            return modularExponentiation(A,M-2,M);
        }
        
        public static long modInverse(long A,long M)
        {
            return modularExponentiation(A,M-2,M);
        }
        static class Segment{ 
    		int seg[]; 
    		int a[];
    		int lazy[];
    	    Segment (int n,int b[]){
    			seg=new int[4*n];
    			lazy=new int[4*n];
    			a=new int[b.length];
    			a=b.clone();
    		}
    	    public void build(int node,int start,int end) {
    	    	if(start==end) {
    	    		seg[node]=a[start];
    	    		return ;
    	    	}
    	    	int mid=(start+end)/2;
    	    	build(2*node+1,start,mid);
    	    	build(2*node+2,mid+1,end);
    	    	seg[node]=seg[2*node+1]+seg[2*node+2];
    	    }
    	    public void update(int node,int start,int end,int id,int val) {
    	    	if(start==end) {
    	    		seg[node]=a[start]=val;
    	    		return;
    	    	}
    	    	int mid=(start+end)/2;
    	    	if(id>=start && id<=mid) {
    	    		update(2*node+1,start,mid,id,val);
    	    	}
    	    	else
    	    		update(2*node+2,mid+1,end,id,val);
    	    	seg[node]=seg[2*node+1]+seg[2*node+2];
    	    }
    	    public int query(int node,int start,int end,int l,int r) {
    	    	if(l>end || r<start)
    	    		return 0;
    	    	if(start>=l && end<=r)
    	    		return seg[node];
    	    	
    	    	int  mid=(start+end)/2;
    	    	return (query(2*node+1,start,mid,l,r)+query(2*node+2,mid+1,end,l,r));
    	    }
    	    public void updateRange(int node,int start,int end,int l,int r,int val) {
    	    	if(lazy[node]!=0) {
	    			seg[node] += lazy[node];
    	    		if(start!=end) {
    	    			lazy[2*node+1]+=lazy[node];
    	    			lazy[2*node+2]+=lazy[node];
    	    		}
    	    		lazy[node]=0;
    	    	}
    	    	if(l>end || r<start)
    	    		return ;
    	    	if(start>=l && end<=r) {
    	    		seg[node] += val;
    	    		if(start!=end) {
    	    			lazy[2*node+1]+=val;
    	    			lazy[2*node+2]+=val;
    	    		}
    	    		lazy[node]=0;
    	    		return ;
    	    	}
    	    	int mid=(start+end)/2;
    	    	updateRange(2*node+1,start,mid,l,r,val);
    	    	updateRange(2*node+2,mid+1,end,l,r,val);
    	    	seg[node]=seg[2*node+1]+seg[2*node+2];
    	    }
    	    public int queryRange(int node,int start,int end,int l,int r) {
    	    	if(l>end || r<start)
    	    		return 0;
    	    	if(lazy[node]!=0) {
    	    		seg[node] += lazy[node];
    	    		if(start!=end) {
    	    			lazy[2*node+1]+=lazy[node];
    	    			lazy[2*node+2]+=lazy[node];
    	    		}
    	    		lazy[node]=0;
    	    	}
    	    	if(start>=l && end<=r)
    	    		return seg[node];
    	    	
    	    	int  mid=(start+end)/2;
    	    	return (queryRange(2*node+1,start,mid,l,r)+queryRange(2*node+2,mid+1,end,l,r));
    	    }
    	    
    	}
       
        
                    
         
}