Problem:
Score: 600 points

Problem Statement

Takahashi and Aoki are training for long-distance races in an infinitely long straight course running from west to east.

They start simultaneously at the same point and moves as follows towards the east:

Takahashi runs A_1 meters per minute for the first T_1 minutes, then runs at A_2 meters per minute for the subsequent T_2 minutes, and alternates between these two modes forever.

Aoki runs B_1 meters per minute for the first T_1 minutes, then runs at B_2 meters per minute for the subsequent T_2 minutes, and alternates between these two modes forever.

How many times will Takahashi and Aoki meet each other, that is, come to the same point? We do not count the start of the run. If they meet infinitely many times, report that fact.

Constraints

1 \leq T_i \leq 100000

1 \leq A_i \leq 10^{10}

1 \leq B_i \leq 10^{10}

A_1 \neq B_1

A_2 \neq B_2

All values in input are integers.

Input

Input is given from Standard Input in the following format:

T_1 T_2
A_1 A_2
B_1 B_2

Output

Print the number of times Takahashi and Aoki will meet each other.

If they meet infinitely many times, print infinity instead.

Sample Input 1

1 2
10 10
12 4

Sample Output 1

1

They will meet just once, \frac{4}{3} minutes after they start, at \frac{40}{3} meters from where they start.

Sample Input 2

100 1
101 101
102 1

Sample Output 2

infinity

They will meet 101, 202, 303, 404, 505, 606, ... minutes after they start, that is, they will meet infinitely many times.

Sample Input 3

12000 15700
3390000000 3810000000
5550000000 2130000000

Sample Output 3

113

The values in input may not fit into a 32-bit integer type.

Solution in Java8 (OpenJDK 1.8.0) (judge verdict: Wrong Answer)

import java.io.*;
import java.util.Arrays;
import java.util.StringJoiner;
import java.util.StringTokenizer;
import java.util.function.IntPredicate;
import java.util.function.LongPredicate;

public class Main {

    static int T1, T2;
    static long A1, A2, B1, B2;

    public static void main(String[] args) {
        FastScanner sc = new FastScanner(System.in);
        T1 = sc.nextInt();
        T2 = sc.nextInt();
        A1 = sc.nextLong();
        A2 = sc.nextLong();
        B1 = sc.nextLong();
        B2 = sc.nextLong();

        System.out.println(solve());
    }

    static String solve() {
        // 距離にしてしまう
        A1 = A1 * T1;
        A2 = A2 * T2;
        B1 = B1 * T1;
        B2 = B2 * T2;

        if( A1 + A2 == B1 + B2 ) return "infinity";

        // A側を先に行くほうにする
        if( A1 + A2 < B1 + B2 ) {
            long t1 = A1;
            A1 = B1;
            B1 = t1;
            long t2 = A2;
            A2 = B2;
            B2 = t2;
        }

        // 先行する上に前半早いので追いつかない
        if( A1 > B1 ) return "0";

        // Aが後半早い+ 距離も長いのでそのうちBは追いつけなくなる
        // 何ターン目まで追いかけっこが成立するかでわかる
        // 算数するかにぶたんするか
        // ...算数が苦手なのでにぶたんする
        int turn = maximize(0, 100001, t -> {
            // Bが前半のうちにAを上回ることができるか
            return (B1 + B2) * (t-1) + B1 >= (A1 + A2) * (t-1) + A1;
        });

        // コーナーケース
        if( (B1 + B2) * (turn-1) + B1 == (A1 + A2) * (turn-1) + A1 ) {
            return String.valueOf(turn*2 - 2);
        } else {
            return String.valueOf(turn*2 - 1);
        }
    }

    static int maximize(int lo, int hi, IntPredicate p) {
        while(lo < hi) {
            int x = ((hi - lo) >>> 1) + lo;
            if( p.test(x) ) {
                lo = x + 1;
            } else {
                hi = x;
            }
        }
        return lo - 1;
    }

    @SuppressWarnings("unused")
    static class FastScanner {
        private BufferedReader reader;
        private StringTokenizer tokenizer;

        FastScanner(InputStream in) {
            reader = new BufferedReader(new InputStreamReader(in));
            tokenizer = null;
        }

        String next() {
            if (tokenizer == null || !tokenizer.hasMoreTokens()) {
                try {
                    tokenizer = new StringTokenizer(reader.readLine());
                } catch (IOException e) {
                    throw new RuntimeException(e);
                }
            }
            return tokenizer.nextToken();
        }

        String nextLine() {
            if (tokenizer == null || !tokenizer.hasMoreTokens()) {
                try {
                    return reader.readLine();
                } catch (IOException e) {
                    throw new RuntimeException(e);
                }
            }
            return tokenizer.nextToken("\n");
        }

        long nextLong() {
            return Long.parseLong(next());
        }

        int nextInt() {
            return Integer.parseInt(next());
        }

        int[] nextIntArray(int n) {
            int[] a = new int[n];
            for (int i = 0; i < n; i++) a[i] = nextInt();
            return a;
        }

        int[] nextIntArray(int n, int delta) {
            int[] a = new int[n];
            for (int i = 0; i < n; i++) a[i] = nextInt() + delta;
            return a;
        }

        long[] nextLongArray(int n) {
            long[] a = new long[n];
            for (int i = 0; i < n; i++) a[i] = nextLong();
            return a;
        }
    }

    static void writeLines(int[] as) {
        PrintWriter pw = new PrintWriter(System.out);
        for (int a : as) pw.println(a);
        pw.flush();
    }

    static void writeLines(long[] as) {
        PrintWriter pw = new PrintWriter(System.out);
        for (long a : as) pw.println(a);
        pw.flush();
    }

    static void writeSingleLine(int[] as) {
        PrintWriter pw = new PrintWriter(System.out);
        for (int i = 0; i < as.length; i++) {
            if (i != 0) pw.print(" ");
            pw.print(as[i]);
        }
        pw.println();
        pw.flush();
    }

    static int max(int... as) {
        int max = Integer.MIN_VALUE;
        for (int a : as) max = Math.max(a, max);
        return max;
    }

    static int min(int... as) {
        int min = Integer.MAX_VALUE;
        for (int a : as) min = Math.min(a, min);
        return min;
    }

    static void debug(Object... args) {
        StringJoiner j = new StringJoiner(" ");
        for (Object arg : args) {
            if (arg == null) j.add("null");
            else if (arg instanceof int[]) j.add(Arrays.toString((int[]) arg));
            else if (arg instanceof long[]) j.add(Arrays.toString((long[]) arg));
            else if (arg instanceof double[]) j.add(Arrays.toString((double[]) arg));
            else if (arg instanceof Object[]) j.add(Arrays.toString((Object[]) arg));
            else j.add(arg.toString());
        }
        System.err.println(j.toString());
    }

    static void printSingleLine(int[] array) {
        PrintWriter pw = new PrintWriter(System.out);
        for (int i = 0; i < array.length; i++) {
            if (i != 0) pw.print(" ");
            pw.print(array[i]);
        }
        pw.println();
        pw.flush();
    }

    static int lowerBound(int[] array, int value) {
        int lo = 0, hi = array.length, mid;
        while (lo < hi) {
            mid = (hi + lo) / 2;
            if (array[mid] < value) lo = mid + 1;
            else hi = mid;
        }
        return lo;
    }

    static int upperBound(int[] array, int value) {
        int lo = 0, hi = array.length, mid;
        while (lo < hi) {
            mid = (hi + lo) / 2;
            if (array[mid] <= value) lo = mid + 1;
            else hi = mid;
        }
        return lo;
    }
}