Problem:
Score : 800 points

Problem Statement

There are N stores called Store 1, Store 2, \cdots, Store N. Takahashi, who is at his house at time 0, is planning to visit some of these stores.

It takes Takahashi one unit of time to travel from his house to one of the stores, or between any two stores.

If Takahashi reaches Store i at time t, he can do shopping there after standing in a queue for a_i \times t + b_i units of time. (We assume that it takes no time other than waiting.)

All the stores close at time T + 0.5. If Takahashi is standing in a queue for some store then, he cannot do shopping there.

Takahashi does not do shopping more than once in the same store.

Find the maximum number of times he can do shopping before time T + 0.5.

Constraints

All values in input are integers.

1 \leq N \leq 2 \times 10^5

0 \leq a_i \leq 10^9

0 \leq b_i \leq 10^9

0 \leq T \leq 10^9

Input

Input is given from Standard Input in the following format:

N T
a_1 b_1
a_2 b_2
\vdots
a_N b_N

Output

Print the answer.

Sample Input 1

3 7
2 0
3 2
0 3

Sample Output 1

2

Here is one possible way to visit stores:

From time 0 to time 1: in 1 unit of time, he travels from his house to Store 1.

From time 1 to time 3: for 2 units of time, he stands in a queue for Store 1 to do shopping.

From time 3 to time 4: in 1 unit of time, he travels from Store 1 to Store 3.

From time 4 to time 7: for 3 units of time, he stands in a queue for Store 3 to do shopping.

In this way, he can do shopping twice before time 7.5.

Sample Input 2

1 3
0 3

Sample Output 2

0

Sample Input 3

5 21600
2 14
3 22
1 3
1 10
1 9

Sample Output 3

5

Sample Input 4

7 57
0 25
3 10
2 4
5 15
3 22
2 14
1 15

Sample Output 4

3

Solution in C# (Mono 4.6.2.0) (judge verdict: Wrong Answer)

using System;
using System.Collections.Generic;
using System.Linq;
using System.IO;
using System.Threading;
using System.Text;
using System.Text.RegularExpressions;
using System.Diagnostics;
using static util;
using P = pair<int, int>;

class Program {
    static void Main(string[] args) {
        var sw = new StreamWriter(Console.OpenStandardOutput()) { AutoFlush = false };
        var solver = new Solver(sw);
        // var t = new Thread(solver.solve, 1 << 26); // 64 MB
        // t.Start();
        // t.Join();
        solver.solve();
        sw.Flush();
    }
}

class Solver {
    StreamWriter sw;
    Scan sc;
    void Prt(string a) => sw.WriteLine(a);
    void Prt<T>(IEnumerable<T> a) => Prt(string.Join(" ", a));
    void Prt(params object[] a) => Prt(string.Join(" ", a));
    public Solver(StreamWriter sw) {
        this.sw = sw;
        this.sc = new Scan();
    }

    public void solve() {
        int n;
        long t;
        sc.Multi(out n, out t);
        var p = new pair<long, long>[n];
        for (int i = 0; i < n; i++)
        {
            long a, b;
            sc.Multi(out a, out b);
            p[i] = new pair<long, long>(a + 1, a + b + 1);
        }
        Array.Sort(p, (x, y) => x.v2 * y.v1 + y.v2 != y.v2 * x.v1 + x.v2 ? (x.v2 * y.v1 + y.v2).CompareTo(y.v2 * x.v1 + x.v2) : y.v1.CompareTo(x.v1));
        int r = n;
        while (r > 0 && p[r - 1].v1 == 1) --r;
        var dp = new long[36];
        for (int i = 0; i < 36; i++)
        {
            dp[i] = M;
        }
        dp[0] = 0;
        for (int i = 0; i < r; i++)
        {
            for (int j = 35; j > 0 ; j--)
            {
                dp[j] = Math.Min(dp[j], dp[j - 1] * p[i].v1 + p[i].v2);
            }
        }
        int max = 0;
        for (int i = 0; i < 36; i++)
        {
            if (dp[i] <= t) {
                max = Math.Max(max, i);
            }
        }
        long sum = 0;
        int c = 0;
        for (int i = r; i < n; i++)
        {
            ++c;
            sum += p[i].v2;
            for (int j = 0; j < 36; j++)
            {
                if (dp[j] + sum <= t) {
                    max = Math.Max(max, c + j);
                }
            }
        }
        Prt(max);
    }
}

class pair<T, U> : IComparable<pair<T, U>> {
    public T v1;
    public U v2;
    public pair() : this(default(T), default(U)) {}
    public pair(T v1, U v2) { this.v1 = v1; this.v2 = v2; }
    public int CompareTo(pair<T, U> a) {
        int c = Comparer<T>.Default.Compare(v1, a.v1);
        return c != 0 ? c : Comparer<U>.Default.Compare(v2, a.v2);
    }
    public override string ToString() => v1 + " " + v2;
    public void Deconstruct(out T a, out U b) { a = v1; b = v2; }
}
static class util {
    public static readonly int M = 1000000007;
    // public static readonly int M = 998244353;
    public static readonly long LM = 1L << 60;
    public static readonly double eps = 1e-11;
    public static void DBG(string a) => Console.Error.WriteLine(a);
    public static void DBG<T>(IEnumerable<T> a) => DBG(string.Join(" ", a));
    public static void DBG(params object[] a) => DBG(string.Join(" ", a));
    public static void Assert(params bool[] conds) {
        foreach (var cond in conds) if (!cond) throw new Exception();
    }
    public static pair<T, U> make_pair<T, U>(T v1, U v2) => new pair<T, U>(v1, v2);
    public static int CompareList<T>(IList<T> a, IList<T> b) where T : IComparable<T> {
        for (int i = 0; i < a.Count && i < b.Count; i++)
            if (a[i].CompareTo(b[i]) != 0) return a[i].CompareTo(b[i]);
        return a.Count.CompareTo(b.Count);
    }
    public static bool inside(int i, int j, int h, int w) => i >= 0 && i < h && j >= 0 && j < w;
    static readonly int[] dd = { 0, 1, 0, -1 };
    // static readonly string dstring = "RDLU";
    public static P[] adjacents(int i, int j)
        => Enumerable.Range(0, dd.Length).Select(k => new P(i + dd[k], j + dd[k ^ 1])).ToArray();
    public static P[] adjacents(int i, int j, int h, int w)
        => Enumerable.Range(0, dd.Length).Select(k => new P(i + dd[k], j + dd[k ^ 1]))
                                         .Where(p => inside(p.v1, p.v2, h, w)).ToArray();
    public static P[] adjacents(this P p) => adjacents(p.v1, p.v2);
    public static P[] adjacents(this P p, int h, int w) => adjacents(p.v1, p.v2, h, w);
    public static Dictionary<T, int> compress<T>(this IEnumerable<T> a)
        => a.Distinct().OrderBy(v => v).Select((v, i) => new { v, i }).ToDictionary(p => p.v, p => p.i);
    public static Dictionary<T, int> compress<T>(params IEnumerable<T>[] a) => compress(a.Aggregate(Enumerable.Union));
    public static T[] inv<T>(this Dictionary<T, int> dic) {
        var res = new T[dic.Count];
        foreach (var item in dic) res[item.Value] = item.Key;
        return res;
    }
    public static void swap<T>(ref T a, ref T b) where T : struct { var t = a; a = b; b = t; }
    public static void swap<T>(this IList<T> a, int i, int j) where T : struct { var t = a[i]; a[i] = a[j]; a[j] = t; }
    public static T[] copy<T>(this IList<T> a) {
        var ret = new T[a.Count];
        for (int i = 0; i < a.Count; i++) ret[i] = a[i];
        return ret;
    }
    public static void Deconstruct<T>(this IList<T> v, out T a) {
        a = v[0];
    }
    public static void Deconstruct<T>(this IList<T> v, out T a, out T b) {
        a = v[0]; b = v[1];
    }
    public static void Deconstruct<T>(this IList<T> v, out T a, out T b, out T c) {
        a = v[0]; b = v[1]; c = v[2];
    }
    public static void Deconstruct<T>(this IList<T> v, out T a, out T b, out T c, out T d) {
        a = v[0]; b = v[1]; c = v[2]; d = v[3];
    }
    public static void Deconstruct<T>(this IList<T> v, out T a, out T b, out T c, out T d, out T e) {
        a = v[0]; b = v[1]; c = v[2]; d = v[3]; e = v[4];
    }
}

class Scan {
    StreamReader sr;
    public Scan() { sr = new StreamReader(Console.OpenStandardInput()); }
    public Scan(string path) { sr = new StreamReader(path); }
    public int Int => int.Parse(Str);
    public long Long => long.Parse(Str);
    public double Double => double.Parse(Str);
    public string Str => sr.ReadLine().Trim();
    public pair<T, U> Pair<T, U>() {
        T a; U b;
        Multi(out a, out b);
        return new pair<T, U>(a, b);
    }
    public P P => Pair<int, int>();
    public int[] IntArr => StrArr.Select(int.Parse).ToArray();
    public long[] LongArr => StrArr.Select(long.Parse).ToArray();
    public double[] DoubleArr => StrArr.Select(double.Parse).ToArray();
    public string[] StrArr => Str.Split(new[]{' '}, StringSplitOptions.RemoveEmptyEntries);
    bool eq<T, U>() => typeof(T).Equals(typeof(U));
    T ct<T, U>(U a) => (T)Convert.ChangeType(a, typeof(T));
    T cv<T>(string s) => eq<T, int>()    ? ct<T, int>(int.Parse(s))
                       : eq<T, long>()   ? ct<T, long>(long.Parse(s))
                       : eq<T, double>() ? ct<T, double>(double.Parse(s))
                       : eq<T, char>()   ? ct<T, char>(s[0])
                                         : ct<T, string>(s);
    public void Multi<T>(out T a) => a = cv<T>(Str);
    public void Multi<T, U>(out T a, out U b) {
        var ar = StrArr; a = cv<T>(ar[0]); b = cv<U>(ar[1]);
    }
    public void Multi<T, U, V>(out T a, out U b, out V c) {
        var ar = StrArr; a = cv<T>(ar[0]); b = cv<U>(ar[1]); c = cv<V>(ar[2]);
    }
    public void Multi<T, U, V, W>(out T a, out U b, out V c, out W d) {
        var ar = StrArr; a = cv<T>(ar[0]); b = cv<U>(ar[1]); c = cv<V>(ar[2]); d = cv<W>(ar[3]);
    }
    public void Multi<T, U, V, W, X>(out T a, out U b, out V c, out W d, out X e) {
        var ar = StrArr; a = cv<T>(ar[0]); b = cv<U>(ar[1]); c = cv<V>(ar[2]); d = cv<W>(ar[3]); e = cv<X>(ar[4]);
    }
}