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++14 (GCC 5.4.1) (judge verdict: Wrong Answer)

// >>> TEMPLATES
#include <bits/stdc++.h>
using namespace std;
using ll = long long;
using ld = long double;
using i32 = int32_t;
using i64 = int64_t;
#define int ll
#define double ld
#define rep(i,n) for (int i = 0; i < (int)(n); i++)
#define rep1(i,n) for (int i = 1; i <= (int)(n); i++)
#define repR(i,n) for (int i = (int)(n)-1; i >= 0; i--)
#define rep1R(i,n) for (int i = (int)(n); i >= 1; i--)
#define loop(i,a,B) for (int i = a; i B; i++)
#define loopR(i,a,B) for (int i = a; i B; i--)
#define all(x) (x).begin(), (x).end()
#define allR(x) (x).rbegin(), (x).rend()
#define pb push_back
#define eb emplace_back
#define mp make_pair
#define fst first
#define snd second
auto constexpr INF32 = numeric_limits<int32_t>::max()/2-1;
auto constexpr INF64 = numeric_limits<int64_t>::max()/2-1;
auto constexpr INF   = numeric_limits<int>::max()/2-1;
#ifdef LOCAL
#include "debug.hpp"
#define dump(...) cerr << "[" << setw(3) << __LINE__ << ":" << __FUNCTION__ << "] ", dump_impl(#__VA_ARGS__, __VA_ARGS__)
#define say(x) cerr << "[" << __LINE__ << ":" << __FUNCTION__ << "] " << x << endl
#define debug if (1)
#else
#define dump(...) (void)(0)
#define say(x) (void)(0)
#define debug if (0)
#endif
template <class T> using pque_max = priority_queue<T>;
template <class T> using pque_min = priority_queue<T, vector<T>, greater<T> >;
template <class T, class = typename T::iterator, class = typename enable_if<!is_same<T, string>::value>::type>
ostream& operator<<(ostream& os, T const& v) { bool f = true; for (auto const& x : v) os << (f ? "" : " ") << x, f = false; return os; }
template <class T, class = typename T::iterator, class = typename enable_if<!is_same<T, string>::value>::type>
istream& operator>>(istream& is, T &v) { for (auto& x : v) is >> x; return is; }
template <class T, class S> istream& operator>>(istream& is, pair<T,S>& p) { return is >> p.first >> p.second; }
struct IOSetup { IOSetup() { cin.tie(nullptr); ios::sync_with_stdio(false); cout << fixed << setprecision(15); } } iosetup;
template <class F> struct FixPoint : private F {
    constexpr FixPoint(F&& f) : F(forward<F>(f)) {}
    template <class... T> constexpr auto operator()(T&&... x) const { return F::operator()(*this, forward<T>(x)...); }
};
struct MakeFixPoint {
    template <class F> constexpr auto operator|(F&& f) const { return FixPoint<F>(forward<F>(f)); }
};
#define MFP MakeFixPoint()|
#define def(name, ...) auto name = MFP [&](auto &&name, __VA_ARGS__)
template <class T, size_t d> struct vec_impl {
    using type = vector<typename vec_impl<T,d-1>::type>;
    template <class... U> static type make_v(size_t n, U&&... x) { return type(n, vec_impl<T,d-1>::make_v(forward<U>(x)...)); }
};
template <class T> struct vec_impl<T,0> { using type = T; static type make_v(T const& x = {}) { return x; } };
template <class T, size_t d = 1> using vec = typename vec_impl<T,d>::type;
template <class T, size_t d = 1, class... Args> auto make_v(Args&&... args) { return vec_impl<T,d>::make_v(forward<Args>(args)...); }
template <class T> void quit(T const& x) { cout << x << endl; exit(0); }
template <class T> constexpr bool chmin(T& x, T const& y) { if (x > y) { x = y; return true; } return false; }
template <class T> constexpr bool chmax(T& x, T const& y) { if (x < y) { x = y; return true; } return false; }
template <class It> constexpr auto sumof(It b, It e) { return accumulate(b,e,typename iterator_traits<It>::value_type{}); }
template <class T> int sz(T const& x) { return x.size(); }
template <class C, class T> int lbd(C const& v, T const& x) {
    return lower_bound(v.begin(), v.end(), x)-v.begin();
}
template <class C, class T> int ubd(C const& v, T const& x) {
    return upper_bound(v.begin(), v.end(), x)-v.begin();
}
template <class C, class F> int ppt(C const& v, F f) {
    return partition_point(v.begin(), v.end(), f)-v.begin();
}
// <<<
// >>> reord
void reord_impl(vector<int> const&) { }
template <class T, class... Args>
void reord_impl(vector<int> const& idx, vector<T> &v, Args&&... args) {
    vector<T> t(v.size());
    rep (i,v.size()) t[i] = v[idx[i]];
    swap(v,t);
    reord_impl(idx, forward<Args>(args)...);
}
template <class Comp, class T, class... Args,
          class = decltype(declval<Comp>()(0,0))>
void reord(Comp comp, vector<T> &v, Args&&... args) {
    vector<int> idx(v.size());
    iota(idx.begin(), idx.end(), 0);
    sort(idx.begin(), idx.end(), comp);
    reord_impl(idx, v, args...);
}
template <class T, class... Args>
void reord(vector<T> &v, Args&&... args) {
    vector<int> idx(v.size());
    iota(idx.begin(), idx.end(), 0);
    sort(idx.begin(), idx.end(), [&](int i, int j) { return v[i] < v[j]; });
    reord_impl(idx, v, args...);
}
// <<<

int32_t main() {
    int n,T; cin >> n >> T;
    vector<int> a(n),b(n);
    rep (i,n) cin >> a[i] >> b[i], b[i]++;

    vector<int> c = { 0 };
    rep (i,n) if (a[i] == 0) c.eb(b[i]);
    sort(all(c));
    dump(c);
    rep (i,c.size()-1) c[i+1] += c[i];
    dump(c);

    reord([&](int i, int j) { return a[i]*b[j] > a[j]*b[i]; }
        ,a,b);
    repR (i,n) {
        if (a[i] == 0) {
            a.pop_back();
            b.pop_back();
        } else {
            break;
        }
    }
    rep (i,a.size()) assert(a[i] > 0);
    dump(a);
    dump(b);

    const int NN = 33;
    auto dp = make_v<int,2>(a.size()+1,NN,INF);
    dp[0][0] = 0;
    rep (i,a.size()) rep (j,NN) {
        if (dp[i][j] == INF) continue;
        chmin(dp[i+1][j], dp[i][j]);
        int t = (a[i]+1)*dp[i][j] + b[i];
        if (t <= T) {
            assert(j+1 < NN);
            chmin(dp[i+1][j+1], t);
        }
    }
    dump(as_mat(dp));

    int ma = 0;
    rep (j,NN) {
        int t = dp[a.size()][j];
        if (t == INF) continue;
        assert(t <= T);
        int cnt = ubd(c,T-t)-1;
        dump(j,t,T-t,cnt);
        chmax(ma, j+cnt);
    }

    cout << ma << endl;


}