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)

#include <bits/stdc++.h>
#include <ext/pb_ds/assoc_container.hpp>
#include <ext/pb_ds/tree_policy.hpp>

using namespace std;
using namespace __gnu_pbds;

typedef tree<int, null_type, less<int>, rb_tree_tag,tree_order_statistics_node_update> ordered_set;
typedef gp_hash_table<int, null_type,hash<int>, equal_to<int>, direct_mask_range_hashing<int>, linear_probe_fn<>,
    hash_standard_resize_policy<hash_exponential_size_policy<>, hash_load_check_resize_trigger<true>,true>> hash_set;

#define scan(x) do{while((x=getchar())<'0'); for(x-='0'; '0'<=(_=getchar()); x=(x<<3)+(x<<1)+_-'0');}while(0)
char _;
#define complete_unique(a) a.erase(unique(a.begin(),a.end()),a.end())
#define all(a) a.begin(),a.end()
#define println printf("\n");
#define readln(x) getline(cin,x);
#define pb push_back
#define endl "\n"
#define INT_INF 0x3f3f3f3f
#define LL_INF 0x3f3f3f3f3f3f3f3f
#define EPS 1e-9
#define MOD 1000000007
#define MOD2 1494318097
#define SEED 131
#define mp make_pair
#define fastio cin.tie(0); cin.sync_with_stdio(0);

#define MAXN 200005
#define LOGN 32

typedef unsigned long long ull;
typedef long long ll;
typedef long double ld;
typedef pair<int,int> pii;
typedef pair<double,double> pdd;
typedef pair<ll,ll> pll;
typedef pair<int,pii> triple;
typedef int8_t byte;

const ld PI = (ld)4*atanl(1);

mt19937 g1(chrono::steady_clock::now().time_since_epoch().count());

int randint(int a, int b){return uniform_int_distribution<int>(a, b)(g1);}
ll randlong(ll a,ll b){return uniform_int_distribution<long long>(a, b)(g1);}

ll gcd(ll a, ll b){return b == 0 ? a : gcd(b, a % b);}
ll lcm(ll a, ll b){return a*b/gcd(a,b);}
ll fpow(ll  b, ll exp, ll mod){if(exp == 0) return 1;ll t = fpow(b,exp/2,mod);if(exp&1) return t*t%mod*b%mod;return t*t%mod;}
ll divmod(ll i, ll j, ll mod){i%=mod,j%=mod;return i*fpow(j,mod-2,mod)%mod;}

int len,T,res;
pii arr[MAXN];
bool poss[MAXN][LOGN];
ll dp[MAXN][LOGN];

int main(){
    scanf(" %d %d",&len,&T);
    for(int i=1; i<=len; i++)
        scanf(" %d %d",&arr[i].first,&arr[i].second);
    sort(arr+1,arr+len+1,[](pii a, pii b){
        return a.first/(a.second+1)<b.first/(b.second+1);
    });
    int pt = len+1;
    for(int i=1; i<=len; i++){
        if(arr[i].first){
            pt = i;
            break;
        }
    }
    memset(poss[0],true,sizeof poss[0]);
    for(int i=0; i<MAXN; i++) dp[i][0] = 0, poss[i][0] = true;
    for(int i=pt; i<=len; i++){
        for(int k=1; k<=min(i,LOGN-1); k++){
            if(poss[i-1][k]) dp[i][k] = dp[i-1][k], poss[i][k] = true;
            if(poss[i-1][k-1]){
                ll t = dp[i-1][k-1]+(dp[i-1][k-1]+1)*arr[i].first+arr[i].second;
                if(poss[i-1][k]) dp[i][k] = min(dp[i][k],t);
                else dp[i][k] = t;
                poss[i][k] = true;
            }
        }
    }
    for(int k=0; k<=min(len,LOGN-1); k++){
        if(!poss[len][k]) continue;
        ll sum = dp[len][k];
        if(sum <= T) res = max(res,k);
        for(int i=1; i<pt; i++){
            sum = sum+arr[i].second+1;
            if(sum <= T)
                res = max(res,k+i);
        }
    }
    printf("%d\n",res);
}