Problem: You have a malfunctioning microwave in which you want to put some bananas. You have n time-steps before the microwave stops working completely. At each time-step, it displays a new operation.

Let k be the number of bananas in the microwave currently. Initially, k = 0. In the i-th operation, you are given three parameters t_i, x_i, y_i in the input. Based on the value of t_i, you must do one of the following:

Type 1: (t_i=1, x_i, y_i) — pick an a_i, such that 0 ≤ a_i ≤ y_i, and perform the following update a_i times: k:=⌈ (k + x_i) ⌉.

Type 2: (t_i=2, x_i, y_i) — pick an a_i, such that 0 ≤ a_i ≤ y_i, and perform the following update a_i times: k:=⌈ (k ⋅ x_i) ⌉.

Note that x_i can be a fractional value. See input format for more details. Also, ⌈ x ⌉ is the smallest integer ≥ x.

At the i-th time-step, you must apply the i-th operation exactly once.

For each j such that 1 ≤ j ≤ m, output the earliest time-step at which you can create exactly j bananas. If you cannot create exactly j bananas, output -1.

Input

The first line contains two space-separated integers n (1 ≤ n ≤ 200) and m (2 ≤ m ≤ 10^5).

Then, n lines follow, where the i-th line denotes the operation for the i-th timestep. Each such line contains three space-separated integers t_i, x'_i and y_i (1 ≤ t_i ≤ 2, 1≤ y_i≤ m).

Note that you are given x'_i, which is 10^5 ⋅ x_i. Thus, to obtain x_i, use the formula x_i= \dfrac{x'_i} {10^5}.

For type 1 operations, 1 ≤ x'_i ≤ 10^5 ⋅ m, and for type 2 operations, 10^5 < x'_i ≤ 10^5 ⋅ m.

Output

Print m integers, where the i-th integer is the earliest time-step when you can obtain exactly i bananas (or -1 if it is impossible).

Examples

Input


3 20
1 300000 2
2 400000 2
1 1000000 3


Output


-1 -1 1 -1 -1 1 -1 -1 -1 3 -1 2 3 -1 -1 3 -1 -1 -1 3 


Input


3 20
1 399999 2
2 412345 2
1 1000001 3


Output


-1 -1 -1 1 -1 -1 -1 1 -1 -1 3 -1 -1 -1 3 -1 2 -1 3 -1 

Note

In the first sample input, let us see how to create 16 number of bananas in three timesteps. Initially, k=0.

  * In timestep 1, we choose a_1=2, so we apply the type 1 update — k := ⌈(k+3)⌉ — two times. Hence, k is now 6. 
  * In timestep 2, we choose a_2=0, hence value of k remains unchanged. 
  * In timestep 3, we choose a_3=1, so we are applying the type 1 update k:= ⌈(k+10)⌉ once. Hence, k is now 16. 



It can be shown that k=16 cannot be reached in fewer than three timesteps with the given operations.

In the second sample input, let us see how to create 17 number of bananas in two timesteps. Initially, k=0.

  * In timestep 1, we choose a_1=1, so we apply the type 1 update — k := ⌈(k+3.99999)⌉ — once. Hence, k is now 4. 
  * In timestep 2, we choose a_2=1, so we apply the type 2 update — k := ⌈(k⋅ 4.12345)⌉ — once. Hence, k is now 17. 



It can be shown that k=17 cannot be reached in fewer than two timesteps with the given operations.

Solution (in CPP):

Solution:
#include <bits/stdc++.h>
#define ull uint64_t
#define ll long long int
#define pb push_back
#define mp make_pair
#define pi pair<int, int>
#define vi vector<int>
#define ff first
#define ss second
#define mx5 100005
#define mx52 200005
#define mx6 1000005
#define mod 1000000007
#define smod 998244353
#define nfs                       \
    ios_base::sync_with_stdio(0); \
    cin.tie(0);                   \
    cout.tie(0);
using namespace std;

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

template <typename T>
bool MinPlace(T &a, const T &b)
{
    if (a > b)
    {
        a = b;
        return true;
    }
    return false;
}

template <typename T>
bool MaxPlace(T &a, const T &b)
{
    if (a < b)
    {
        a = b;
        return true;
    }
    return false;
}

template <typename S, typename T>
ostream &operator<<(ostream &out, const pair<S, T> &p)
{
    out << "{" << p.ff << ", " << p.ss << "}";
    return out;
}

template <typename T>
ostream &operator<<(ostream &out, const vector<T> &v)
{
    out << "[";
    for (int i = 0; i < (int)v.size(); i++)
    {
        out << v[i];
        if (i != (int)v.size() - 1)
            out << ", ";
    }
    out << "]";
    return out;
}

ll p5 = 100000;
ll get_prev(ll cur, ll x, int t)
{
    switch (t)
    {
    case 1:
        return cur - ceil(x / ((double)p5));
        break;
    case 2:
        return (1ll * p5 * cur) / x;
        break;
    default:
        return 0;
        break;
    }
}

ll get_next(ll cur, ll x, int t)
{
    switch (t)
    {
    case 1:
        return cur + ceil(x / ((double)p5));
        break;
    case 2:
        return 1ll * (ceil(x * cur / ((double)p5)));
        break;
    default:
        return 0;
        break;
    }
}

int main()
{
    nfs;
    int n, m;
    cin >> n >> m;
    vi gotcha(m + 1, -1);
    gotcha[0] = 0;

    for (int i = 0; i < n; i++)
    {
        int t, y;
        ll x;

        cin >> t >> x >> y;
        vi left(m + 1, y);
        for (int j = 1; j <= m; j++)
        {
            if (gotcha[j] != -1)
                continue;

            ll prev = get_prev(j, x, t);
            if (prev >= 0 and gotcha[prev] != -1 and left[prev] and get_next(prev, x, t) == j)
            {
                gotcha[j] = i + 1;
                left[j] = left[prev] - 1;
            }
        }
    }
    for (int i = 1; i <= m; i++)
        cout << gotcha[i] << " ";
};