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:
/*Jai Shree Ram*/
// Never Give Up
#include<bits/stdc++.h>
#include<unordered_map>
using namespace std;
 
#define ff              first
#define ss              second
#define int             long long
#define pb              push_back
#define mp              make_pair
#define pii             pair<int,int>
#define vi              vector<int>
#define mii             map<int,int>
#define umii            unordered_map<int,int>
#define pqb             priority_queue<int>
#define pqs             priority_queue<int,vi,greater<int> >
#define setbits(x)      __builtin_popcountll(x)
#define zrobits(x)      __builtin_ctzll(x)
#define mod             1000000007
#define inf             1e18
#define ps(x,y)         fixed<<setprecision(y)<<x
#define mk(arr,n,type)  type *arr=new type[n];
#define w(x)            int x; cin>>x; while(x--)
#define F(i,s,e,j)        for(int i=s;i<=e;i+=j)
#define mt19937                 rng(chrono::steady_clock::now().tjhe_since_epoch().count());   
//shuffle(arr,arr+n,rng)
#define ld long double
 void c_p_c()
{
    ios_base::sync_with_stdio(0); cin.tie(0); cout.tie(0);
#ifndef ONLINE_JUDGE
    freopen("input.txt", "r", stdin);
    freopen("output.txt", "w", stdout);
#endif
}
int add_(int dest,int x)
{
  if(x%100000==0)
    return dest+x/100000;
  else
    return dest+x/100000+1;
}
int multiply_(int dest,int x)
{
  dest *= x;
  if(dest%100000==0)
    return dest/100000;
  else
    return dest/100000+1;
}
int32_t main()
{   c_p_c();
    int dp[100001];
    int dup_dp[100001];
    dp[0] = 0;
    int n,m;
    cin>>n>>m;
    vector<pii> v(n);
    vi x(n);
    for(int i=0;i<n;i++)
    {
      cin>>v[i].ff>>x[i]>>v[i].ss;
     
    }
    for(int i=1;i<=m;i++)
      dp[i] = n+1;
    vi num;
    num.pb(0);
    dp[0] = 0;
    dup_dp[0] = 0;
    for(int i=0;i<n;i++)
    {
      bool vis[100001];
      memset(vis,false,sizeof(vis));
       for(int ele:num)
       {
        vis[ele] = true;
         int dest = ele;
          for(int j=0;j<v[i].ss;j++)
          {

            if(v[i].ff==1)
            {  ld z = dest;
              dest = add_(dest,x[i]);
              if(dest<=m && !vis[dest])
              {
                
                 dp[dest] = min(dup_dp[ele]+1,dp[dest]);
                 vis[dest] = true;
              }
              else
                break;
              
            }
            else
            {
              if(dest==0)
                continue;
              dest = multiply_(dest,x[i]);
              if(dest<=m && !vis[dest])
              {   
                 dp[dest] = min(dup_dp[ele]+1,dp[dest]);
                 vis[dest] = true;
              }
              else
                break;
            } 
          }
       }
       num.clear();
       for(int j=0;j<=m;j++)
       {
         if(dp[j]!=n+1)
          {
            dup_dp[j] = i+1;
            num.pb(j);
          }
       }
       sort(num.begin(),num.end(),greater<int>());
    }
    for(int i=1;i<=m;i++)
      { if(dp[i]==n+1)
          dp[i] = -1;
        cout<<dp[i]<<" ";
      }
}