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>
using namespace std;
#define ll long long
#define ld long double
#define pb push_back
#define vll vector<ll>
#define pll pair<ll,ll>
#define vpll vector<pll>
#define ub upper_bound
#define lb lower_bound
#define all(v) ((v).begin()),((v).end())
#define allr(v) ((v).rbegin()),((v).rend())
#define ff first
#define ss second
#define mp make_pair
#define pll pair<ll,ll> 
#define fo(i,n) for(ll i=0;i<n;i++)
#define foa(i,s,e) for(ll i=(s);i<=e;i++)
#define fod(i,s,e) for(ll i= (s);i>=(e);i--)
#define max3(a,b,c) max(max(a,b),c)
#define min3(a,b,c) min(min(a,b),c)
#define deb(x) cerr<<#x<<' '<<'='<<' '<<x<<'\n'
#define sz(x) (ll)(x.size())
#define ANS cout<<ans<<'\n'
#define YES cout<<"YES\n"
#define NO cout<<"NO\n"
#define Yes cout<<"Yes\n"
#define No cout<<"No\n"
const ld pi = 3.14159265358979323846;
ll MOD = 1e9 + 7;
//ll MOD = 998244353;
const char nl = '\n';
const ll inf = 1e15;
#define fill(a,b) memset(a, b, sizeof(a))
#define setbits(x) __builtin_popcountll(x)
#define vout(v) for(auto &x : v){cout << x << " ";}
#define vin(v) for (auto &x : v){cin >> x;}
#define print2d(dp,n,m) fo(i, n){fo(j, m)cout<<dp[i][j]<<" ";cout<<"\n";}
ll nxt(){ll x; cin >> x; return x;}
ll mul(ll x,ll y){
    return (1ll* (x%MOD)*(y%MOD));
}
ll modpow(ll x,ll y){ll z=1;while(y>0){if(y%2)z=mul(z,x);x =mul(x,x) ;y/=2;}return z;}
ll power(ll x,ll y){ll z=1;while(y>0){if(y%2)z=z*x;x =x*x ;y/=2;}return z;}
ll gcd(ll a,ll b){if(a<b) return gcd(b,a);if(b==0) return a;return gcd(b,a%b);} 
ll min(ll a,ll b){if(a<b)return a;return b;}
ll max(ll a,ll b){if(a>b)return a;return b;}
ll sq(ll a){
    ll ans = (1ll*a*a);
    return ans;
}
const ll N = 1e5;

void solve(){
    ll n, m;
    cin >> n >> m;
    vll ans(m + 1, -1);
    vll vis(m + 1);
    vis[0] = 1;
    fo(i, n){
        ll t, x, y;
        cin >> t >> x >> y;
        fod(j, m, 0){
            if(vis[j]){
                ll jj = j;
                foa(k, 1, y){
                    if(t == 2)jj = (jj*x + N - 1)/N;
                    else jj = (jj + (x + N-1)/N);
                    if(jj > m)break;
                    if(vis[jj])break;
                    vis[jj] = 1;
                    ans[jj] = i+1;
                }
            }
        }
    }
    foa(i, 1, m){
        cout << ans[i] << " ";
    }
}
int main(){ 
    ios::sync_with_stdio(false);
    cin.tie(0),cout.tie(0);
    #ifndef ONLINE_JUDGE
    freopen("inputf.txt" , "r" , stdin) ;
    freopen("outputf.txt" , "w" , stdout) ;
    freopen("error.txt" , "w" , stderr) ;
    #endif
    ll TC = 1;
    //cin>>TC;
    fo(TT, TC){
        //cout << "Case #"<< TT + 1 << ": ";
        solve();
    }
    cerr << "Time : " << 1000 * ((double)clock()) / (double)CLOCKS_PER_SEC << "ms\n";
}