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:
/*
输出m个数字，其中第i个要输出从0变换到i的最小步骤，步骤按照输入的n个操作任选
暴力：n次操作，每次枚举已到达的数（包括0）做操作，用桶数组记录操作
优化：
   贪心：每次从m到0开始操作，如果已经操作过，就退出
   或者每次从0到m，每个数就操作一次，因为循环到后面还会操作到
   要注意a<=y的判断
复杂度O(n*m)
*/
#include <iostream>
#include <cstdio>
#include <map>
#include <vector>
#include <cmath>
#include <algorithm>
#include <queue>
#include <cstring>
using namespace std;
typedef long long ll;
struct Cmd {
  ll t, x, y;
};

const int N=205, M=1e5+5, inf=0x3f3f3f3f;
int n,m, d[M],a[M];
Cmd cmd[N];

void solve() {
  for(int i=1; i<=m; i++) d[i] = -1;
  d[0] = 0;
  for(int i=1; i<=n; i++) {
    memset(a, 0, sizeof(a));
    for(int j=0; j<=m; j++) {
      if(d[j]==-1) continue;
      ll dest;
      if(cmd[i].t == 1) {
        ll tmp = (cmd[i].x+99999)/100000;
        dest = j+tmp;
      } else {
        double tmp = cmd[i].x*1.0/100000;
        dest = j*tmp+0.9999999999L;
      }
	  if(dest > m || dest < 0) break;//数据超出
	  if(a[j]+1 > cmd[i].y) continue;//超出y的限制
	  if(d[dest] == -1) {
		d[dest] = i;
		a[dest] = a[j]+1;
	  }
    }
  }
  for(int i=1; i<=m; i++)
    printf("%d ", d[i]);
  cout<<endl;
}

int main() {
  cin>>n>>m;
  for(int i=1; i<=n; i++)
    cin>>cmd[i].t>>cmd[i].x>>cmd[i].y;
  solve();
  
  return 0;
}