# Codeforces 916 C. Jamie and Interesting Graph （构造）

## Description

Jamie has recently found undirected weighted graphs with the following properties very interesting:

• The graph is connected and contains exactly n vertices and m edges.
• All edge weights are integers and are in range [1, 10^9] inclusive.
• The length of shortest path from 1 to n is a prime number.
• The sum of edges' weights in the minimum spanning tree (MST) of the graph is a prime number.
• The graph contains no loops or multi-edges.

If you are not familiar with some terms from the statement you can find definitions of them in notes section.

Help Jamie construct any graph with given number of vertices and edges that is interesting!

## Input

First line of input contains 2 integers n, m $(2≤n≤10^5, n-1≤m≤\min(\frac{n(n-1)}{2},10^5))$ — the required number of vertices and edges.

## Output

In the first line output 2 integers sp, mstw (1 ≤ sp, mstw ≤ 10^14) — the length of the shortest path and the sum of edges' weights in the minimum spanning tree.

In the next m lines output the edges of the graph. In each line output 3 integers u, v, w (1 ≤ u, v ≤ n, 1 ≤ w ≤ 10^9) describing the edge connecting u and v and having weight w.

## Examples input

4 4


## Examples output

7 7
1 2 3
2 3 2
3 4 2
2 4 4


## AC 代码

#include<bits/stdc++.h>
#define IO ios::sync_with_stdio(false);\
cin.tie(0);\
cout.tie(0);
using namespace std;
typedef __int64 LL;
const int maxn = 3e5+10;

int n,m;
const int prime = 1e5+3;

int main()
{
IO;
cin>>n>>m;
int last = m - n + 1;
cout<<prime<<" "<<prime<<endl;
cout<<"1 2 "<<prime - n + 2<<endl;
for(int i=2; i<=n-1; i++)
cout<<i<<" "<<i+1<<" "<<1<<endl;
for(int i=1; i<=n-1; i++)
for(int j=i+2; j<=n; j++)
{
if(last--==0)
return 0;
cout<<i<<" "<<j<<" "<<(prime<<1)<<endl;
}
return 0;
}