D-Jamie and Interesting Graph （CodeForces-916C）（構造）

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, 109] 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  — the required number of vertices and edges.

Output

In the first line output 2 integers sp, mstw (1 ≤ sp, mstw ≤ 1014) — 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 ≤ 109) describing the edge connecting u and v and having weight w.

Examples

Input

4 4

Output

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

Input

5 4

Output

7 13
1 2 2
1 3 4
1 4 3
4 5 4

Note

The graph of sample 1:  Shortest path sequence: {1, 2, 3, 4}. MST edges are marked with an asterisk (*).

Definition of terms used in the problem statement:

A shortest path in an undirected graph is a sequence of vertices (v1, v2, ... , vk) such that vi is adjacent to vi + 1 1 ≤ i < k and the sum of weight  is minimized where w(i, j) is the edge weight between i and j. (https://en.wikipedia.org/wiki/Shortest_path_problem)

A prime number is a natural number greater than 1 that has no positive divisors other than 1 and itself. (https://en.wikipedia.org/wiki/Prime_number)

A minimum spanning tree (MST) is a subset of the edges of a connected, edge-weighted undirected graph that connects all the vertices together, without any cycles and with the minimum possible total edge weight. (https://en.wikipedia.org/wiki/Minimum_spanning_tree)

https://en.wikipedia.org/wiki/Multiple_edges

題意：給出 n 個點, m 個點. 要求組成一個最小生成樹權重之和及始點到終點的最短路權重之和都爲質數的圖. 輸出爲最短路權重之和, 最小生成樹權重之和一行, 兩個點和連接它們的邊的權一行。

思路：這道題的話，我們可以先構造一條邊，路徑上包括了所有 n 個結點. 我們接下來找到大於 n 的某個質數, 直接令這條路徑作爲生成樹和最短路, 其權重之和等於這個質數，這樣的話，我們將前n-2條邊設爲1, 最後一條設爲質數-n+2。然後剩下的m-（n-1）條邊統一分配1000000的權值。不知道因爲這個質數的範圍是怎麼判定的......連wa9發，最後把priime=100010改成100003就AC了？？？！！（我傻逼了，prime是一個質數）≥﹏≤​​​​​​​

AC代碼：

#include <stdio.h>
#include <string>
#include <string.h>
#include <iostream>
#include <algorithm>
#include <math.h>
#include <queue>
#include <stack>
#include <map>
#include <set>
typedef long long ll;
const int maxx=100003;
const int inf=0x3f3f3f3f;
using namespace std;
int main()
{
    int n,m;
    scanf("%d%d",&n,&m);
    int prime=maxx;
    printf("%d %d\n",prime,prime);
    printf("1 2 %d\n",prime-n+2);
    for(int i=2; i<n; i++)
        printf("%d %d 1\n",i,i+1);
    int ans=m-(n-1);
    for(int i=1; i<=n-1; i++)
    {
        for(int j=i+2; j<=n; j++)
        {
            if(!ans)
                return 0;
            printf("%d %d %d\n",i,j,1000000);
            ans--;
        }
    }
    return 0;
}