Problem: 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 <image> — 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: <image> 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 <image> 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>

Solution (in JAVA):

Solution:
		     
		import java.io.*;
		        		    import java.math.*;
		        		    import java.util.*;
	import java.util.regex.Pattern;
	
	import javafx.scene.shape.Line;
		    	     
		        		    public class Main{
		        		  	private static InputStream stream;
		        		    	private static byte[] buf = new byte[1024];
		        		    	private static int curChar;
		        		    	private static int numChars;
		        		    	private static SpaceCharFilter filter;
		        		    	private static PrintWriter pw;
		        		    	private static long count = 0,mod=(long)1e9+7;
		        		    //	private static TreeSet<Integer> ts=new TreeSet[200000];
		public final static int INF = (int) 1E9;
		
		public static void main(String args[]) {
	    	
			InputReader(System.in);
			pw = new PrintWriter(System.out); 
		    new Thread(null ,new Runnable(){
		       public void run(){
		           try{
		        		
		               solve();
	
		               pw.close();
		           } catch(Exception e){
		               e.printStackTrace();
		           }
		       }
		   },"1",1<<26).start();
		   	   }
		    static StringBuilder sb;
		    public static void test() throws IOException{
		    	 sb=new StringBuilder();
		    	int t=nextInt();
		    	// int t=1;
		    	 while(t-->0){
		    		
		    		solve();
		    		//pw.println();
		    		//sb.append("\n");
		    	}
		    	pw.println(sb);
		    }
		    
		    public static long pow(long n, long p,long mod) {
				if(p==0)
					return 1;
				if(p==1)
					return n%mod;
				if(p%2==0){
					long temp=pow(n, p/2,mod);
				return (temp*temp)%mod;
				}else{
					 	long temp=pow(n,p/2,mod);
					 	temp=(temp*temp)%mod;
					 	return(temp*n)%mod;
					 	
				}
			}
		    public static long pow(long n, long p) {
				if(p==0)
					return 1;
				if(p==1)
					return n;
				if(p%2==0){
					long temp=pow(n, p/2);
				return (temp*temp);
				}else{
					 	long temp=pow(n,p/2);
					 	temp=(temp*temp);
					 	return(temp*n);
					 	
				}
			}
		    public static void Merge(long a[],int p,int r){
		        if(p<r){
		            int q = (p+r)/2;
		            Merge(a,p,q);
		            Merge(a,q+1,r);
		            Merge_Array(a,p,q,r);
		        }
		    }
		    public static void Merge_Array(long a[],int p,int q,int r){
		       long b[] = new long[q-p+1];
		        long c[] = new long[r-q];
		        for(int i=0;i<b.length;i++)
		            b[i] = a[p+i];
		        for(int i=0;i<c.length;i++)
		            c[i] = a[q+i+1];
		        int i = 0,j = 0;
		        for(int k=p;k<=r;k++){
		            if(i==b.length){
		                a[k] = c[j];
		                j++;
		            }
		            else if(j==c.length){
		                a[k] = b[i];
		                i++;
		            }
		            else if(b[i]<c[j]){
		                a[k] = b[i];
		                i++;
		            }
		            else{
		                a[k] = c[j];
		                j++;
		            }
		        }
		    }
		    
		  
			public static long gcd(long x, long y) {
				if (x == 0)
					return y;
				else
					return gcd( y % x,x);
			}	
			
			public static boolean isPrime(int n) {
				if (n <= 1)
					return false;
				if (n <= 3)
					return true;
		 
				if (n % 2 == 0 || n % 3 == 0)
					return false;
		 
				for (int i = 5; i * i <= n; i = i + 6)
					if (n % i == 0 || n % (i + 2) == 0)
						return false;
		 
				return true;
			}
			
		        static LinkedList<Integer> adj[],adj2[];
		        static boolean Visited[];
		        static HashSet<Integer> exc;
		        static long oddsum[]=new long[1000001];
		        static long co=0;
		    
		    	private static void buildgraph(int n){
		    		adj=new LinkedList[n+1];
		    		adj2=new LinkedList[n+1];
		    		Visited=new boolean[n+1];
		    		levl=new int[n+1];
		    		
		    		for(int i=0;i<=n;i++){
		    			adj[i]=new LinkedList<Integer>();
		    		
		    		}
		
		
		    	}
		      
		       
		        static int[] levl;
		        static int[] eat;
		        static int n,m;
		        static int price[];
		        //ind frog crab
		    
		        
		        static long d,x,y;
				static long modInverse(long A, long M)
				{
				extendedEuclid(A,M);
				return (x%M+M)%M;    //x may be negative
				}
				static void extendedEuclid(long A, long B) {
				if(B == 0) {
				d = A;
				x = 1;
				y = 0;
				}
				else {
				extendedEuclid(B, A%B);
				long temp = x;
				x = y;
				y = temp - (A/B)*y;
				}
				}
		        static double distance(int x1,int y1,int x2,int y2){
		        	return Math.sqrt((x1-x2)*(x1-x2) + (y1-y2)*(y1-y2));
		        }
		        static double area(int x1, int y1, int x2, int y2, int x3, int y3)
		        {
		           return Math.abs((x1*(y2-y3) + x2*(y3-y1)+ x3*(y1-y2))/2.0);
		        }
		        static boolean isInside(int x1, int y1, int x2, int y2, int x3, int y3, int x, int y)
		        {   
		           double A = area (x1, y1, x2, y2, x3, y3);
		         
		           double A1 = area (x, y, x2, y2, x3, y3);
		         
		           double A2 = area (x1, y1, x, y, x3, y3);
		         
		           double A3 = area (x1, y1, x2, y2, x, y);
		           
		          return (A == A1 + A2 + A3);
		        }
		      
				static int col[];
		    public static boolean isVowel(char c){
		    	if(c=='a' || c=='e'||c=='i' || c=='o' || c=='u')
		    		return true;
		    	return false;
		    }
		static long arr[], lazy[],ans[];
		static int c[];
		public static void solve() throws IOException{
		
			int n=nextInt();
			int m=nextInt();
			
			TreeSet<Integer> ts=new TreeSet<Integer>();
			ts.add(2);
			for(int i=3;i<=1000000;i++){
				if(isPrime(i))
					ts.add(i);
			}
			pw.println(ts.higher(n-2)+" "+ts.higher(n-2));
			for(int i=0;i<n-2;i++){	
				pw.println((i+1)+" "+(i+2)+" "+1);
				m--;
			}
			int get =ts.higher(n-2)-n+2;
			pw.println((n-1)+ " "+n+" "+get);
			int deg[]=new int[n+1];
			Arrays.fill(deg, 2);
			deg[1]=1;
			deg[n]=1;
			m--;
			int start=1;
			int end=3;
			
			 while (m>0){
			        for(int i=start+2;i<=n&&m>0;i++,m--){
			            pw.println(start+" "+i+" "+1000000000+"\n");
			        }
			        start++;
			    }
		}
	
	
		   static void DFS(int cyc,int n, int vert, int start) {
	    
	   // mark the vertex vert as visited
	   vis[vert] = true;
	    
	   // if the path of length (n-1) is found
	   if (cyc == 0) {
	        
	       // mark vert as un-visited to 
	       // make it usable again
	      vis[vert] = false;
	        
	       // Check if vertex vert end 
	       // with vertex start
	       if (adj[vert].contains(start)) {
	           count++;
	           return;
	       } else
	           return;
	   }
	    
	   // For searching every possible 
	   // path of length (n-1)
	   for (int i = 0; i < n; i++)
	       if (!vis[i] && adj[vert].contains(i))
	        
	           // DFS for searching path by
	           // decreasing length by 1
	           DFS(cyc-1,n, i, start);
	    
	   // marking vert as unvisited to make it
	   // usable again
	   vis[vert] = false;
	}
	
		static int cnt=0;
		
		static int dista[];
		private static void dfs2(int curr,int dist){
			Visited[curr]=true;
			dista[curr]=dist;
			for(int i:adj[curr]){
				if(!Visited[i]){
					dfs2(i,dist+1);
				}
			}
		}
		static long tot=0;
		static int par[]=new int[1000001];
		static long size[]=new long[1000001];
		static boolean vis[]=new boolean[1000001];
		public static void dfs1(int curr)
		{
			vis[curr]=true;
			size[curr]=1;
			for(int x:adj[curr])
			{
				if(!vis[x])
				{
					par[x]=curr;
					dfs1(x);
					size[curr]+=size[x];
				}
			}
		}
		
	  
	  static boolean getString (char[][] matrix, int x, int y, char[] target) {
	      if (matrix == null || matrix.length == 0 || matrix[0].length == 0) {
	          return false;
	      }
	      
	      if (target == null || target.length == 0) {
	          return false;
	      }
	      
	      if (matrix[x][y] != target[0]) {
	          return false;
	      }
	      
	      int row = matrix.length;
	      int column = matrix[0].length;
	      
	      int[] dirx = {0, 0, 1, -1, 1, 1, -1, -1}; // array, int[]!!!!
	      int[] diry = {1, -1, 0, 0, 1, -1, 1, -1}; // array, int[]!!!!
	      
	      for (int i = 0; i < 8; i++) {
	          int nextx = x;  // define !!
	          int nexty = y;  // define !!
	          int k = 1;
	          while (k < target.length) {
	              nextx += dirx[i];
	              nexty += diry[i];
	              
	              if (nextx < 0 || nexty < 0 || nextx >= row || nexty >= column) {
	                  break;
	              }
	              
	              if (matrix[nextx][nexty] != target[k]) {
	                  break;
	              }
	              k++;
	          }
	          
	          if (k == target.length) {
	              return true;
	          }
	      }
	      
	      return false;
	  }
		
		
		
		static int no_vert=0,timer=1;
		
		private static void dfs(int s,int lev){
			Visited[s]=true;
			
			for(int x:adj[s]){
				if(!Visited[x]){
				
					dfs(x,lev+1);
				}
				
			}
			//System.out.println(lev);
			no_vert=Math.max(no_vert, lev);
		}
		
		
		    private static boolean Check(int x,int y,int n){
				if(x>=0 && x<n && y>=0 && y<n)
					return true;
				return false;
			}
		    
		    static long[][] dp;
			static long dp2[];
		    static ArrayList<Integer> pri[],pri2[];
		
		  private static void dfs3(int curr,int par,int co){
				 Visited[curr]=true;
				 for(int x:adj[curr]){
					 if(!Visited[x]){
						 dfs3(x,curr,co);
					 }
				 }
				 if(col[curr]==1){
					 dp2[curr]++;
				 }else{
					 dp2[curr]--;
				 }
				 if(dp2[curr]>0){
					 pri2[par].add(curr);
				 dp2[par]+=dp2[curr];
				 }
			  }
		    public static String reverseString(String s) {
				StringBuilder sb = new StringBuilder(s);
				sb.reverse();
				return (sb.toString());
			}
		    
		  /*  
		   private static void BFS(int sou){
		    	Queue<Integer> q=new LinkedList<Integer>();
		    	q.add(sou);
		    	Visited[sou]=true;
		    	levl[sou]=0;
		    	while(!q.isEmpty()){
		    		int top=q.poll();
		    		
		    		for(int i:adj[top]){
		    			//pw.println(i+" "+top);
					if(!Visited[i])
					{
						
						q.add(i);
						levl[i]=levl[top]+1;
					}
					
					Visited[i]=true;
					
					}
				}
			}*/
			
		
		
		
		    		      static int indeg[];
		    		   /* private static void kahn(int n){
		    		    	
		    		    	PriorityQueue<Integer> q=new PriorityQueue<Integer>();
		    				for(int i=1;i<=n;i++){
		    					if(indeg[i]==0){
		    						q.add(i);
		    					}
		    				}
		    				while(!q.isEmpty()){
		    					int top=q.poll();
		    					st.push(top);
		    					for(Node i:adj[top]){
		    						indeg[i.to]--;
		    						if(indeg[i.to]==0){
		    							q.add(i.to);
		    						}
		    					}
		    				}
		    		    }
		    		        
		    		        static int state=1;
		    		        static long no_exc=0,no_vert=0;
		    		      static Stack<Integer> st;
		    		      static HashSet<Integer> inset;
		    		     /*   private static void topo(int curr){
		    		        	
		    		        	Visited[curr]=true;
		    		        	inset.add(curr);
		    		        	for(int x:adj[curr]){
		    		        		if(adj[x].contains(curr) || inset.contains(x)){
		    		        			state=0;
		    		        			return;
		    		        		}
		    		        		if(state==0)
		    		        			return;
		    		        		
		    		        	}
		    		        	st.push(curr);
		    		        	
		    		        	inset.remove(curr);
		    		        }*/
		    		        static HashSet<Integer> hs;
		    		       
		    		     
		    		     	static boolean prime[];
							static int spf[];
							public static void sieve(int n){
								prime=new boolean[n+1];
								spf=new int[n+1];
								
								Arrays.fill(spf, 1);
								Arrays.fill(prime, true);
							prime[1]=false;
								spf[2]=2;
								
							for(int i=4;i<=n;i+=2){
								spf[i]=2;
							}
							for(int i=3;i<=n;i+=2){
								if(prime[i]){
									spf[i]=i;
									for(int j=2*i;j<=n;j+=i){
										
										prime[j]=false;
									if(spf[j]==1){
										spf[j]=i;
									}
									}
								}
							}
							
								
							}
		    		     	
		    		    	// To Get Input
		// Some Buffer Methods
		 
		    		     	public static void sort(long a[]){
		    		     		Merge(a, 0, a.length-1);
		    		     	}
		    		    	public static void InputReader(InputStream stream1) {
		    		    		stream = stream1;
		    		    	}
		 
		    		    	private static boolean isWhitespace(int c) {
		    		    		return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
		    		    	}
		 
		    		    	private static boolean isEndOfLine(int c) {
		    		    		return c == '\n' || c == '\r' || c == -1;
		    		    	}
		 
		    		    	private static int read() {
		    		    		if (numChars == -1)
		    		    			throw new InputMismatchException();
		    		    		if (curChar >= numChars) {
		    		    			curChar = 0;
		    		    			try {
		    		    				numChars = stream.read(buf);
		    		    			} catch (IOException e) {
		    		    				throw new InputMismatchException();
		    		    			}
		    		    			if (numChars <= 0)
		    		    				return -1;
		    		    		}
		    		    		return buf[curChar++];
		    		    	}
		 
		    		    	private static int nextInt() {
		    		    		int c = read();
		    		    		while (isSpaceChar(c))
		    		    			c = read();
		    		    		int sgn = 1;
		    		    		if (c == '-') {
				sgn = -1;
				c = read();
			}
			int res = 0;
			do {
				if (c < '0' || c > '9')
					throw new InputMismatchException();
				res *= 10;
				res += c - '0';
		    		    			c = read();
		    		    		} while (!isSpaceChar(c));
		    		    		return res * sgn;
		    		    	}
		 
		    		    	private static long nextLong() {
		    		    		int c = read();
		    		    		while (isSpaceChar(c))
		    		    			c = read();
		    		    		int sgn = 1;
		    		    		if (c == '-') {
				sgn = -1;
				c = read();
			}
			long res = 0;
			do {
				if (c < '0' || c > '9')
					throw new InputMismatchException();
				res *= 10;
				res += c - '0';
		    		    			c = read();
		    		    		} while (!isSpaceChar(c));
		    		    		return res * sgn;
		    		    	}
		 
		    		    	private static String nextToken() {
		    		    		int c = read();
		    		    		while (isSpaceChar(c))
		    		    			c = read();
		    		    		StringBuilder res = new StringBuilder();
		    		    		do {
		    		    			res.appendCodePoint(c);
		    		    			c = read();
		    		    		} while (!isSpaceChar(c));
		    		    		return res.toString();
		    		    	}
		 
		    		    	private static String nextLine() {
		    		    		int c = read();
		    		    		while (isSpaceChar(c))
		    		    			c = read();
		    		    		StringBuilder res = new StringBuilder();
		    		    		do {
		    		    			res.appendCodePoint(c);
		    		    			c = read();
		    		    		} while (!isEndOfLine(c));
		    		    		return res.toString();
		    		    	}
		 
		    		    	private static int[] nextIntArray(int n) {
		    		    		int[] arr = new int[n];
		    		    		for (int i = 0; i < n; i++) {
		    		    			arr[i] = nextInt();
		    		    		}
		    		    		return arr;
		    		    	}
		 
		    		    	private static long[][] next2dArray(int n, int m) {
		    		    		long[][] arr = new long[n][m];
		    		    		for (int i = 0; i < n; i++) {
		    		    			for (int j = 0; j < m; j++) {
		    		    				arr[i][j] = nextLong();
		    		    			}
		    		    		}
		    		    		return arr;
		    		    	}
		    		    	private static char[][] nextCharArray(int n,int m){
		    		    		char [][]c=new char[n][m];
		    		    		for(int i=0;i<n;i++){
		    		    			String s[]=nextLine().split(" ");
		    		    			for(int j=0;j<s.length;j++){
		    		    				c[i][j]=s[j].charAt(0);
		    		    			}
		    		    		}
		    		    		return c;
		    		    	}
		 
		    		    	private static long[] nextLongArray(int n) {
		    		    		long[] arr = new long[n];
		    		    		for (int i = 0; i < n; i++) {
		    		    			arr[i] = nextLong();
		    		    		}
		    		    		return arr;
		    		    	}
		 
		    		    	private static void pArray(int[] arr) {
		    		    		for (int i = 0; i < arr.length; i++) {
		    		    			pw.print(arr[i] + " ");
		    		    		}
		    		    		pw.println();
		    		    		return;
		    		    	}
		 
		    		    	private static void pArray(long[] arr) {
		    		    		for (int i = 0; i < arr.length; i++) {
		    		    			pw.print(arr[i] + " ");
		    		    		}
		    		    		pw.println();
		    		    		return;
		    		    	}
		 
		    		    	private static void pArray(boolean[] arr) {
		    		    		for (int i = 0; i < arr.length; i++) {
		    		    			pw.print(arr[i] + " ");
		    		    		}
		    		    		pw.println();
		    		    		return;
		    		    	}
		 
		    		    	private static boolean isSpaceChar(int c) {
		    		    		if (filter != null)
		    		    			return filter.isSpaceChar(c);
		    		    		return isWhitespace(c);
		    		    	}
		 
		    		    	private interface SpaceCharFilter {
		    		    		public boolean isSpaceChar(int ch);
		    		    	}
		    		    	
		
		}
		    		    
		    		        class Node{
		    		    	int to;
		    		    	long dist;
		    		    	Node(int to,long dist){
		    		    		this.to=to;
		    		    		this.dist=dist;
		    		    	}
		    		    	
		    		    }
		    		        class Qu{
		    		    		long a0,a1,a2,a3;
		    		    		public Qu(long a0,long a1,long a2,long a3) {
		    		    			this.a0=a0;
		    		    			this.a1=a1;
		    		    			this.a2=a2;
		    		    			this.a3=a3;
		    		    		}
		    		    }
		    		
		class Dsu{
		private int rank[], parent[] ,n;
		long str[],si[],larg[];
		long max=0;
		int cnt=0;
		private static int[] parent1;
		Dsu(int size){
			this.n=size+1;
			rank=new int[n];
			cnt=n-1;
			//parent=new int[n];
		    		    		    		parent=new int[n];
		    		    		    		str=new long[n];
		    		    		    		si=new long[n];
		    		    		
		    		    		    		larg=new long[n];
		    		    		    		makeSet();
		    		    		
		    		    		    	}
		    		    		    	
		    		    		    	void makeSet(){
		    		    		    		for(int i=0;i<n;i++){
		    		    		    			parent[i]=i;
		    		    		    			si[i]=1;
		    		    		    		}
		    		    		    	}
		    		    		    	
		    		    		    	int find(int x){
		    		    		    		if(parent[x]!=x){
		    		    		    			
		    		    		    			parent[x]=find(parent[x]);
		    		    		    		}
		    		    		    		return parent[x];
		    		    		    	}
		    		    		    	
		    		    		    	void join(int ind,long val){
		    		    		    		if(str[ind]==0){
		    		    		    			str[ind]=val;
		    		    		    			larg[ind]=val;
		    		    		    			max=Math.max(max, str[ind]);
		    		    		    		}
		    		    		    		int prev_ind=(ind-1);
		    		    		    		int next_ind=(ind+1);
		    		    		    		if(prev_ind>0 && larg[prev_ind]!=0){
		    		    		    			union(prev_ind,ind);
		    		    		    		}
		    		    		    		if(next_ind<n && larg[next_ind]!=0){
		    		    		    			union(next_ind,ind);
		    		    		    		}
		    		    		    		
		    		    		    	}
		    		    		    
		    		    		    	
		    		    		    	boolean union(int x,int y){
		    		    		    		int xRoot=find(x);
		    		    		    		int yRoot=find(y);
		    		    		    
		    		    		    	
		    		    		    		if(xRoot==yRoot)
		    		    		    			return false;
		    		    		    		if(rank[xRoot]<rank[yRoot]){
		    		    		    		parent[xRoot]=yRoot;
		    		    		    		
		    		    		    		larg[yRoot]=Math.max(larg[xRoot], larg[yRoot]);
		    		    		    		
		    		    		    		si[yRoot]+=si[xRoot];
		    		    		    		str[yRoot]=larg[yRoot]*si[yRoot];
		    		    		    			max=Math.max(str[yRoot], max);
		    		    		    		}else if(rank[yRoot]<rank[xRoot]){
		    		    		    			parent[yRoot]=xRoot;
		     
		    		    		    			larg[xRoot]=Math.max(larg[xRoot], larg[yRoot]);
		        		    		    		
		        		    		    		si[xRoot]+=si[yRoot];
		        		    		    		str[xRoot]=larg[xRoot]*si[xRoot];
		    			    		    		max=Math.max(str[xRoot], max);
		    		    		    		}else{
		    		    		    			parent[yRoot]=xRoot;
		    		    		    			rank[xRoot]++;
		     
		    		    		    			larg[xRoot]=Math.max(larg[xRoot], larg[yRoot]);
		        		    		    		
		        		    		    		si[xRoot]+=si[yRoot];
		        		    		    		str[xRoot]=larg[xRoot]*si[xRoot];
		    			    		    		max=Math.max(str[xRoot], max);
		    		    		    		
		    		    		    		}
		    		    		    		cnt--;
		    		    		    		return true;
		    		    		    	}
		    	
		    		    		     
		    		    		    }
	class Pair1 implements Comparable<Pair1>{
			int ind;
			String v;
			@Override
			public int compareTo(Pair1 arg0) {
				if(v==arg0.v)
					return 1;
				return this.v.compareTo(arg0.v);
				
			}
		
		
		}