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.BigInteger;
	import java.util.*;
	
	import javax.sound.midi.Synthesizer;

	
	
	public class Main
	{
		private InputStream is;
		private PrintWriter out;
		int time = 0, freq[], start[], end[], dist[], black[], MOD = (int) (1e9 + 7), arr[], weight[][], x[], y[], parent[];
		int MAX = 1000001, N, K;
		long red[];
		int ans = 0;
	
		ArrayList<Integer>[] amp;
		ArrayList<Pair>[] pmp;
		boolean b[];
		boolean boo[][], b1[];
		Pair prr[];
		HashMap<Pair, Integer> hm = new HashMap();
		int Dp[][] = new int[1100][1100];
	
		void soln() 
		{
			is = System.in;
			out = new PrintWriter(System.out);
			long s = System.currentTimeMillis();
			solve();
	
			// out.close();
			out.flush();
			// tr(System.currentTimeMillis() - s + "ms");
		}
		
		 class ST1 // min ST
		{
			int arr[], st[];
			int size;
	
			ST1(int a[]) {
				arr = a.clone();
				size = 10 * arr.length;
				st = new int[size];
				build(0, arr.length - 1, 1);
			}
	
			void build(int ss, int se, int si) {
				if (ss == se) {
					st[si] = arr[ss];
					return;
				}
				int mid = (ss + se) / 2;
				int val = 2 * si;
				build(ss, mid, val);
				build(mid + 1, se, val + 1);
				st[si] = gcd(st[val], st[val + 1]);
			}
	
			/*void update(int ss, int se, int idx, long val, int si) {
				if (ss == se) {
					// if(si==idx+1)
					st[si] = val;
					return;
				}
				int mid = (ss + se) / 2;
				if (ss <= idx && idx <= mid) {
					update(ss, mid, idx, val, 2 * si);
				} else {
					update(mid + 1, se, idx, val, 2 * si + 1);
				}
				int v = 2 * si;
				st[si] = Math.min(st[v], st[v + 1]);
			}*/
	
			int get(int ss, int se, int l, int r, int si) {
				if (l > se || r < ss || l > r)
					return 0;
				if (l <= ss && r >= se)
					return st[si];
				int mid = (ss + se) / 2;
				int val = 2 * si;
				return gcd(get(ss, mid, l, r, val), get(mid + 1, se, l, r, val + 1));
			}
		}
	
		public static void main(String[] args) throws Exception
		{
			new Thread(null, new Runnable() 
			{
				public void run() 
				{
					try 
					{
						// new Main().soln();
					} catch (Exception e) 
					{
						System.out.println(e);
					}
				}
			}, "1", 1 << 26).start();
			new Main().soln();
		}
	
		int D[][];
		char ch[][], ch1[];
		int hash = 29;
		int x2, y2;
		HashSet<Integer>[] hs = (HashSet<Integer>[]) new HashSet[110];
		cell[] c;
		 boolean ar[] = new boolean[1000];
		Pair[] p = new Pair[4];
		 int a1[] = new int[7];
		 int a2[] = new int[7];
		 int a3[] = new int[7];
		 int a4[] = new int[7];
		 private static class Comp implements Comparable<Comp>{
				int ind;
				BigInteger v;

				@Override
				public int compareTo(Comp arg0) {
					if(v==arg0.v)
						return this.ind-arg0.ind;
					return this.v.compareTo(arg0.v);
				}
			}
		 private static class Comp1 implements Comparable<Comp1>{
				int ind;
				String v;

				@Override
				public int compareTo(Comp1 arg0) {
					if(v.equals(arg0.v))
						return this.ind-arg0.ind;
					return this.v.compareTo(arg0.v);
				}
			}
		 int n1, n2;
		 void solve()
		 {
			 int n = ni(), m = ni();
			 int val = 1000000000-1;
			 int ans = 2*(n-2);
			 seive();
			 for(int i = 2; i<10000000; i++) {
				 if(!b[i]) {
					 if(!b[i+ans]) {
						 out.println(i+" "+(ans+i));
						 for(int j = 2;j<n;j++) {
							 out.println(1+" "+j+" "+2);
						 }
						 out.println(1+" "+n+" "+i);
						 m -= (n-1);
						 //System.out.println(m);
						 for(int j = 2;j<=n;j++) {
							 for(int k = j+1;k<=n;k++) {
								 if(m==0) return;
								 m--;
								 out.println(j+" "+k+" "+val);
								 if(m==0) return;
							 }
						 }
						 if(m==0) return;
					 }
					 if(m==0) return;
				 }
				 if(m==0) return;
			 }
		 }
		 void seive() {
			 b = new boolean[10000000];
			 for(int i = 2;i<10000000;i++) {
				 if(!b[i])
				 for(int j = 2*i;j<10000000;j+=i) {
					 b[j] = true;
				 }
			 }
		 }
		 void time(int x) {
			 if((n2-x)<0) {
				 n1--;
				 n2 = (n2-x+60)%60;
			 }
			 else {
				 n2 -= x;
			 }
			 n1 = (n1+24)%24;
		 }
		 boolean check(int x, int y) {
			 if(Integer.toString(x).contains("7") || Integer.toString(y).contains("7")) return true;
			 return false;
		 }
		 void dfs(int x, int dis) {
			 Queue<Integer> q = new LinkedList<Integer>();
			 b[x] = true;
			 dist[x] = dis;
			 q.add(x);
			 while(!q.isEmpty()) {
				 x = q.poll();
			 for(int i : amp[x]) {
				 	dist[i] = min(dist[i],dist[x]+1);
				 	if(!b[i]) {
				 		b[i] = true;
				 		q.add(i);
				 	}
			 	}
			 }
		 }
		 String check(String[] s) {
			 char ch[] = new char[] {'a','a','a','a'};
			 boolean b = false;
			 for(int i = 0;i<4;i++) {
				 if(i>0) {
					 if(ch[i]=='a') continue;
				 }
				 for(int j = i+1;j<4;j++) {
					 if(!s[i].equals(s[j])) {
						 if(ch[i] == 'a' && ch[j]=='a') ch[j] = 'b';
						 else if(ch[j]=='a') continue;
						 else {
							 System.out.println("NO");
							 System.exit(0);
						 }
					 }
					 else b = true;
				 }
			 }
			 return new String(ch);
		 }
		 boolean isVowel(char c) {
			 if(c=='a' || c=='e' ||c=='i' ||c=='o' ||c=='u' ) return true;
					 return false;
		 }
		 void recur1(int[] a1, int[] a2) {
			 for(int i = 1; i< 7;i++) {
				 for(int j = 1; j< 7;j++) {
					 ar[a1[i]*10+a2[j]] = true;
					 ar[a2[j]*10+a1[i]] = true;
				 }
			 }
		 }
		boolean binaryS(int a, int b, int c, int d) {
			double l = 0, r = 90;
			for(int count = 0;count<=300;count++)
			{
				double mid = (l + r) / 2;
				double temp = mid * Math.PI / 180;
				double x1 = Math.cos(temp) * c;
				double x2 = Math.sin(temp) * c;
				temp = Math.PI / 2 - temp;
				double y1 = Math.cos(temp) * d;
				double y2 = Math.sin(temp) * d;
				if ((x1 + y1 <= a) && (x2 + y2 <= b)) return true;
				else if (x1 + y1 > a) l = mid;
				else r = mid;
			}
			return false;
		}
		/*void bfs(int s, int n) {
			b = new boolean[n];
			dist = new int[n];
			Arrays.fill(dist, 1000000);
			dist[s] = 0;
			b[s] = true;
			Queue<Integer> q = new LinkedList<>();
			q.add(s);
			while(!q.isEmpty()) {
				int y = q.poll();
				for(int i : amp[y]) {
					dist[i] = min(dist[i],dist[y]+1);
					if(!b[i]) {
						b[i] = true;
						q.add(i);
					}
				}
			}
		}*/
		boolean check(String s, String s1) {
			char ch1[] = s.toCharArray(), ch2[] = s1.toCharArray();
			int arr[] = new int[10];
			for(char c : ch1) {
				arr[c-'0']++;
			}
			int ans = 0;
			for(char c:ch2) {
				arr[c-'0']--;
			}
			
			for(int i:arr) ans += ((i>0)?i:0);
			return ans==3;
		}
		void seive(int n)
		{
			start = new int[n];
			for(int i = 2;i<n;i++) {
				if(start[i]==0) {
					for(int j = 2*i;j<n;j+=i) {
						start[j] = i;
					}
				}
			}
		}
		void print(int[][] arr) 
		{
			int seed = 110, n = arr.length - 220;
			for (int i = 0; i < n; i++) {
				for (int j = 0; j < n; j++) {
					System.out.print(arr[i + seed][j + seed] + " ");
				}
				System.out.println();
			}
			System.out.println();
		}
	
		 class cell implements Comparable<cell>
		 {
			int s, d, p, i;
	
			cell(int t, int d, int p, int i) {
				this.s = t;
				this.p = p;
				this.d = d;
				this.i = i;
			}
	
			public int compareTo(cell other) {
				// return Integer.compare(val, other.val);
				return Long.compare(d, other.d) != 0 ? (Long.compare(d, other.d)): (Long.compare(i,other.i));
												// other.v));//((Long.compare(u, other.u) != 0 ? (Long.compare(u, other.u)):
												// (Long.compare(v, other.v)))
				// &(Long.compare(u, other.v) != 0 ? (Long.compare(u, other.v)):
				// (Long.compare(v, other.u))));
			}
	
			public String toString() {
				return this.d + " " + this.s +" "+this.p+" "+this.i;
			}
		}
	
		int abs(int x)
		{
			return ((x > 0) ? x : -x);
		}
	
		long ret(int p) 
		{
			if (p >= 0)
				return 0;
			else
				return 1;
		}
	
		long val(int p, int a, int b) 
		{
			if (p >= 0) {
				return (a * 1l * p);
			}
			return (b * 1l * p);
		}
	
		
	
	
		public int getParent(int x) 
		{
			while (parent[x] != x) {
				parent[x] = parent[parent[x]];
				x = parent[x];
			}
			return x;
		}
	
		void getFactors(int n, int x)
		{
			for (int i = 1; i * i <= n; i++) {
				if (n % i == 0) {
					hs[x].add(i);
					hs[x].add(n / i);
				}
			}
		}
	
		void recur(int a, int b, int k) 
		{
			if (k == 0) {
				if (a == x2 && b == y2)
					ans++;
				return;
			}
			recur(a, b + 1, k - 1);
			recur(a, b - 1, k - 1);
			recur(a + 1, b, k - 1);
			recur(a - 1, b, k - 1);
		}
	
		int min(int a, int b) 
		{
			return (a < b) ? a : b;
		}
	
		/*private class Cell implements Comparable<Cell> {
			int u, v, s;
	
			public Cell(int u, int v, int s) {
				this.u = u;
				this.v = v;
				this.s = s;
			}
	
			public int hashCode() {
				return Objects.hash();
			}
	
			public int compareTo(Cell other) {
				return (Long.compare(s, other.s) != 0 ? (Long.compare(s, other.s))
						: (Long.compare(v, other.v) != 0 ? Long.compare(v, other.v) : Long.compare(u, other.u)))
						& ((Long.compare(s, other.s) != 0 ? (Long.compare(s, other.s))
								: (Long.compare(u, other.v) != 0 ? Long.compare(u, other.v) : Long.compare(v, other.u))));
			}
	
			public String toString() {
				return this.u + " " + this.v;
			}
		}*/

		
		class Pair implements Comparable<Pair>
		{
			int u ,v,i;
	
			Pair(int u, int v) {
				this.u = u;
				this.i = v;
			}
	
			Pair(int u, int v, int i) {
				this.u = u;
				this.v = v;
				this.i = i;
			}
	
			public int hashCode() {
				return Objects.hash();
			}
	
			public boolean equals(Object o) {
				Pair other = (Pair) o;
				return ((u == other.u && v == other.v));
			}
	
			public int compareTo(Pair other) {
				// return Integer.compare(val, other.val);
				return Long.compare(u, other.u) != 0 ? (Long.compare(u, other.u)) : (Long.compare(i, other.i));// ((Long.compare(u,
			
			}									
			public String toString() {
				return this.u + " " + this.v +" "+this.i;
			}
		}
	
		int max(int a, int b) 
		{
			if (a > b)
				return a;
			return b;
		}
	
		static class FenwickTree 
		{
	
			int[] array; // 1-indexed array, In this array We save cumulative
							// information to perform efficient range queries and
							// updates
	
			public FenwickTree(int size) {
				array = new int[size + 1];
			}
	
			public int rsq(int ind) {
				assert ind > 0;
				int sum = 0;
				while (ind > 0) {
					sum += array[ind];
					// Extracting the portion up to the first significant one of the
					// binary representation of 'ind' and decrementing ind by that
					// number
					ind -= ind & (-ind);
				}
				return sum;
			}
	
			public int rsq(int a, int b) {
				assert b >= a && a > 0 && b > 0;
				return rsq(b) - rsq(a - 1);
			}
	
			public void update(int ind, int value) {
				assert ind > 0;
				while (ind < array.length) {
					array[ind] += value;
					// Extracting the portion up to the first significant one of the
					// binary representation of 'ind' and incrementing ind by that
					// number
					ind += ind & (-ind);
				}
			}
	
			public int size() {
				return array.length - 1;
			}
		}
		void buildGraph(int n)
		{
			for (int i = 0; i < n; i++) {
				int x1 = ni(), y1 = ni();
				amp[x1-1].add(y1-1);
				amp[y1-1].add(x1-1);
			}
		}
		long modInverse(long a, long mOD2)
		{
			return power(a, mOD2 - 2, mOD2);
		}
	
		long power(long x, long y, long m) 
		{
			if (y == 0)
				return 1;
			long p = power(x, y / 2, m) % m;
			p = (p * p) % m;
	
			return (y % 2 == 0) ? p : (x * p) % m;
		}
	
		public int gcd(int a, int b)
		{
			if (b == 0)
				return a;
			return gcd(b, a % b);
		}
	
		/*static class ST
		{
			int arr[], lazy[], n;
	
			ST(int a) {
				n = a;
				arr = new int[10 * n];
				lazy = new int[10 * n];
			}
	
			void up(int l, int r, int val) {
				update(0, n - 1, 0, l, r, val);
			}
	
			void update(int l, int r, int c, int x, int y, int val) {
				if (lazy[c] != 0) {
					lazy[2 * c + 1] += lazy[c];
					lazy[2 * c + 2] += lazy[c];
					if (l == r)
						arr[c] += lazy[c];
					lazy[c] = 0;
				}
				if (l > r || x > y || l > y || x > r)
					return;
				if (x <= l && y >= r)
	
				{
					lazy[c] += val;
					return;
				}
				int mid = l + r >> 1;
				update(l, mid, 2 * c + 1, x, y, val);
				update(mid + 1, r, 2 * c + 2, x, y, val);
				arr[c] = Math.max(arr[2 * c + 1], arr[2 * c + 2]);
			}
	
			int an(int ind) {
				return ans(0, n - 1, 0, ind);
			}
	
			int ans(int l, int r, int c, int ind) {
				if (lazy[c] != 0) {
					lazy[2 * c + 1] += lazy[c];
					lazy[2 * c + 2] += lazy[c];
					if (l == r)
						arr[c] += lazy[c];
					lazy[c] = 0;
				}
				if (l == r)
					return arr[c];
				int mid = l + r >> 1;
				if (mid >= ind)
					return ans(l, mid, 2 * c + 1, ind);
				return ans(mid + 1, r, 2 * c + 2, ind);
			}
		}*/
	
		public static int[] shuffle(int[] a, Random gen)
		{
			for (int i = 0, n = a.length; i < n; i++) {
				int ind = gen.nextInt(n - i) + i;
				int d = a[i];
				a[i] = a[ind];
				a[ind] = d;
			}
			return a;
		}
	
		long power(long x, long y, int mod)
		{
			long ans = 1;
			while (y > 0) {
				if (y % 2 == 0) {
					x = (x * x) % mod;
					y /= 2;
				} else {
					ans = (x * ans) % mod;
					y--;
				}
			}
			return ans;
		}
	
		// To Get Input
		// Some Buffer Methods
		private byte[] inbuf = new byte[1024];
		public int lenbuf = 0, ptrbuf = 0;
	
		private int readByte() 
		{
			if (lenbuf == -1)
				throw new InputMismatchException();
			if (ptrbuf >= lenbuf) {
				ptrbuf = 0;
				try {
					lenbuf = is.read(inbuf);
				} catch (IOException e) {
					throw new InputMismatchException();
				}
				if (lenbuf <= 0)
					return -1;
			}
			return inbuf[ptrbuf++];
		}
	
		private boolean isSpaceChar(int c) {
			return !(c >= 33 && c <= 126);
		}
	
		private int skip() {
			int b;
			while ((b = readByte()) != -1 && isSpaceChar(b))
				;
			return b;
		}
	
		private double nd() {
			return Double.parseDouble(ns());
		}
	
		private char nc() {
			return (char) skip();
		}
	
	/*	private String ns() {
			int b = skip();
			StringBuilder sb = new StringBuilder();
			while (!(isSpaceChar(b) && b!=' ')) { // when nextLine, (isSpaceChar(b) && b != '
										// ')
				sb.appendCodePoint(b);
				b = readByte();
			}
			return sb.toString();
		}
	*/
		private String ns()
		{
			int b = skip();
			StringBuilder sb = new StringBuilder();
			while (!(isSpaceChar(b)))
			{ // when nextLine, (isSpaceChar(b) && b != '
										// ')
				sb.appendCodePoint(b);
				b = readByte();
			}
			return sb.toString();
		}
		
		private char[] ns(int n) {
			char[] buf = new char[n];
			int b = skip(), p = 0;
			while (p < n && !(isSpaceChar(b))) {
				buf[p++] = (char) b;
				b = readByte();
			}
			return n == p ? buf : Arrays.copyOf(buf, p);
		}
	
		private char[][] nm(int n, int m) {
			char[][] map = new char[n][];
			for (int i = 0; i < n; i++)
				map[i] = ns(m);
			return map;
		}
	
		private int[] na(int n) {
			int[] a = new int[n];
			for (int i = 0; i < n; i++)
				a[i] = ni();
			return a;
		}
	
		private int ni() {
			int num = 0, b;
			boolean minus = false;
			while ((b = readByte()) != -1 && !((b >= '0' && b <= '9') || b == '-'))
				;
			if (b == '-') {
				minus = true;
				b = readByte();
			}
	
			while (true) {
				if (b >= '0' && b <= '9') {
					num = num * 10 + (b - '0');
				} else {
					return minus ? -num : num;
				}
				b = readByte();
			}
		}
	
		private long nl() {
			long num = 0;
			int b;
			boolean minus = false;
			while ((b = readByte()) != -1 && !((b >= '0' && b <= '9') || b == '-'))
				;
			if (b == '-') {
				minus = true;
				b = readByte();
			}
	
			while (true) {
				if (b >= '0' && b <= '9') {
					num = num * 10 + (b - '0');
				} else {
					return minus ? -num : num;
				}
				b = readByte();
			}
		}
	
		private boolean oj = System.getProperty("ONLINE_JUDGE") != null;
	
		private void tr(Object... o) {
			if (!oj)
				System.out.println(Arrays.deepToString(o));
		}
	}