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.util.HashMap;
import java.util.Map;

public class P916C {
    private static class HpReader {
        private BufferedReader in;

        public HpReader(String dir, String inFile, String outFile) {
            initAndRedirectInOut(dir, inFile, outFile);
        }

        private int ivl(String val) {
            return Integer.parseInt(val);
        }

        private long lvl(String val) {
            return Long.parseLong(val);
        }

        private void initAndRedirectInOut(String dir, String inFile, String outFile) {
            if (dir != null) {
                try {
                    String containingDirPath = dir.endsWith(File.separator) ? dir : dir + File.separator;
                    if (isDebug && inFile != null) System.setIn(new FileInputStream(new File(containingDirPath + inFile)));
                    if (isDebug && outFile != null) System.setOut(new PrintStream(new File(containingDirPath + outFile)));
                } catch (FileNotFoundException e) {
                    // Do nothing, stdin & stdout are not redirected
                }
            }
            in = new BufferedReader(new InputStreamReader(System.in));
            out = new PrintWriter(System.out);
        }

        private String nextSingleStr() throws IOException {
            return in.readLine();
        }

        private String[] nextLineStr() throws IOException {
            return nextLineStr(0);
        }

        private String[] nextLineStr(int offset) throws IOException {
            String[] inp = nextSingleStr().split(" ");
            String[] rs = new String[offset + inp.length];
            System.arraycopy(inp, 0, rs, offset, inp.length);
            return rs;
        }

        private int nextSingleInt() throws IOException {
            return ivl(in.readLine());
        }

        private int[] nextLineInt() throws IOException {
            return nextLineInt(0);
        }

        private int[] nextLineInt(int offset) throws IOException {
            String[] inp = nextLineStr();
            int[] rs = new int[offset + inp.length];
            for (int i = 0; i < inp.length; i++) rs[offset + i] = ivl(inp[i]);
            return rs;
        }

        private long nextSingleLong() throws IOException {
            return lvl(in.readLine());
        }

        private long[] nextLineLong() throws IOException {
            return nextLineLong(0);
        }

        private long[] nextLineLong(int offset) throws IOException {
            String[] inp = nextLineStr();
            long[] rs = new long[offset + inp.length];
            for (int i = 0; i < inp.length; i++) rs[offset + i] = lvl(inp[i]);
            return rs;
        }

        private int[][] nextMatInt(int lineCount) throws IOException {
            return nextMatInt(lineCount, 0, 0);
        }

        private int[][] nextMatInt(int lineCount, int rowOffset, int colOffset) throws IOException {
            int[][] rs = new int[rowOffset + lineCount][];
            for (int i = rowOffset; i < rs.length; i++) rs[i] = nextLineInt(colOffset);
            return rs;
        }
    }

    private static class HpHelper {
        private static final String LOCAL_DEBUG_FLAG = "COM_PROG_DEBUG";

        private static boolean isDebug() {
            try {
                return Boolean.parseBoolean(System.getenv(HpHelper.LOCAL_DEBUG_FLAG));
            } catch (Exception e) {
                return false;
            }
        }

        private static String createDelimiter(String delimiter) {
            return delimiter == null ? " " : delimiter;
        }

        private static void println(int[] data, String delimiter) {
            delimiter = createDelimiter(delimiter);
            for (int t : data) out.print(t + delimiter);
            out.println();
        }

        private static void println(long[] data, String delimiter) {
            delimiter = createDelimiter(delimiter);
            for (long t : data) out.print(t + delimiter);
            out.println();
        }

        private static <T> void println(T[] data, String delimiter) {
            delimiter = createDelimiter(delimiter);
            for (T t : data) {
                if (t instanceof int[]) {
                    println((int[]) t, delimiter);
                } else if (t instanceof long[]) {
                    println((long[]) t, delimiter);
                } else if (t instanceof Object[]) {
                    println((Object[]) t, delimiter);
                } else {
                    out.print(t + delimiter);
                }
            }
            out.println();
        }
    }

    private static class Path implements Comparable<Path> {
        public int x, y;

        public Path(int x, int y) {
            this.x = x;
            this.y = y;
        }


        @Override
        public int compareTo(Path o) {
            if (Math.min(x, y) == Math.min(o.x, o.y) && Math.max(x, y) == Math.max(o.x, o.y)) return 0;
            if (x != o.x) return x - o.x;
            return y - o.y;
        }

        @Override
        public int hashCode() {
            return x * 100000 + y;
        }
    }

    private static boolean isDebug = HpHelper.isDebug();
    private static HpReader in = new HpReader("/Users/apple/Work/WorkSpaces/CompetitiveProg/", "in.txt", null);
    private static PrintWriter out;

    private static boolean[] sieve(int n) {
        boolean[] isPrime = new boolean[n + 1];
        for (int i = 2; i <= n; i++) {
            isPrime[i] = true;
        }

        for (int factor = 2; factor * factor <= n; factor++) {
            if (isPrime[factor]) {
                for (int j = factor; factor * j <= n; j++) {
                    isPrime[factor * j] = false;
                }
            }
        }

        return isPrime;
    }

    public static void main(String[] args) throws IOException {
        int inp[] = in.nextLineInt(), n = inp[0], m = inp[1], mstw = 0;
        Map<Path, Integer> mapW = new HashMap<>(200000);
        boolean[] sieve = sieve(500000);

        for (int i = 2 * (n - 1); i < sieve.length; i++) {
            if (sieve[i]) {
                mstw = i;
                mapW.put(new Path(1, 2), i - 2 * (n - 2));
                for (int j = 3; j <= n; j++) {
                    mapW.put(new Path(1, j), 2);
                }
                break;
            }
        }

        m -= (n - 1);
        LEFT:
        for (int i = 2; i <= n - 1; i++) {
            for (int j = i + 1; j <= n; j++) {
                if (m == 0) break LEFT;
                mapW.put(new Path(i, j), 1_000_000_000);
                m -= 1;
            }
        }

        out.println("2 " + mstw);
        for (Path p : mapW.keySet()) {
            int d = mapW.get(p);
            out.println(String.format("%d %d %d", p.x, p.y, d));
        }

        out.flush();
    }
}