Problem: You are given a weighted undirected connected graph consisting of n vertices and m edges. It is guaranteed that there are no self-loops or multiple edges in the given graph.

Let's define the weight of the path consisting of k edges with indices e_1, e_2, ..., e_k as ∑_{i=1}^{k}{w_{e_i}} - max_{i=1}^{k}{w_{e_i}} + min_{i=1}^{k}{w_{e_i}}, where w_i — weight of the i-th edge in the graph.

Your task is to find the minimum weight of the path from the 1-st vertex to the i-th vertex for each i (2 ≤ i ≤ n).

Input

The first line contains two integers n and m (2 ≤ n ≤ 2 ⋅ 10^5; 1 ≤ m ≤ 2 ⋅ 10^5) — the number of vertices and the number of edges in the graph.

Following m lines contains three integers v_i, u_i, w_i (1 ≤ v_i, u_i ≤ n; 1 ≤ w_i ≤ 10^9; v_i ≠ u_i) — endpoints of the i-th edge and its weight respectively.

Output

Print n-1 integers — the minimum weight of the path from 1-st vertex to the i-th vertex for each i (2 ≤ i ≤ n).

Examples

Input


5 4
5 3 4
2 1 1
3 2 2
2 4 2


Output


1 2 2 4 


Input


6 8
3 1 1
3 6 2
5 4 2
4 2 2
6 1 1
5 2 1
3 2 3
1 5 4


Output


2 1 4 3 1 


Input


7 10
7 5 5
2 3 3
4 7 1
5 3 6
2 7 6
6 2 6
3 7 6
4 2 1
3 1 4
1 7 4


Output


3 4 2 7 7 3 

Solution (in JAVA):

Solution:
//package ecr102;
import java.io.*;
import java.util.ArrayDeque;
import java.util.Arrays;
import java.util.InputMismatchException;
import java.util.Queue;

public class E {
	InputStream is;
	FastWriter out;
	String INPUT = "";
	
	void solve() {
		int n = ni();
		int m = ni();
		int[] from = new int[m];
		int[] to = new int[m];
		int[] ws = new int[m];
		for (int i = 0; i < m; i++) {
			from[i] = ni() - 1;
			to[i] = ni() - 1;
			ws[i] = ni();
		}

		int[][][] g = packWU(n, from, to, ws);

		long[] ans = new long[n];
		Arrays.fill(ans, Long.MAX_VALUE);

		// min->max
		{
			long[] td = new long[3*n];

			Arrays.fill(td, Long.MAX_VALUE / 2);
			MinHeapL q = new MinHeapL(3*n);
			q.add(0, 0);
			td[0] = 0;

			while(q.size() > 0){
				int cur = q.argmin();
				q.remove(cur);
				int node = cur % n, phase = cur / n;

				for(int[] e : g[node]){
					{
						int next = e[0] + phase * n;
						long nd = td[cur] + e[1];
						if (nd < td[next]) {
							td[next] = nd;
							q.update(next, nd);
						}
					}
					if(phase == 0){
						int next = e[0] + (phase + 1) * n;
						long nd = td[cur] + 2*e[1];
						if (nd < td[next]) {
							td[next] = nd;
							q.update(next, nd);
						}
					}
					if(phase == 1){
						int next = e[0] + (phase + 1) * n;
						long nd = td[cur];
						if (nd < td[next]) {
							td[next] = nd;
							q.update(next, nd);
						}
					}
				}
			}

			for(int i = 0;i < n;i++){
				ans[i] = Math.min(ans[i], td[2*n+i]);
			}
		}

		// max->min
		{
			long[] td = new long[3*n];

			Arrays.fill(td, Long.MAX_VALUE / 2);
			MinHeapL q = new MinHeapL(3*n);
			q.add(0, 0);
			td[0] = 0;

			while(q.size() > 0){
				int cur = q.argmin();
				q.remove(cur);
				int node = cur % n, phase = cur / n;

				for(int[] e : g[node]){
					{
						int next = e[0] + phase * n;
						long nd = td[cur] + e[1];
						if (nd < td[next]) {
							td[next] = nd;
							q.update(next, nd);
						}
					}
					if(phase == 1){
						int next = e[0] + (phase + 1) * n;
						long nd = td[cur] + 2*e[1];
						if (nd < td[next]) {
							td[next] = nd;
							q.update(next, nd);
						}
					}
					if(phase == 0){
						int next = e[0] + (phase + 1) * n;
						long nd = td[cur];
						if (nd < td[next]) {
							td[next] = nd;
							q.update(next, nd);
						}
					}
				}
			}

			for(int i = 0;i < n;i++){
				ans[i] = Math.min(ans[i], td[2*n+i]);
			}
		}

		// min=max
		for(int[] e : g[0]){
			ans[e[0]] = Math.min(ans[e[0]], e[1]);
		}

		for(int i = 1;i < n;i++){
			out.print(ans[i] + " ");
		}
		out.println();
	}

	public static class MinHeapL {
		public long[] a;
		public int[] map;
		public int[] imap;
		public int n;
		public int pos;
		public static long INF = Long.MAX_VALUE;

		public MinHeapL(int m)
		{
			n = Integer.highestOneBit((m+1)<<1);
			a = new long[n];
			map = new int[n];
			imap = new int[n];
			Arrays.fill(a, INF);
			Arrays.fill(map, -1);
			Arrays.fill(imap, -1);
			pos = 1;
		}

		public long add(int ind, long x)
		{
			int ret = imap[ind];
			if(imap[ind] < 0){
				a[pos] = x; map[pos] = ind; imap[ind] = pos;
				pos++;
				up(pos-1);
			}
			return ret != -1 ? a[ret] : x;
		}

		public long update(int ind, long x)
		{
			int ret = imap[ind];
			if(imap[ind] < 0){
				a[pos] = x; map[pos] = ind; imap[ind] = pos;
				pos++;
				up(pos-1);
			}else{
				a[ret] = x;
				up(ret);
				down(ret);
			}
			return x;
		}

		public long remove(int ind)
		{
			if(pos == 1)return INF;
			if(imap[ind] == -1)return INF;

			pos--;
			int rem = imap[ind];
			long ret = a[rem];
			map[rem] = map[pos];
			imap[map[pos]] = rem;
			imap[ind] = -1;
			a[rem] = a[pos];
			a[pos] = INF;
			map[pos] = -1;

			up(rem);
			down(rem);
			return ret;
		}

		public long min() { return a[1]; }
		public int argmin() { return map[1]; }
		public int size() {	return pos-1; }

		private void up(int cur)
		{
			for(int c = cur, p = c>>>1;p >= 1 && a[p] > a[c];c>>>=1, p>>>=1){
				long d = a[p]; a[p] = a[c]; a[c] = d;
				int e = imap[map[p]]; imap[map[p]] = imap[map[c]]; imap[map[c]] = e;
				e = map[p]; map[p] = map[c]; map[c] = e;
			}
		}

		private void down(int cur)
		{
			for(int c = cur;2*c < pos;){
				int b = a[2*c] < a[2*c+1] ? 2*c : 2*c+1;
				if(a[b] < a[c]){
					long d = a[c]; a[c] = a[b]; a[b] = d;
					int e = imap[map[c]]; imap[map[c]] = imap[map[b]]; imap[map[b]] = e;
					e = map[c]; map[c] = map[b]; map[b] = e;
					c = b;
				}else{
					break;
				}
			}
		}
	}



	public static int[][][] packWU(int n, int[] from, int[] to, int[] w) {
		return packWU(n, from, to, w, from.length);
	}

	public static int[][][] packWU(int n, int[] from, int[] to, int[] w, int sup) {
		int[][][] g = new int[n][][];
		int[] p = new int[n];
		for (int i = 0; i < sup; i++) p[from[i]]++;
		for (int i = 0; i < sup; i++) p[to[i]]++;
		for (int i = 0; i < n; i++) g[i] = new int[p[i]][2];
		for (int i = 0; i < sup; i++) {
			--p[from[i]];
			g[from[i]][p[from[i]]][0] = to[i];
			g[from[i]][p[from[i]]][1] = w[i];
			--p[to[i]];
			g[to[i]][p[to[i]]][0] = from[i];
			g[to[i]][p[to[i]]][1] = w[i];
		}
		return g;
	}


	void run() throws Exception
	{
		is = oj ? System.in : new ByteArrayInputStream(INPUT.getBytes());
		out = new FastWriter(System.out);
		
		long s = System.currentTimeMillis();
		solve();
		out.flush();
		tr(System.currentTimeMillis()-s+"ms");
	}
	
	public static void main(String[] args) throws Exception { new E().run(); }
	
	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))){ // 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 int[] na(int n)
	{
		int[] a = new int[n];
		for(int i = 0;i < n;i++)a[i] = ni();
		return a;
	}

	private long[] nal(int n)
	{
		long[] a = new long[n];
		for(int i = 0;i < n;i++)a[i] = nl();
		return a;
	}

	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[][] nmi(int n, int m) {
		int[][] map = new int[n][];
		for(int i = 0;i < n;i++)map[i] = na(m);
		return map;
	}

	private int ni() { return (int)nl(); }

	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();
		}
	}

	public static class FastWriter
	{
		private static final int BUF_SIZE = 1<<13;
		private final byte[] buf = new byte[BUF_SIZE];
		private final OutputStream out;
		private int ptr = 0;

		private FastWriter(){out = null;}

		public FastWriter(OutputStream os)
		{
			this.out = os;
		}

		public FastWriter(String path)
		{
			try {
				this.out = new FileOutputStream(path);
			} catch (FileNotFoundException e) {
				throw new RuntimeException("FastWriter");
			}
		}

		public FastWriter write(byte b)
		{
			buf[ptr++] = b;
			if(ptr == BUF_SIZE)innerflush();
			return this;
		}

		public FastWriter write(char c)
		{
			return write((byte)c);
		}

		public FastWriter write(char[] s)
		{
			for(char c : s){
				buf[ptr++] = (byte)c;
				if(ptr == BUF_SIZE)innerflush();
			}
			return this;
		}

		public FastWriter write(String s)
		{
			s.chars().forEach(c -> {
				buf[ptr++] = (byte)c;
				if(ptr == BUF_SIZE)innerflush();
			});
			return this;
		}

		private static int countDigits(int l) {
			if (l >= 1000000000) return 10;
			if (l >= 100000000) return 9;
			if (l >= 10000000) return 8;
			if (l >= 1000000) return 7;
			if (l >= 100000) return 6;
			if (l >= 10000) return 5;
			if (l >= 1000) return 4;
			if (l >= 100) return 3;
			if (l >= 10) return 2;
			return 1;
		}

		public FastWriter write(int x)
		{
			if(x == Integer.MIN_VALUE){
				return write((long)x);
			}
			if(ptr + 12 >= BUF_SIZE)innerflush();
			if(x < 0){
				write((byte)'-');
				x = -x;
			}
			int d = countDigits(x);
			for(int i = ptr + d - 1;i >= ptr;i--){
				buf[i] = (byte)('0'+x%10);
				x /= 10;
			}
			ptr += d;
			return this;
		}

		private static int countDigits(long l) {
			if (l >= 1000000000000000000L) return 19;
			if (l >= 100000000000000000L) return 18;
			if (l >= 10000000000000000L) return 17;
			if (l >= 1000000000000000L) return 16;
			if (l >= 100000000000000L) return 15;
			if (l >= 10000000000000L) return 14;
			if (l >= 1000000000000L) return 13;
			if (l >= 100000000000L) return 12;
			if (l >= 10000000000L) return 11;
			if (l >= 1000000000L) return 10;
			if (l >= 100000000L) return 9;
			if (l >= 10000000L) return 8;
			if (l >= 1000000L) return 7;
			if (l >= 100000L) return 6;
			if (l >= 10000L) return 5;
			if (l >= 1000L) return 4;
			if (l >= 100L) return 3;
			if (l >= 10L) return 2;
			return 1;
		}

		public FastWriter write(long x)
		{
			if(x == Long.MIN_VALUE){
				return write("" + x);
			}
			if(ptr + 21 >= BUF_SIZE)innerflush();
			if(x < 0){
				write((byte)'-');
				x = -x;
			}
			int d = countDigits(x);
			for(int i = ptr + d - 1;i >= ptr;i--){
				buf[i] = (byte)('0'+x%10);
				x /= 10;
			}
			ptr += d;
			return this;
		}

		public FastWriter write(double x, int precision)
		{
			if(x < 0){
				write('-');
				x = -x;
			}
			x += Math.pow(10, -precision)/2;
			//		if(x < 0){ x = 0; }
			write((long)x).write(".");
			x -= (long)x;
			for(int i = 0;i < precision;i++){
				x *= 10;
				write((char)('0'+(int)x));
				x -= (int)x;
			}
			return this;
		}

		public FastWriter writeln(char c){
			return write(c).writeln();
		}

		public FastWriter writeln(int x){
			return write(x).writeln();
		}

		public FastWriter writeln(long x){
			return write(x).writeln();
		}

		public FastWriter writeln(double x, int precision){
			return write(x, precision).writeln();
		}

		public FastWriter write(int... xs)
		{
			boolean first = true;
			for(int x : xs) {
				if (!first) write(' ');
				first = false;
				write(x);
			}
			return this;
		}

		public FastWriter write(long... xs)
		{
			boolean first = true;
			for(long x : xs) {
				if (!first) write(' ');
				first = false;
				write(x);
			}
			return this;
		}

		public FastWriter writeln()
		{
			return write((byte)'\n');
		}

		public FastWriter writeln(int... xs)
		{
			return write(xs).writeln();
		}

		public FastWriter writeln(long... xs)
		{
			return write(xs).writeln();
		}

		public FastWriter writeln(char[] line)
		{
			return write(line).writeln();
		}

		public FastWriter writeln(char[]... map)
		{
			for(char[] line : map)write(line).writeln();
			return this;
		}

		public FastWriter writeln(String s)
		{
			return write(s).writeln();
		}

		private void innerflush()
		{
			try {
				out.write(buf, 0, ptr);
				ptr = 0;
			} catch (IOException e) {
				throw new RuntimeException("innerflush");
			}
		}

		public void flush()
		{
			innerflush();
			try {
				out.flush();
			} catch (IOException e) {
				throw new RuntimeException("flush");
			}
		}

		public FastWriter print(byte b) { return write(b); }
		public FastWriter print(char c) { return write(c); }
		public FastWriter print(char[] s) { return write(s); }
		public FastWriter print(String s) { return write(s); }
		public FastWriter print(int x) { return write(x); }
		public FastWriter print(long x) { return write(x); }
		public FastWriter print(double x, int precision) { return write(x, precision); }
		public FastWriter println(char c){ return writeln(c); }
		public FastWriter println(int x){ return writeln(x); }
		public FastWriter println(long x){ return writeln(x); }
		public FastWriter println(double x, int precision){ return writeln(x, precision); }
		public FastWriter print(int... xs) { return write(xs); }
		public FastWriter print(long... xs) { return write(xs); }
		public FastWriter println(int... xs) { return writeln(xs); }
		public FastWriter println(long... xs) { return writeln(xs); }
		public FastWriter println(char[] line) { return writeln(line); }
		public FastWriter println(char[]... map) { return writeln(map); }
		public FastWriter println(String s) { return writeln(s); }
		public FastWriter println() { return writeln(); }
	}

	public void trnz(int... o)
	{
		for(int i = 0;i < o.length;i++)if(o[i] != 0)System.out.print(i+":"+o[i]+" ");
		System.out.println();
	}

	// print ids which are 1
	public void trt(long... o)
	{
		Queue<Integer> stands = new ArrayDeque<>();
		for(int i = 0;i < o.length;i++){
			for(long x = o[i];x != 0;x &= x-1)stands.add(i<<6|Long.numberOfTrailingZeros(x));
		}
		System.out.println(stands);
	}

	public void tf(boolean... r)
	{
		for(boolean x : r)System.out.print(x?'#':'.');
		System.out.println();
	}

	public void tf(boolean[]... b)
	{
		for(boolean[] r : b) {
			for(boolean x : r)System.out.print(x?'#':'.');
			System.out.println();
		}
		System.out.println();
	}

	public void tf(long[]... b)
	{
		if(INPUT.length() != 0) {
			for (long[] r : b) {
				for (long x : r) {
					for (int i = 0; i < 64; i++) {
						System.out.print(x << ~i < 0 ? '#' : '.');
					}
				}
				System.out.println();
			}
			System.out.println();
		}
	}

	public void tf(long... b)
	{
		if(INPUT.length() != 0) {
			for (long x : b) {
				for (int i = 0; i < 64; i++) {
					System.out.print(x << ~i < 0 ? '#' : '.');
				}
			}
			System.out.println();
		}
	}

	private boolean oj = System.getProperty("ONLINE_JUDGE") != null;
	private void tr(Object... o) { if(!oj)System.out.println(Arrays.deepToString(o)); }
}