Problem: The Alice's computer is broken, so she can't play her favorite card game now. To help Alice, Bob wants to answer n her questions. 

Initially, Bob holds one card with number 0 in the left hand and one in the right hand. In the i-th question, Alice asks Bob to replace a card in the left or right hand with a card with number k_i (Bob chooses which of two cards he changes, Bob must replace exactly one card).

After this action, Alice wants the numbers on the left and right cards to belong to given segments (segments for left and right cards can be different). Formally, let the number on the left card be x, and on the right card be y. Then after the i-th swap the following conditions must be satisfied: a_{l, i} ≤ x ≤ b_{l, i}, and a_{r, i} ≤ y ≤ b_{r,i}.

Please determine if Bob can answer all requests. If it is possible, find a way to do it.

Input

The first line contains two integers n and m (2 ≤ n ≤ 100 000, 2 ≤ m ≤ 10^9) — the number of questions and the maximum possible value on the card.

Then n queries are described. Every description contains 3 lines.

The first line of the description of the i-th query contains a single integer k_i (0 ≤ k_i ≤ m) — the number on a new card.

The second line of the description of the i-th query contains two integers a_{l, i} and b_{l, i} (0 ≤ a_{l, i} ≤ b_{l, i} ≤ m) — the minimum and maximum values of the card at the left hand after the replacement.

The third line of the description of the i-th query contains two integers a_{r, i} and b_{r,i} (0 ≤ a_{r, i} ≤ b_{r,i} ≤ m) — the minimum and maximum values of the card at the right hand after the replacement.

Output

At the first line, print "Yes", if Bob can answer all queries, and "No" otherwise.

If Bob can answer all n queries, then at the second line print n numbers: a way to satisfy all requirements. If in i-th query Bob needs to replace the card in the left hand, print 0, otherwise print 1. If there are multiple answers, print any.

Examples

Input


2 10
3
0 3
0 2
2
0 4
0 2


Output


Yes
0 1 

Input


2 10
3
0 3
0 2
2
3 4
0 1


Output


No

Input


5 10
3
0 3
0 3
7
4 7
1 3
2
2 3
3 7
8
1 8
1 8
6
1 6
7 10


Output


Yes
1 0 0 1 0 

Solution (in JAVA):

Solution:
//package round727;
import java.io.*;
import java.util.*;

public class E {
	InputStream is;
	FastWriter out;
	String INPUT = "";
	
	void solve()
	{
		int n = ni(), m = ni();
		int[] ks = new int[n];
		int[][] rs = new int[n][];
		for(int i = 0;i < n;i++){
			ks[i] = ni();
			rs[i] = na(4);
		}
		int[] xs = new int[5*n+1];
		int p = 0;
		for(int i = 0;i < n;i++){
			xs[p++] = ks[i];
		}
		for(int i = 0;i < n;i++){
			for(int j = 0;j < 4;j++){
				xs[p++] = rs[i][j];
			}
		}

		xs = shrink(xs);

		p = 0;
		for(int i = 0;i < n;i++){
			ks[i] = xs[p++];
		}
		for(int i = 0;i < n;i++){
			for(int j = 0;j < 4;j++){
				rs[i][j] = xs[p++];
			}
		}

		int[] L = new int[5*n+1];
		int[] R = new int[5*n+1];
		Arrays.fill(L, -1);
		Arrays.fill(R, -1);

		long[] lhist = new long[2*n+4];
		int[] lv = new int[2*n+4];
		long[] rhist = new long[2*n+4];
		int[] rv = new int[2*n+4];
		int lp = 0, rp =  0;

		LST lfix = new LST(5*n+1);
		LST rfix = new LST(5*n+1);
		rfix.set(0);
		R[0] = 0;
		rhist[rp] = 0L<<32|0; rv[rp] = -1; rp++;

		for(int i = 0;i < n;i++){
			int preval = i == 0 ? 0 : ks[i-1];
			boolean rr = rfix.next(0) != -1;
			int rn = rfix.next(0);
			boolean ll = lfix.next(0) != -1;
			int ln = lfix.next(0);
			if(rr){
				lfix.set(preval);
				lhist[lp] = (long)(i+1)<<32|preval; lv[lp] = L[preval]; lp++;
				L[preval] = rn;
			}
			if(ll){
				rfix.set(preval);
				rhist[rp] = (long)(i+1)<<32|preval; rv[rp] = R[preval]; rp++;
				R[preval] = ln;
			}
			if(rs[i][0] <= ks[i] && ks[i] <= rs[i][1]){
				while(true){
					int ne = lfix.next(0);
					if(ne != -1 && ne < rs[i][2]){
						lfix.unset(ne);
						lhist[lp] = (long)(i+1)<<32|ne; lv[lp] = L[ne]; lp++;
						L[ne] = -1;
					}else{
						break;
					}
				}
				while(true){
					int ne = lfix.prev(5*n);
					if(ne != -1 && ne > rs[i][3]){
						lfix.unset(ne);
						lhist[lp] = (long)(i+1)<<32|ne; lv[lp] = L[ne]; lp++;
						L[ne] = -1;
					}else{
						break;
					}
				}
			}else{
				while(true){
					int ne = lfix.next(0);
					if(ne != -1){
						lfix.unset(ne);
						lhist[lp] = (long)(i+1)<<32|ne; lv[lp] = L[ne]; lp++;
						L[ne] = -1;
					}else{
						break;
					}
				}
			}

			if(rs[i][2] <= ks[i] && ks[i] <= rs[i][3]){
				while(true){
					int ne = rfix.next(0);
					if(ne != -1 && ne < rs[i][0]){
						rfix.unset(ne);
						rhist[rp] = (long)(i+1)<<32|ne; rv[rp] = R[ne]; rp++;
						R[ne] = -1;
					}else{
						break;
					}
				}
				while(true){
					int ne = rfix.prev(5*n);
					if(ne != -1 && ne > rs[i][1]){
						rfix.unset(ne);
						rhist[rp] = (long)(i+1)<<32|ne; rv[rp] = R[ne]; rp++;
						R[ne] = -1;
					}else{
						break;
					}
				}
			}else{
				while(true){
					int ne = rfix.next(0);
					if(ne != -1){
						rfix.unset(ne);
						rhist[rp] = (long)(i+1)<<32|ne; rv[rp] = R[ne]; rp++;
						R[ne] = -1;
					}else{
						break;
					}
				}
			}
//			tr(lfix);
//			tr(rfix);
//			tr(lp, rp);
		}

//		tr(lhist);
//		tr(lv);
//		tr(rhist);
//		tr(rv);

		if(lfix.next(0) == -1 && rfix.next(0) == -1){
			out.println("No");
			return;
		}
		out.println("Yes");
//		tr(lfix, rfix, ks, rs);
		int[] route = new int[n];

		int other = 0;
		int isrfix = 0;
		if(lfix.next(0) != -1){
			isrfix = 0;
			other = lfix.next(0);
		}else{
			isrfix = 1;
			other = rfix.next(0);
		}
		for(int i = n-1;i >= 0;i--){
			route[i] = isrfix;
//			tr(isrfix, other, lfix, rfix);
			int from = isrfix == 1 ? R[other] : L[other];

			while(rp > 0 && rhist[rp-1]>>>32 >= i+1){
				int pos = (int)rhist[rp-1];
				int val = rv[rp-1];
				if(val >= 0){
					rfix.set(pos);
				}else{
					rfix.unset(pos);
				}
				R[pos] = val;
				rp--;
			}
			while(lp > 0 && lhist[lp-1]>>>32 >= i+1){
				int pos = (int)lhist[lp-1];
				int val = lv[lp-1];
				if(val >= 0){
					lfix.set(pos);
				}else{
					lfix.unset(pos);
				}
				L[pos] = val;
				lp--;
			}

			if(isrfix == 1){
				if(rfix.get(other)){
				}else{
					isrfix ^= 1;
					other = from;
				}
			}else{
				if(lfix.get(other)){
				}else{
					isrfix ^= 1;
					other = from;
				}
			}
		}
//		tr(isrfix, other);
		out.println(route);
	}

	public static class LST {
		public long[][] set;
		public int n;
		//	public int size;

		public LST(int n) {
			this.n = n;
			int d = 1;
			for(int m = n;m > 1;m>>>=6, d++);

			set = new long[d][];
			for(int i = 0, m = n>>>6;i < d;i++, m>>>=6){
				set[i] = new long[m+1];
			}
			//		size = 0;
		}

		// [0,r)
		public LST setRange(int r)
		{
			for(int i = 0;i < set.length;i++, r=r+63>>>6){
				for(int j = 0;j < r>>>6;j++){
					set[i][j] = -1L;
				}
				if((r&63) != 0)set[i][r>>>6] |= (1L<<r)-1;
			}
			return this;
		}

		// [0,r)
		public LST unsetRange(int r)
		{
			if(r >= 0){
				for(int i = 0;i < set.length;i++, r=r+63>>>6){
					for(int j = 0;j < r+63>>>6;j++){
						set[i][j] = 0;
					}
					if((r&63) != 0)set[i][r>>>6] &= ~((1L<<r)-1);
				}
			}
			return this;
		}

		public LST set(int pos)
		{
			if(pos >= 0 && pos < n){
				//			if(!get(pos))size++;
				for(int i = 0;i < set.length;i++, pos>>>=6){
					set[i][pos>>>6] |= 1L<<pos;
				}
			}
			return this;
		}

		public LST unset(int pos)
		{
			if(pos >= 0 && pos < n){
				//			if(get(pos))size--;
				for(int i = 0;i < set.length && (i == 0 || set[i-1][pos] == 0L);i++, pos>>>=6){
					set[i][pos>>>6] &= ~(1L<<pos);
				}
			}
			return this;
		}

		public boolean get(int pos)
		{
			return pos >= 0 && pos < n && set[0][pos>>>6]<<~pos<0;
		}

		public LST toggle(int pos)
		{
			return get(pos) ? unset(pos) : set(pos);
		}

		public int prev(int pos)
		{
			for(int i = 0;i < set.length && pos >= 0;i++, pos>>>=6, pos--){
				int pre = prev(set[i][pos>>>6], pos&63);
				if(pre != -1){
					pos = pos>>>6<<6|pre;
					while(i > 0)pos = pos<<6|63-Long.numberOfLeadingZeros(set[--i][pos]);
					return pos;
				}
			}
			return -1;
		}

		public int next(int pos)
		{
			for(int i = 0;i < set.length && pos>>>6 < set[i].length;i++, pos>>>=6, pos++){
				int nex = next(set[i][pos>>>6], pos&63);
				if(nex != -1){
					pos = pos>>>6<<6|nex;
					while(i > 0)pos = pos<<6|Long.numberOfTrailingZeros(set[--i][pos]);
					return pos;
				}
			}
			return -1;
		}

		private static int prev(long set, int n)
		{
			long h = set<<~n;
			if(h == 0L)return -1;
			return -Long.numberOfLeadingZeros(h)+n;
		}

		private static int next(long set, int n)
		{
			long h = set>>>n;
			if(h == 0L)return -1;
			return Long.numberOfTrailingZeros(h)+n;
		}

		@Override
		public String toString()
		{
			List<Integer> list = new ArrayList<Integer>();
			for(int pos = next(0);pos != -1;pos = next(pos+1)){
				list.add(pos);
			}
			return list.toString();
		}
	}


	public static int[] shrink(int[] a) {
		int n = a.length;
		long[] b = new long[n];
		for (int i = 0; i < n; i++) b[i] = (long) a[i] << 32 | i;
		Arrays.sort(b);
		int[] ret = new int[n];
		int p = 0;
		for (int i = 0; i < n; i++) {
			if (i > 0 && (b[i] ^ b[i - 1]) >> 32 != 0) p++;
			ret[(int) b[i]] = p;
		}
		return ret;
	}


	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)); }
}