Problem: You are given the following concurrent program. There are N processes and the i-th process has the following pseudocode: 
    
    
    repeat ni times  
        yi := y  
        y := yi + 1  
    end repeat  
    

Here y is a shared variable. Everything else is local for the process. All actions on a given row are atomic, i.e. when the process starts executing a row it is never interrupted. Beyond that all interleavings are possible, i.e. every process that has yet work to do can be granted the rights to execute its next row. In the beginning y = 0. You will be given an integer W and ni, for i = 1, ... , N. Determine if it is possible that after all processes terminate, y = W, and if it is possible output an arbitrary schedule that will produce this final value.

Input

In the first line of the input you will be given two space separated integers N (1 ≤ N ≤ 100) and W ( - 109 ≤ W ≤ 109). In the second line there are N space separated integers ni (1 ≤ ni ≤ 1000).

Output

On the first line of the output write Yes if it is possible that at the end y = W, or No otherwise. If the answer is No then there is no second line, but if the answer is Yes, then on the second line output a space separated list of integers representing some schedule that leads to the desired result. For more information see note.

Examples

Input

1 10
11


Output

No


Input

2 3
4 4


Output

Yes
1 1 2 1 2 2 2 2 2 1 2 1 1 1 1 2


Input

3 6
1 2 3


Output

Yes
1 1 2 2 2 2 3 3 3 3 3 3

Note

For simplicity, assume that there is no repeat statement in the code of the processes, but the code from the loop is written the correct amount of times. The processes are numbered starting from 1. The list of integers represent which process works on its next instruction at a given step. For example, consider the schedule 1 2 2 1 3. First process 1 executes its first instruction, then process 2 executes its first two instructions, after that process 1 executes its second instruction, and finally process 3 executes its first instruction. The list must consists of exactly 2·Σ i = 1...N ni numbers.

Solution (in JAVA):

Solution:
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.math.BigInteger;
import java.util.InputMismatchException;

/**
 * @author Egor Kulikov (egor@egork.net)
 *         Created on 14.03.2010
 */
public class TaskE implements Runnable {
	private InputReader in;
	private PrintWriter out;

	public static void main(String[] args) {
		new Thread(new TaskE()).start();
//		new Template().run();
	}

	public TaskE() {
//		String id = getClass().getName().toLowerCase();
//		try {
//			System.setIn(new FileInputStream(id + ".in"));
//			System.setOut(new PrintStream(new FileOutputStream(id + ".out")));
//			System.setIn(new FileInputStream("input.txt"));
//			System.setOut(new PrintStream(new FileOutputStream("output.txt")));
//		} catch (FileNotFoundException e) {
//			throw new RuntimeException();
//		}
		in = new InputReader(System.in);
		out = new PrintWriter(System.out);
	}

	public void run() {
//        int numTests = in.readInt();
//        for (int testNumber = 0; testNumber < numTests; testNumber++) {
//			out.print("Case " + (testNumber + 1) + ": ");
//        }
		int n = in.readInt();
		int w = in.readInt();
		int[] q = new int[n];
		for (int i = 0; i < n; i++)
			q[i] = in.readInt();
		int min = Integer.MAX_VALUE;
		int sum = 0;
		for (int i = 0; i < n; i++) {
			sum += q[i];
			min = Math.min(min, q[i]);
		}
		if (w < 2 && w < min || w > sum || w < min && n == 1) {
			out.println("No");
			out.close();
			return;
		}
		int c = 0;
		int[] ans = new int[2 * sum];
		if (w < min) {
			ans[c++] = 1;
			for (int i = 2; i < n; i++) {
				for (int j = 0; j < q[i]; j++) {
					ans[c++] = i + 1;
					ans[c++] = i + 1;
				}
			}
			for (int j = 0; j < q[1] - w + 1; j++) {
				ans[c++] = 2;
				ans[c++] = 2;
			}
			ans[c++] = 1;
			ans[c++] = 2;
			for (int j = 0; j < q[0] - 1; j++) {
				ans[c++] = 1;
				ans[c++] = 1;
			}
			ans[c++] = 2;
			for (int j = 0; j < w - 2; j++) {
				ans[c++] = 2;
				ans[c++] = 2;
			}
		} else {
			int y = 0;
			int pos = -1;
			for (int i = 0; i < n; i++) {
				if (q[i] == min)
					pos = i;
			}
			w -= min;
			for (int i = 0; i < n && y != w; i++) {
				if (i == pos)
					continue;
				for (; q[i] != 0 && y != w;) {
					y++;
					ans[c++] = i + 1;
					ans[c++] = i + 1;
					q[i]--;
				}
			}
			ans[c++] = pos + 1;
			for (int i = 0; i < n; i++) {
				if (i == pos)
					continue;
				for (int j = 0; j < q[i]; j++) {
					y++;
					ans[c++] = i + 1;
					ans[c++] = i + 1;
				}
			}
			for (int i = 0; i < 2 * q[pos] - 1; i++)
				ans[c++] = pos + 1;
		}
		out.println("Yes");
		out.print(ans[0]);
		for (int i = 1; i < ans.length; i++) {
			out.print(" " + ans[i]);
		}
		out.println();
		out.close();
	}

	private static class InputReader {
		private InputStream stream;
		private byte[] buf = new byte[1000];
		private int curChar, numChars;

		public InputReader(InputStream stream) {
			this.stream = stream;
		}

		private 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++];
		}

		public int readInt() {
			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;
		}

		public long readLong() {
			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;
		}

		public String readString() {
			int c = read();
			while (isSpaceChar(c))
				c = read();
			StringBuffer res = new StringBuffer();
			do {
				res.appendCodePoint(c);
				c = read();
			} while (!isSpaceChar(c));
			return res.toString();
		}

		private boolean isSpaceChar(int c) {
			return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
		}

		private String readLine0() {
			StringBuffer buf = new StringBuffer();
			int c = read();
			while (c != '\n' && c != -1) {
				buf.appendCodePoint(c);
				c = read();
			}
			return buf.toString();
		}

		public String readLine() {
			String s = readLine0();
			while (s.trim().length() == 0)
				s = readLine0();
			return s;
		}

		public String readLine(boolean ignoreEmptyLines) {
			if (ignoreEmptyLines)
				return readLine();
			else
				return readLine0();
		}

		public BigInteger readBigInteger() {
			try {
				return new BigInteger(readString());
			} catch (NumberFormatException e) {
				throw new InputMismatchException();
			}
		}

		public char readCharacter() {
			int c = read();
			while (isSpaceChar(c))
				c = read();
			return (char) c;
		}

		public double readDouble() {
			int c = read();
			while (isSpaceChar(c))
				c = read();
			int sgn = 1;
			if (c == '-') {
				sgn = -1;
				c = read();
			}
			double res = 0;
			while (!isSpaceChar(c) && c != '.') {
				if (c < '0' || c > '9')
					throw new InputMismatchException();
				res *= 10;
				res += c - '0';
				c = read();
			}
			if (c == '.') {
				c = read();
				double m = 1;
				while (!isSpaceChar(c)) {
					if (c < '0' || c > '9')
						throw new InputMismatchException();
					m /= 10;
					res += (c - '0') * m;
					c = read();
				}
			}
			return res * sgn;
		}
	}
}