Package for this problem was not updated by the problem writer or Codeforces administration after we’ve upgraded the judging servers. To adjust the time limit constraint, solution execution time will be multiplied by 2. For example, if your solution works for 400 ms on judging servers, then value 800 ms will be displayed and used to determine the verdict.

Virtual contest is a way to take part in past contest, as close as possible to participation on time. It is supported only ACM-ICPC mode for virtual contests.
If you've seen these problems, a virtual contest is not for you - solve these problems in the archive.
If you just want to solve some problem from a contest, a virtual contest is not for you - solve this problem in the archive.
Never use someone else's code, read the tutorials or communicate with other person during a virtual contest.

No tag edit access

E. Multithreading

time limit per test

2 secondsmemory limit per test

256 megabytesinput

standard inputoutput

standard outputYou are given the following concurrent program. There are *N* processes and the *i*-th process has the following pseudocode:

repeatn_{i}times

y_{i}:=y

y:=y_{i}+ 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 *n*_{i}, 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* ( - 10^{9} ≤ *W* ≤ 10^{9}). In the second line there are *N* space separated integers *n*_{i} (1 ≤ *n*_{i} ≤ 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} *n*_{i} numbers.

Codeforces (c) Copyright 2010-2017 Mike Mirzayanov

The only programming contests Web 2.0 platform

Server time: May/01/2017 03:34:44 (p1).

Desktop version, switch to mobile version.
User lists

Name |
---|