Multithreading

Description:

repeat ni times
    yi := y
    y := yi + 1
end repeat

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 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.

Sample Input:

1 10
11

Sample Output:

No

Sample Input:

2 3
4 4

Sample Output:

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

Sample Input:

3 6
1 2 3

Sample 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.