Problem Statement

You are given integers $N$, $K$, and a sequence $A = (A_1, \ldots, A_N)$ of length $N$.

Determine whether it is possible to make $A$ non-decreasing by performing the following operation at most $500000$ times, and if possible, provide one sequence of operations to do so.

• Choose an integer $i$ between $1$ and $N-1$, inclusive. Simultaneously replace $A_i$ with $A_{i+1} + K$, and $A_{i+1}$ with $A_i$.

Constraints

• All input numbers are integers.
• $2 \leq N \leq 50$
• $1 \leq K \leq 50$
• $1 \leq A_i \leq 50$

Input

The input is given from Standard Input in the following format:

N K
A_1 \ldots A_N

Output

If it is impossible to make $A$ non-decreasing within $500000$ operations, print No. Otherwise, print a solution in the following format, where $M$ is the number of operations $(0 \leq M \leq 500000)$, and $i_k$ is the $i$ chosen in the $k$-th operation $(1 \leq k \leq M)$:

Yes
M
i_1 \ldots i_M

If multiple valid solutions exist, any of them will be considered correct.