A9588. Pillars

Marmot found a row with $n$ pillars. The $i$ -th pillar has the height of $h_{i}$ meters. Starting from one pillar $i_{1}$ , Marmot wants to jump on the pillars $i_{2}$ , ..., $i_{k}$ . ( $1<=i_{1}<i_{2}<...<i_{k}<=n$ ). From a pillar $i$ Marmot can jump on a pillar $j$ only if $i<j$ and $|h_{i}-h_{j}|>=d$ , where $|x|$ is the absolute value of the number $x$ .

Now Marmot is asking you find out a jump sequence with maximal length and print it.

The first line contains two integers n and d (1 ≤ n ≤ 10^5, 0 ≤ d ≤ 10^9).

The second line contains n numbers h1, h2, ..., hn (1 ≤ hi ≤ 10^15).

The first line should contain one integer k, the maximal length of a jump sequence.

The second line should contain k integers i1, i2, ..., ik (1 ≤ i1 < i2 < ... < ik ≤ n), representing the pillars' indices from the maximal length jump sequence.

If there is more than one maximal length jump sequence, print any.

In the first example Marmot chooses the pillars $1$ , $2$ , $3$ , $5$ with the heights $1$ , $3$ , $6$ , $4$ . Another jump sequence of length $4$ is $1$ , $2$ , $4$ , $5$ .