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.

Input

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

The second line contains $*n*$ numbers $*h*_{1}, *h*_{2}, ..., *h*_{*n*}$ ($1 ≤ *h*_{*i*} ≤ 10^{15}$).

Output

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

The second line should contain $*k*$ integers $*i*_{1}, *i*_{2}, ..., *i*_{*k*}$ ($1 ≤ *i*_{1} < *i*_{2} < ... < *i*_{*k*} ≤ *n*$), representing the pillars' indices from the maximal length jump sequence.

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

Note

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 $1$, $2$, $4$, $5$.