Pillars
Description
Marmot found a row with n pillars. The i-th pillar has the height of hi meters. Starting from one pillar i1, Marmot wants to jump on the pillars i2, ..., ik. (1 ≤ i1 < i2 < ... < ik ≤ n). From a pillar i Marmot can jump on a pillar j only if i < j and |hi - hj| ≥ 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 ≤ 105, 0 ≤ d ≤ 109).
The second line contains n numbers h1, h2, ..., hn (1 ≤ hi ≤ 1015).
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.
Input
The first line contains two integers n and d (1 ≤ n ≤ 105, 0 ≤ d ≤ 109).
The second line contains n numbers h1, h2, ..., hn (1 ≤ hi ≤ 1015).
Output
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.
Samples
5 2
1 3 6 7 4
4
1 2 3 5
10 3
2 1 3 6 9 11 7 3 20 18
6
1 4 6 7 8 9
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.