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E. Pillars
time limit per test
1 second
memory limit per test
256 megabytes
input
standard input
output
standard output

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 ≤ 105, 0 ≤ d ≤ 109).

The second line contains n numbers h 1, h 2, ..., h n (1 ≤ h i ≤ 1015).

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.

Examples
Input
5 21 3 6 7 4
Output
41 2 3 5
Input
10 32 1 3 6 9 11 7 3 20 18
Output
61 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.