Marmot found a row with n pillars. The i-th pillar has the height of h_i meters. Starting from one pillar i₁, Marmot wants to jump on the pillars i₂, ..., i_k. (1 ≤ i₁ < i₂ < ... < 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 ≤ 10⁵, 0 ≤ d ≤ 10⁹).

The second line contains n numbers h₁, h₂, ..., h_n (1 ≤ h_i ≤ 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, ..., i_k (1 ≤ i₁ < i₂ < ... < 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.