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.

输入描述:

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).

输出描述:

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.

备注:

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.