Please note that the memory limit differs from the standard.

You really love to listen to music. During the each of next s days you will listen to exactly m songs from the playlist that consists of exactly n songs. Let's number the songs from the playlist with numbers from 1 to n, inclusive. The quality of song number i is a_i.

On the i-th day you choose some integer v (l_i≤v≤r_i) and listen to songs number v,v+1,...,v+m-1. On the i-th day listening to one song with quality less than q_i increases your displeasure by exactly one.

Determine what minimum displeasure you can get on each of the s next days.

The first line contains two positive integers n, m (1≤m≤n≤2·10⁵). The second line contains n positive integers a₁,a₂,...,a_n (0≤a_i<2³⁰) − the description of songs from the playlist.

The next line contains a single number s (1≤s≤2·10⁵) − the number of days that you consider.

The next s lines contain three integers each l_i,r_i,x_i (1≤l_i≤r_i≤n-m+1; 0≤x_i<2³⁰) − the description of the parameters for the i-th day. In order to calculate value q_i, you need to use formula: , where ans_i is the answer to the problem for day i. Assume that ans₀=0.

Print exactly s integers ans₁,ans₂,...,ans_s, where ans_i is the minimum displeasure that you can get on day i.