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 ai.

On the i-th day you choose some integer v (li \le v \le ri) and listen to songs number v,v+1,...,v+m-1. On the i-th day listening to one song with quality less than qi 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 \le m \le n \le 2 \cdot 105). The second line contains n positive integers a1,a2,...,an (0 \le ai \lt 230) - the description of songs from the playlist.

The next line contains a single number s (1 \le s \le 2 \cdot 105) - the number of days that you consider.

The next s lines contain three integers each li,ri,xi (1 \le li \le ri \le n-m+1; 0 \le xi \lt 230) - the description of the parameters for the i-th day. In order to calculate value qi, you need to use formula: , where ansi is the answer to the problem for day i. Assume that ans0=0.

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