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E. Listening to Music

time limit per test

7 secondsmemory limit per test

64 megabytesinput

standard inputoutput

standard outputPlease 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.

Input

The first line contains two positive integers *n*, *m* (1 ≤ *m* ≤ *n* ≤ 2·10^{5}). The second line contains *n* positive integers *a*_{1}, *a*_{2}, ..., *a*_{n} (0 ≤ *a*_{i} < 2^{30}) — the description of songs from the playlist.

The next line contains a single number *s* (1 ≤ *s* ≤ 2·10^{5}) — 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} < 2^{30}) — 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 *ans*_{0} = 0.

Output

Print exactly *s* integers *ans*_{1}, *ans*_{2}, ..., *ans*_{s}, where *ans*_{i} is the minimum displeasure that you can get on day *i*.

Examples

Input

5 3

1 2 1 2 3

5

1 1 2

1 3 2

1 3 3

1 3 5

1 3 1

Output

2

0

2

3

1

Codeforces (c) Copyright 2010-2021 Mike Mirzayanov

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