Competitions

# K-th Number

You are working for Macrohard company in data structures department. After failing your previous task about key insertion you were asked to write a new data structure that would be able to return quickly k-th order statistics in the array segment.

That is, given an array a[1...n] of different integer numbers, your program must answer a series of questions Q(i, j, k) in the form: "What would be the k-th number in a[i...j] segment, if this segment was sorted?"

For example, consider the array a = (1, 5, 2, 6, 3, 7, 4). Let the question be Q(2, 5, 3). The segment a[2...5] is (5, 2, 6, 3). If we sort this segment, we get (2, 3, 5, 6), the third number is 5, and therefore the answer to the question is 5.

#### Input

The first line contains n - the size of the array, and m - the number of questions to answer (1n100000, 1m5000).

The second line contains n different integer numbers not exceeding `109` by their absolute values - the array for which the answers should be given.

The following m lines contain question descriptions, each description consists of three numbers: i, j and k (0ijn, 0kj - i + 1) and represents the question Q(i, j, k).

#### Output

For each question output the answer to it - the k-th number in sorted a[i...j] segment.

Time limit 1 second
Memory limit 128 MiB
Input example #1
```7 3
1 5 2 6 3 7 4
2 5 3
4 4 1
1 7 3
```
Output example #1
```5
6
3
```

Example description: This problem has huge input,so please use c-style input(scanf,printf),or you may got time limit exceed.

Source 2004 NEERC, Northern Subregion, October 30, Problem K