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2722.   K-th Number
Time Limit: 10.0 Seconds   Memory Limit: 65536K
Total Runs: 1299   Accepted Runs: 364    Multiple test files
Case Time Limit: 2.0 Seconds

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 of the input contains n — the size of the array, and m — the number of questions to answer (1 ≤ n ≤ 100000, 1 ≤ m ≤ 5000).

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 (1 ≤ ijn, 1 ≤ kj - 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.

### Sample Input

7 3
1 5 2 6 3 7 4
2 5 3
4 4 1
1 7 3


### Sample Output

5
6
3


Source: Northeastern Europe 2004 Northern Subregion
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