## MKTHNUM - K-th Number

English | Vietnamese |

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 10^9 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 ≤ i ≤ j ≤ n, 1 ≤ k ≤ j - i + 1) and represents the question Q(i, j, k).

SAMPLE INPUT 7 3 1 5 2 6 3 7 4 2 5 3 4 4 1 1 7 3

### Output

For each question output the answer to it — the k-th number in sorted a[i ... j] segment. SAMPLE OUTPUT 5 6 3

**Note : naive solution will not work!!!**

Added by: | ~!(*(@*!@^& |

Date: | 2009-02-24 |

Time limit: | 0.115s-0.667s |

Source limit: | 50000B |

Memory limit: | 1536MB |

Cluster: | Cube (Intel G860) |

Languages: | All except: ERL JS-RHINO |

Resource: | Northeastern Europe 2004 Northern Subregion |