2022 was a difficult year for the Bajtcorp company. Poor business decisions combined with an uninteresting market situation meant that the company could not afford raises for its employees. In preparation for uncomfortable questions from employees, the HR department invented a way to prove that an employee does not deserve a raise.

Based on data regarding the total revenue generated by an employee on consecutive days, it is possible to divide the year (which in Bajtocia does not necessarily have 365 days) into time intervals that indicate that the employee is not developing at work. More precisely, the HR department would like to divide the sequence of revenues into $k$ contiguous intervals such that each element of the sequence belongs to exactly one interval. A partition is correct if it is not possible to select one element from each interval in such a way that the selected elements form a strictly increasing sequence.

The future of Bajtcorp is in your hands. Write a program that reads the sequence of revenues generated by an employee and the number $k$, and then divides it into $k$ intervals in accordance with the HR department's guidelines, or determines that it is impossible.

Input

The first line of standard input contains two integers $n$ and $k$ ($2 \le k \le n \le 500\,000$), representing the length of the revenue sequence generated by the employee and the required number of intervals, respectively.

The next line consists of $n$ integers $a_1, a_2, \dots, a_n$ ($1 \le a_i \le 10^9$), which form the revenue sequence.

Output

If it is not possible to divide the sequence according to the guidelines, the only line of output should contain the word ‘NIE’.

Otherwise, in the first line, print the word ‘TAK’, and in the second line, print a sequence of $k - 1$ integers $v_1, \dots, v_{k-1}$ ($1 \le v_i < n$; $v_i < v_{i+1}$), which are the indices of the ends of the consecutive intervals in a correct partition, excluding the end of the last interval, which always ends at index $n$.

If there are multiple correct answers, print any one of them.

Examples

Input 1

6 3
3 5 4 8 3 7

Output 1

TAK
3 5

Input 2

4 2
2 3 2 3

Output 2

NIE

Note

In the first example test, after dividing the sequence into intervals $[3, 5, 4]$, $[8, 3]$, and $[7]$, regardless of which element we choose in the first subsequence, in the second we would have to choose $8$ to form an increasing sequence. In the last subsequence, we have only one choice, which is not greater than $8$, so we are unable to create an increasing sequence, and the partition is in accordance with the guidelines.