Note: This is an approximate problem. There is no exact solution. You must find the most optimal solution. Please, take a look at the sample explanation to ensure that you understand the problem correctly.

Problem statement

Given an array A of N integers. We need to decompose A into K consecutive non empty subarrays such that every integer is present in only one subarray.

Say subarrays are S[1], S[2], S[3], .... , S[K]. Choose an array B , which is a permutation of 1 to K i.e. it is of size K and include every element from 1 to K.

Now, form a new array V = S[B[1]] + S[B[2]] + ......  + S[B[K]]. 

Aim is to maximize X for array V.

• \(X = LIS \times LDS - LIS \oplus LDS\), where \(\oplus\) denotes bitwise xor operator.

Note:

• 1 based indexing is followed.
• LIS stands for longest increasing subsequence of \(V\) i.e. every element in the subsequence is greater than the previous one.
• LDS stands for longest decreasing subsequence of \(V\) i.e. every element in the subsequence is less than the previous one.

Input format

• First line contains two space-separated integers : N and K 
• Second line contains N space-separated integers denoting the array A. 

Output format

• In the first K lines, print one integer denoting end index of i-th subarray (indexes are 1 based).
• In next line print K space separated integers, denoting array B (permutation of 1 to K)
• End index of subarrays should be in increasing order.

Verdict and scoring

• Your score is equal to the sum of the values of all test files. The value of each test file is equal to the value of X that you found.

  If decomposition of array A is invalid, or array B is invalid you will receive a wrong answer verdict.

Constraints

• \(N = 10^3\)
• \(50 \le K \le 10^2\)
• \(1 \le A[i] \le 10^5\)