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

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