Odd Sum Segments
Contest: Codeforces Round 575 (Div. 3)
Difficulty rating: 1200
Tags: constructive algorithms, math

You are given an array $$$a$$$ consisting of $$$n$$$ integers $$$a_1, a_2, \dots, a_n$$$. You want to split it into exactly $$$k$$$ non-empty non-intersecting subsegments such that each subsegment has odd sum (i. e. for each subsegment, the sum of all elements that belong to this subsegment is odd). It is impossible to rearrange (shuffle) the elements of a given array. Each of the $$$n$$$ elements of the array $$$a$$$ must belong to exactly one of the $$$k$$$ subsegments.

Let's see some examples of dividing the array of length $$$5$$$ into $$$3$$$ subsegments (not necessarily with odd sums): $$$[1, 2, 3, 4, 5]$$$ is the initial array, then all possible ways to divide it into $$$3$$$ non-empty non-intersecting subsegments are described below:

- $$$[1], [2], [3, 4, 5]$$$;
- $$$[1], [2, 3], [4, 5]$$$;
- $$$[1], [2, 3, 4], [5]$$$;
- $$$[1, 2], [3], [4, 5]$$$;
- $$$[1, 2], [3, 4], [5]$$$;
- $$$[1, 2, 3], [4], [5]$$$.

Of course, it can be impossible to divide the initial array into exactly $$$k$$$ subsegments in such a way that each of them will have odd sum of elements. In this case print "NO". Otherwise, print "YES" and any possible division of the array. See the output format for the detailed explanation.

You have to answer $$$q$$$ independent queries.

Input format:
The first line contains one integer $$$q$$$ ($$$1 \le q \le 2 \cdot 10^5$$$) — the number of queries. Then $$$q$$$ queries follow.

The first line of the query contains two integers $$$n$$$ and $$$k$$$ ($$$1 \le k \le n \le 2 \cdot 10^5$$$) — the number of elements in the array and the number of subsegments, respectively.

The second line of the query contains $$$n$$$ integers $$$a_1, a_2, \dots, a_n$$$ ($$$1 \le a_i \le 10^9$$$), where $$$a_i$$$ is the $$$i$$$-th element of $$$a$$$.

It is guaranteed that the sum of $$$n$$$ over all queries does not exceed $$$2 \cdot 10^5$$$ ($$$\sum n \le 2 \cdot 10^5$$$).

Output format:
For each query, print the answer to it. If it is impossible to divide the initial array into exactly $$$k$$$ subsegments in such a way that each of them will have odd sum of elements, print "NO" in the first line. Otherwise, print "YES" in the first line and any possible division of the array in the second line. The division can be represented as $$$k$$$ integers $$$r_1$$$, $$$r_2$$$, ..., $$$r_k$$$ such that $$$1 \le r_1 < r_2 < \dots < r_k = n$$$, where $$$r_j$$$ is the right border of the $$$j$$$-th segment (the index of the last element that belongs to the $$$j$$$-th segment), so the array is divided into subsegments $$$[1; r_1], [r_1 + 1; r_2], [r_2 + 1, r_3], \dots, [r_{k - 1} + 1, n]$$$. Note that $$$r_k$$$ is always $$$n$$$ but you should print it anyway.

Constraints:
Time limit: 3.0 s
Memory limit: 256.0 MB

Example input:
3
5 3
7 18 3 14 1
5 4
1 2 3 4 5
6 2
1 2 8 4 10 2

Example output:
YES
1 3 5
NO
NO

Editorial:
Firstly, let $$$cnt$$$ be the number of odd elements in the array. Note that even elements are don't matter at all because they cannot change the parity of the sum.
If $$$cnt < k$$$ then it is obviously impossible to split the given array into $$$k$$$ subsegments with odd sum. And if $$$cnt \% 2 \ne k \% 2$$$ then it is impossible to split the array into $$$k$$$ subsegments with odd sum also because at least one of $$$k$$$ segments will have even number of odd elements (so will have odd sum).
In other cases the answer is always "YES" and you can print $$$k-1$$$ leftmost positions of odd elements and $$$n$$$ as right borders of segments (it means that when you find one odd element, you end one segment). Because $$$cnt \% 2 = k \% 2$$$ now, the last segment will have odd number of odd elements so it will have odd sum also.