1363A · Odd Selection

Problem: Shubham has an array $a$ of size $n$, and wants to select exactly $x$ elements from it, such that their sum is odd. These elements do not have to be consecutive. The elements of the array are not guaranteed to be distinct.

Tell him whether he can do so.

Input Format: The first line of the input contains a single integer $t$ $(1\le t \le 100)$ — the number of test cases. The description of the test cases follows.

The first line of each test case contains two integers $n$ and $x$ $(1 \le x \le n \le 1000)$ — the length of the array and the number of elements you need to choose.

The next line of each test case contains $n$ integers $a_1, a_2, \dots, a_n$ $(1 \le a_i \le 1000)$ — elements of the array.

Output Format: For each test case, print "Yes" or "No" depending on whether it is possible to choose $x$ elements such that their sum is odd.

You may print every letter in any case you want.

Note: For $1$st case: We must select element $999$, and the sum is odd.

For $2$nd case: We must select element $1000$, so overall sum is not odd.

For $3$rd case: We can select element $51$.

For $4$th case: We must select both elements $50$ and $51$  — so overall sum is odd.

For $5$th case: We must select all elements  — but overall sum is not odd.