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

The first line of the input contains a single integer t (1≤ t ≤ 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 ≤ x ≤ n ≤ 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, ..., a_n (1 ≤ a_i ≤ 1000) — elements of the array.

Output

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.

Example

Input


5
1 1
999
1 1
1000
2 1
51 50
2 2
51 50
3 3
101 102 103


Output


Yes
No
Yes
Yes
No

Note

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

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

For 3rd case: We can select element 51.

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

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

Solution (in JAVA):

Solution:
import java.io.*;
import java.util.*;

public class Main
{   
    // static int findMinSubscriptions(int[] shows, int k, int d)
    // {
    //     int min = k, crr = 0;
    //     HashMap<Integer,Integer> subscribed = new HashMap<>();

    //     for(int i=0; i<shows.length; i++)
    //     {
    //         if(i < d)
    //         {
    //             if(subscribed.get(shows[i]) != null)
    //                 subscribed.put(shows[i],subscribed.get(shows[i])+1);
		  //      else
		  //      {
		  //          subscribed.put(shows[i],1);
		  //          crr++;
		  //      }
		  //      if(i == d - 1) min = crr;
    //         }
    //         else
    //         {
    //             subscribed.put(shows[i-d],subscribed.get(shows[i-d])-1);
                
    //             if(subscribed.get(shows[i-d]) == 0)
    //             {
    //                 subscribed.remove(shows[i-d]);
    //                 crr--;
    //             }
 
    //             if(subscribed.get(shows[i]) != null)
    //                 subscribed.put(shows[i], subscribed.get(shows[i])+1);
    //             else
    //             {
    //                 subscribed.put(shows[i],1);
    //                 crr++;
    //             }

    //             min = Math.min(crr,min);
    //         }
    //     }
    //     return min;
    // }
    
    public static void main(String[] args) throws IOException 
	{
        BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
		StringTokenizer st = new StringTokenizer(br.readLine());
		int t = Integer.parseInt(st.nextToken()), n,x;
		
        while(t-- > 0)
        {
            st = new StringTokenizer(br.readLine());
            n = Integer.parseInt(st.nextToken());
            x = Integer.parseInt(st.nextToken());
		    int[] arr = new int[n];
            int odd = 0, even = 0;
            
		    st = new StringTokenizer(br.readLine());
		    for(int i=0; i<n; i++)
		    {
		        arr[i] = Integer.parseInt(st.nextToken());
		        if(arr[i] %2 == 0) even++;
		        else odd++;
		    }
		    if(odd %2 == 0 && odd > 0) odd--;
		    if(odd %2 == 1 && even == 0 && x %2 == 0) System.out.println("No");
		    else if(odd %2 == 1 && even >= Math.max(x - odd,0)) System.out.println("Yes");
		    else System.out.println("No");
		    //System.out.println(odd %2 == 1 && even >= Math.max(x - odd,0) ? "Yes": "No");
        }
    }

    static double findDistanceBetweenTwoPoints(int x1, int y1, int x2, int y2){
        return Math.sqrt(Math.pow(x2-x1,2) + Math.pow(y2-y1,2));
    }

    static int[] countLetterFreqeuncy(String str, int[] ltrs){
        for(int i=0; i<str.length(); i++)
            ltrs[(int) (str.charAt(i) - 'a')]++;
        return ltrs;
    }
	
    static long gcd(long a, long b) { 
        if (a == 0) 
            return b;  
        return gcd(b % a, a);  
    } 
      
    static long lcm(long a, long b) { 
        return (a*b)/
        gcd(a, b); 
    } 

    // Arrays.sort(arr, new Comparator<Integer[]>() {
    //     @Override
    //             //arguments to this method represent the arrays to be sorted   
    //     public int compare(Integer[] arr1, Integer[] arr2) {
    //             //get the item ids which are at index 0 of the array
    //             Integer item1 = arr1[0];
    //             Integer item2 = arr2[0];
    //         // sort based on price
    //         return item1.compareTo(item2);
    //     }
    // });

    //String.join("", Collections.nCopies(n-1, "");

    static int binarySearch(int left, int right, int find, int[] arr){
        int mid = left + (right-left)/2;
        if(find == arr[mid]) return mid;
        else if(find < arr[mid]) return binarySearch(left,mid-1,find,arr);
        else return binarySearch(mid+1,right,find,arr);
    }

    static ArrayList<Integer> separateDigits(int num){
         int pow = 0;
         ArrayList<Integer> arr = new ArrayList<>();
         while(num != 0)
         {
             if(num % 10 != 0)
             {
                 arr.add((num % 10) * (int) Math.pow(10, pow));
             }
             num /= 10;
             pow++;
         }
         return arr;
     }

     //find pattern
//     for(int i = 0; i<n-1; i++)
//     {
//         for(int j = 0; j<m-1; j++)
//         {
//                 if(pixel[i].charAt(j)*pixel[i+1].charAt(j)*pixel[i].charAt(j+1)*pixel[i+1].charAt(j+1) == 'f'*'a'*'c'*'e')
//                     faceNum++;
//         }
//     }


// row and column checking
    // static boolean checkAllRows(String[] board)
    // {
    //     for(int i=0; i<board.length; i++)
    //     {
    //         for(int j=0; j<board.length; j++)
    //         {
    //             if(board[i].charAt(j) == 'B')
    //             {
    //                 return false;
    //             } 
    //         }
    //     }
    //     return true;
    // }

    

    class Pair implements Comparable<Pair>{
        int x;
        int y;
     
        public Pair(int x, int y)
        {
            this.x = x;
            this.y = y;
        }
        @Override
        public int compareTo(Pair p)
        {
            if(p.y == y)
            return x - p.x;
            return p.y - y;
        }
    }
}