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.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.math.BigInteger;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.Collections;
import java.util.Comparator;
import java.util.HashMap;
import java.util.HashSet;
import java.util.List;
import java.util.Map;
import java.util.Set;

public class CodeForces {
	
	static class Track{
		
		int start;
		int end;
		
		public Track(int start, int end) {
			super();
			this.start = start;
			this.end = end;
		}

		@Override
		public String toString() {
			return "Track [start=" + start + ", end=" + end + "]";
		}

		@Override
		public int hashCode() {
			final int prime = 31;
			int result = 1;
			result = prime * result + end;
			result = prime * result + start;
			return result;
		}
		
		
		
		
	}

	static class Range {

		String s;

		public Range(String s) {
			this.s = s;
		}

		@Override
		public String toString() {
			return s;
		}
	}

	static class RangeComparator implements Comparator<Range> {

		public int compare(Range o1, Range o2) {
			String[] v1 = o1.s.split("#");
			String[] v2 = o2.s.split("#");
			int val1 = Integer.parseInt(v1[1]) - Integer.parseInt(v1[0]);
			int val2 = Integer.parseInt(v2[1]) - Integer.parseInt(v2[0]);
			if (val1 > val2) {
				return -1;
			} else if (val2 > val1) {
				return 1;
			}
			return o1.s.compareTo(o2.s);
		}

	}

	public static void printArray(int[] arr) {
		for (int i = 0; i < arr.length; i++) {
			System.out.print(arr[i] + " ");
		}
		System.out.println();
	}

	public static int[] getIntArray(BufferedReader br) throws IOException {
		String line = br.readLine();
		String[] values = line.split(" ");
		int[] arr = new int[values.length];
		for (int i = 0; i < values.length; i++) {
			arr[i] = Integer.parseInt(values[i]);
		}
		return arr;
	}

	public static long[] getLongArray(BufferedReader br) throws IOException {
		String line = br.readLine();
		String[] values = line.split(" ");
		long[] arr = new long[values.length];
		for (int i = 0; i < values.length; i++) {
			arr[i] = Long.parseLong(values[i]);
		}
		return arr;
	}
	
	public static List<Long> getLongList(BufferedReader br) throws IOException {
		String line = br.readLine();
		String[] values = line.split(" ");
		List<Long> list = new ArrayList<>();
		for (int i = 0; i < values.length; i++) {
			list.add(Long.parseLong(values[i]));
		}
		return list;
	}
	
	public static String[] getStringArray(BufferedReader br) throws IOException {
		String line = br.readLine();
		String[] values = line.split(" ");
		return values;
	}

	public static Set<Integer> getFactors(int n) {
		Set<Integer> set = new HashSet<>();
		for (int i = 2; i <= Math.sqrt(n); i++) {
			if (n % i == 0) {
				set.add(i);
				set.add(n / i);
			}
		}
		return set;
	}

	public static int[] decode(String s) {
		String[] v = s.split("#");
		int[] arr = new int[2];
		arr[0] = Integer.parseInt(v[0]);
		arr[1] = Integer.parseInt(v[1]);
		return arr;
	}

	public static String encode(int a, int b) {
		return a + "#" + b;
	}

	public static long lcm(long a, long b) {
		BigInteger bigGCD = BigInteger.valueOf(a).gcd(BigInteger.valueOf(b));
		long val = bigGCD.longValue();
		long prod = a * b;
		return prod / val;
	}

	public static Set<Integer> getPrimes() {
		Set<Integer> primes = new HashSet<>();
		for (int i = 2; i < 20000; i++) {
			int fac = 0;
			for (int j = 1; j <= Math.sqrt(i); j++) {
				if (i % j == 0) {
					fac += 2;
				}
			}

			if (fac == 2) {
				primes.add(i);
			}
		}

		System.out.println(primes.size());

		return primes;
	}
	
	public static long process(long n){
		if(n%2==0){
			return n/2;
		}
		
		long min = n;
		
		for(long i=2;i<=(long)Math.sqrt(n);i++){
			if(n%i==0){
				min =  Math.min(min, i);
				min =  Math.min(min, n/i);
			}
		}
		
		return 1+ process(n-min);
		
	}
	

	public static void main(String[] args) throws Exception {
		BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
		String line = br.readLine();
		int t = Integer.parseInt(line);		
//		int t = 1;
		while (t-- > 0) {
//			line = br.readLine();
//			String ip = br.readLine();
			int[] arr1 = getIntArray(br);
			int[] arr = getIntArray(br);
			
			int n = arr1[0];
			int x = arr1[1];
			
			int o=0;
			int e=0;
			
			for(int val: arr){
				if(val%2==0){
					e++;
				}else{
					o++;
				}
			}
			
			int count=0;
	    	if(o>0){
//    			if(o%2==0){
//	    			count +=Math.min(o-1,x-1);
//	    		}else{
//	    			count +=Math.min(o,x);
//	    		}
	    		
	    		if(x%2==0){
	    			if(o%2==0){
	    				count +=Math.min(x-1, o-1);
	    			}else{
	    				count +=Math.min(x-1, o);
	    			}
	    		}else{
	    			if(o%2==0){
	    				count +=Math.min(x, o-1);
	    			}else{
	    				count +=Math.min(x, o);
	    			}
	    		}
    			
    			count +=e;
    			if(count>=x){
    				System.out.println("Yes");
    			}else{
    				System.out.println("No");
    			}
    		}else{
    			System.out.println("No");
    		}
			
			
			
			
			
		}
		
		

	}
	

}