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 solution {
    static class sort implements Comparator<ArrayList<Integer>> {

        @Override
        public int compare(ArrayList<Integer> o1, ArrayList<Integer> o2) {
            int c = o2.get(1).compareTo(o1.get(1));
            return c;
        }
    }

    public static void merge(long arr[], int l, int m, int r) {
        int n1 = m - l + 1;
        int n2 = r - m;
        long L[] = new long[n1];
        long R[] = new long[n2];
        for (int i = 0; i < n1; ++i)
            L[i] = arr[l + i];
        for (int j = 0; j < n2; ++j)
            R[j] = arr[m + 1 + j];
        int i = 0, j = 0;
        int k = l;
        while (i < n1 && j < n2) {
            if (L[i] <= R[j]) {
                arr[k] = L[i];
                i++;
            } else {
                arr[k] = R[j];
                j++;
            }
            k++;
        }
        while (i < n1) {
            arr[k] = L[i];
            i++;
            k++;
        }
        while (j < n2) {
            arr[k] = R[j];
            j++;
            k++;
        }
    }

    public static void sort(long arr[], int l, int r) {
        if (l < r) {
            int m = (l + r) / 2;
            sort(arr, l, m);
            sort(arr, m + 1, r);
            merge(arr, l, m, r);
        }
    }

    public static long gcd(long a, long b) {
        if (b == 0) {
            return a;
        } else return gcd(b, a % b);
    }

    public static long lcm(long a, long b) {
        long gcd = gcd(a, b);
        long pord = a * b;
        return pord / gcd;
    }

    static class graphs {
        private int V;
        private ArrayList<Integer> adj[];

        graphs(int v) {
            V = v;
            adj = new ArrayList[v];
            for (int i = 0; i < v; i++) {
                adj[i] = new ArrayList<>();
            }
        }

        void addedge(int u, int v) {
            adj[u].add(v);
        }

        void BFS(int v) {
            boolean visited[] = new boolean[V];
            Queue<Integer> Q = new LinkedList<>();
            visited[v] = true;
            Q.add(v);
            while (!Q.isEmpty()) {
                int temp = Q.peek();
                System.out.print(temp + " ");
                Q.remove();
                Iterator<Integer> it = adj[temp].listIterator();
                while (it.hasNext()) {
                    int n = it.next();
                    if (!visited[n]) {
                        visited[n] = true;
                        Q.add(n);
                    }
                }
            }
        }

        void DFSUtil(int v, boolean visited[]) {
            visited[v] = true;
            System.out.print(v + " ");
            Iterator<Integer> it = adj[v].listIterator();
            while (it.hasNext()) {
                int n = it.next();
                if (!visited[n]) {
                    DFSUtil(n, visited);
                }
            }
        }

        void DFS(int v) {
            boolean visited[] = new boolean[V];
            DFSUtil(v, visited);
        }
    }

    public static int Binaraysearch(long a[], int low, int high, long key) {
        while (low <= high) {
            int mid = low + (high - low) / 2;
            if (a[mid] == key) {
                return mid;
            } else if (a[mid] < key) {
                low = mid;
            } else {
                high = mid;
            }
        }
        return -1;
    }

    public static void seive(boolean prime[]) {
        Arrays.fill(prime, true);
        int n = prime.length - 1;
        for (int p = 2; p * p <= n; p++) {
            if (prime[p] == true) {
                for (int i = p * p; i <= n; i += p)
                    prime[i] = false;
            }
        }
    }

    public static boolean random(long a, long b) {
        return a < b;
    }

    public static int subArraySum(int arr[], int n, int sum) {
        int curr_sum = arr[0], start = 0, i;
        for (i = 1; i <= n; i++) {
            // If curr_sum exceeds the sum, then remove the starting elements
            while (curr_sum > sum && start < i - 1) {
                curr_sum = curr_sum - arr[start];
                start++;
            }

            // If curr_sum becomes equal to sum, then return true
            if (curr_sum == sum) {
                int p = i - 1;
                if (p != start)
                    return 1;
            }

            // Add this element to curr_sum
            if (i < n)
                curr_sum = curr_sum + arr[i];

        }
        return 0;
    }

    static class pair {
        int x;
        int dis;

        public pair(int x, int dis) {
            this.x = x;
            this.dis = dis;
        }
    }

    public static void main(String args[]) throws IOException {
        BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
        int t = Integer.parseInt(br.readLine());
        for(int ii=0;ii<t;ii++){
            StringTokenizer st = new StringTokenizer(br.readLine());
            int n = Integer.parseInt(st.nextToken());
            int k = Integer.parseInt(st.nextToken());
            int odd = 0;
            int even = 0;
            st = new StringTokenizer(br.readLine());
            for(int i=0;i<n;i++){
                long b = Long.parseLong(st.nextToken());
                if(b%2 == 1){
                    odd++;
                }
            }
            even = n-odd;
            boolean flag = false;
            for(int i=1;i<=odd && i<=k;i+=2){
                if(k-i<=even){
                    flag = true;
                    break;
                }
            }
            if(flag){
                System.out.println("Yes");
            }
            else{
                System.out.println("No");
            }
        }
    }
}