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:
//package cf646;

import java.io.*;
import java.util.Arrays;
import java.util.Comparator;
import java.util.Random;
import java.util.StringTokenizer;
import java.util.function.Function;
import java.util.stream.Collectors;

// What's the smallest input?
// Check * for int/long overflow.
// Check / for accidental rounding.
// Are you using doubles? Can you avoid it?
// Never compare after taking mod.
// Mod the final result.
// Initialize globals in solve() unless they are independent of the problem input.
// Check for local/global name conflicts (n?).
// Check initial values for max/min (not Integer.MIN_VALUE for long).
public class A {
    static Random rand;
    static boolean MULTIPLE_CASES = true;
    static boolean CONSTRUCTIVE = false;
    static long MOD = (long) 1e9 + 7;
    static long BIG = (long) 2e9 + 10;

    public static void solve(Reader in, PrintWriter out) {
        int n = in.ni(), x = in.ni();
        int odds = 0;
        int evens = 0;
        for (int i = 0; i < n; i++) {
            if (in.ni() % 2 == 0) evens++;
            else odds++;
        }
        // need odd # of odds
        if (odds == 0) {
            out.println("No");
            return;
        }

        // total = biggest odd number <= odds and x
        int oddsAvailable = Math.min(odds, x);
        int total = oddsAvailable % 2 == 0 ? oddsAvailable - 1 : oddsAvailable;
        if (total < x && evens < x - total) {
            out.println("No");
            return;
        }
        out.println("Yes");
    }

    public static void main(String[] args) throws IOException {
        Reader in = null;
        PrintWriter out = null;
        for (String arg : args) {
            if (arg.startsWith("input")) {
                in = new Reader(arg);
            } else if (arg.startsWith("output")) {
                out = new PrintWriter(new FileWriter(arg));
            }
        }
        if (in == null) in = new Reader();
        if (out == null) out = new PrintWriter(new OutputStreamWriter(System.out));

        if (MULTIPLE_CASES) {
            int tests = in.ni();
            for (int t = 0; t < tests; t++) {
                solve(in, out);
            }
        } else {
            solve(in, out);
        }

        out.flush();
    }

    static class Tester {
        public static void main(String[] args) throws IOException {
            Validator validator = new Validator();

            File currentDir = new File(".");
            long before;
            long after;
            for (File inputFile : Arrays.stream(currentDir.listFiles())
                    .sorted(Comparator.comparing(File::getName))
                    .collect(Collectors.toList())) {
                if (!inputFile.getName().startsWith("input")
                        || inputFile.getName().contains("sight")
                        || inputFile.getName().contains("big")) continue;
                System.out.println("Test file: " + inputFile.getName());

                before = System.nanoTime();
                String outputFileName = "output" + inputFile.getName().substring(5);
                A.main(new String[]{inputFile.getName(), outputFileName});
                after = System.nanoTime();

                File outputFile = new File(outputFileName);
                if (!outputFile.exists()) {
                    throw new IllegalStateException("Missing output file " + outputFile);
                }

                // TODO if verifier is implemented, remove this
                if (CONSTRUCTIVE) {
                    System.out.println("INPUT:");
                    printFile(inputFile);
                    System.out.printf("\nOUTPUT: (%d milliseconds)\n", (after - before) / 1000000L);
                    printFile(outputFile);
                    continue;
                }

                if (validator.validate(inputFile, outputFile)) {
                    System.out.printf("OK (%d milliseconds)\n", (after - before) / 1000000L);
                } else {
                    System.out.println("FAILED");
                    System.out.println("\nInput: ");
                    printFile(inputFile);
                    System.out.println("\nIncorrect Output: ");
                    printFile(outputFile);
                    return;
                }
            }
            System.out.println("\n-----------------\n");

            File sightTestInput = new File("input-sight");
            if (sightTestInput.exists()) {
                System.out.println("Running sight test... Input:");
                printFile(sightTestInput);
                before = System.nanoTime();
                System.out.println("\nOutput: ");
                A.main(new String[]{"input-sight"});
                after = System.nanoTime();
                System.out.printf("(%d milliseconds)\n", (after - before) / 1000000L);
                System.out.println("\n-----------------\n");
            }

            File bigTestInput = new File("input-big");
            if (bigTestInput.exists()) {
                System.out.println("Running big test...");
                before = System.nanoTime();
                A.main(new String[]{"input-big"});
                after = System.nanoTime();
                System.out.printf("(%d milliseconds)\n", (after - before) / 1000000L);
            }
        }

        static void printFile(File file) throws FileNotFoundException {
            BufferedReader reader = new BufferedReader(new FileReader(file));
            reader.lines().forEach(System.out::println);
        }
    }

    static class Validator {
        boolean validate(File inputFile, File outputFile) throws IOException {
            File expectedOutputFile = new File("expected-output" + inputFile.getName().substring(5));
            if (CONSTRUCTIVE || !expectedOutputFile.exists()) {
                return validateManual(inputFile, outputFile);
            }
            return areSame(outputFile, expectedOutputFile);
        }

        private boolean validateManual(File inputFile, File outputFile) throws IOException {
            if (CONSTRUCTIVE) {
                // Validate output against input
                Reader inputReader = new Reader(inputFile.getName());
                Reader outputReader = new Reader(outputFile.getName());

                // TODO implement manual validation

                throw new IllegalStateException("Missing expected output file");
            } else {
                File naiveOutput = new File("naive-" + outputFile.getName());
                Naive.main(new String[]{inputFile.getName(), naiveOutput.getName()});

                return areSame(outputFile, naiveOutput);
            }
        }

        private boolean areSame(File file1, File file2) throws IOException {
            BufferedReader reader1 = new BufferedReader(new FileReader(file1));
            BufferedReader reader2 = new BufferedReader(new FileReader(file2));

            String line1;
            while ((line1 = reader1.readLine()) != null) {
                String line2 = reader2.readLine();
                if (line2 == null) line2 = ""; // ok if one has an extra newline
                if (!line1.trim().equals(line2.trim())) {
                    return false;
                }
            }
            String line2;
            while ((line2 = reader2.readLine()) != null) {
                if (!line2.trim().isEmpty()) {
                    return false;
                }
            }
            return true;
        }

    }

    static class Naive {
        public static void solveNaive(Reader in, PrintWriter out) {
            throw new IllegalStateException("missing expected output file");
        }

        public static void main(String[] args) throws IOException {
            Reader in = null;
            PrintWriter out = null;
            for (String arg : args) {
                if (arg.startsWith("input")) {
                    in = new Reader(arg);
                } else if (arg.startsWith("naive-output")) {
                    out = new PrintWriter(new FileWriter(arg));
                }
            }
            if (in == null) in = new Reader();
            if (out == null) out = new PrintWriter(new OutputStreamWriter(System.out));

            int tests = in.ni();
            for (int t = 0; t < tests; t++) {
                solveNaive(in, out);
            }

            out.flush();
            out.close();
        }
    }

    static boolean isPowerOfTwo(int x) {
        return x > 0 & (x & (x - 1)) == 0;
    }

    static int gcd(int a, int b) {
        return b == 0 ? a : gcd(b, a % b);
    }

    static void ruffleSort(int[] a) {
        int n = a.length;
        for (int i = 0; i < n; i++) {
            int oi = rand.nextInt(n), temp = a[oi];
            a[oi] = a[i];
            a[i] = temp;
        }
        Arrays.sort(a);
    }

    static void ruffleSort(long[] a) {
        int n = a.length;
        for (int i = 0; i < n; i++) {
            int oi = rand.nextInt(n);
            long temp = a[oi];
            a[oi] = a[i];
            a[i] = temp;
        }
        Arrays.sort(a);
    }

    ///////////////////////////////////
    //////////   FAST PAIR   //////////
    ///////////////////////////////////

    // Works on -1e9 <= x, y <= 1e9
    static long pair(int x, int y) {
        x = (int) BIG / 2 - x;
        y = (int) BIG / 2 - y;
        return x * BIG + y;
    }

    static int x(long pair) {
        return (int) BIG / 2 - (int) (pair / BIG);
    }

    static int y(long pair) {
        return (int) BIG / 2 - (int) (pair % BIG);
    }

    static String str(long pair) {
        return String.format("(%d, %d)", x(pair), y(pair));
    }

    ///////////////////////////////////
    ////////// BINARY SEARCH //////////
    ///////////////////////////////////

    // return highest in range that still returns true
    // T T T F F F F
    // invariant:
    // -    indicator(min) = true
    // -    indicator(max+1) = false
    static int binarySearchHighest(int min, int max, Function<Integer, Boolean> indicator) {
        int a = min;
        int b = max;
        while (a != b) {
            int mid = (a % 2 != b % 2) ? 1 + (a + b) / 2 : (a + b) / 2;
            if (indicator.apply(mid)) {
                a = mid;
            } else {
                b = mid - 1;
            }
        }
        return a;
    }

    // return lowest in range that still returns true
    // F F F F T T T
    // invariant:
    // -    indicator(min-1) = false
    // -    indicator(max) = true
    static int binarySearchLowest(int min, int max, Function<Integer, Boolean> indicator) {
        int a = min;
        int b = max;
        while (a != b) {
            int mid = (a + b) / 2;
            if (indicator.apply(mid)) {
                b = mid;
            } else {
                a = mid + 1;
            }
        }
        return a;
    }

    static void insist(boolean bool) {
        if (!bool) throw new IllegalStateException();
    }

    static class Reader {
        public BufferedReader reader;
        public StringTokenizer tokenizer;

        public Reader() {
            reader = new BufferedReader(new InputStreamReader(System.in), 32768);
            tokenizer = null;
        }

        public Reader(String fileName) throws FileNotFoundException {
            reader = new BufferedReader(new FileReader(fileName));
        }

        public String next() {
            while (tokenizer == null || !tokenizer.hasMoreTokens()) {
                try {
                    tokenizer = new StringTokenizer(reader.readLine());
                } catch (IOException e) {
                    throw new RuntimeException(e);
                }
            }
            return tokenizer.nextToken();
        }

        public int ni() {
            return Integer.parseInt(next());
        }

        public long nl() {
            return Long.parseLong(next());
        }

        public int[] nis(int n) {
            int[] out = new int[n];
            for (int i = 0; i < n; i++) {
                out[i] = ni();
            }
            return out;
        }

        public long[] nls(int n) {
            long[] out = new long[n];
            for (int i = 0; i < n; i++) {
                out[i] = nl();
            }
            return out;
        }
    }
}