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 PYTHON3):

Solution:
#
#    ------------------------------------------------
#         Fast Tests Competitive Python Template
#    ------------------------------------------------
#    Author: prophet "神"
#    Version: 1V3uJkowFG
#    License: GNU Affero General Public License v3.0
#    Location: 218.92.0.135
#    ------------------------------------------------
#

testing_mode = True

import sys, traceback

test_data = ""
final_output = ""

def input(input_format = 0, multi = 0):

    if multi > 0: return [input(input_format) for x in range(multi)]
    else:
        next_line = next(test_data, None).strip() if test_data else sys.stdin.readline()

        if input_format == 0: formatted_input = [next_line]
        elif input_format == 1: formatted_input = list(map(int, next_line.split()))
        elif input_format == 2: formatted_input = list(map(float, next_line.split()))
        elif input_format == 3: formatted_input = next_line.split()
        elif input_format == 4: formatted_input = (lambda x: [x[0], list(map(int, x[1:]))])(next_line.split())
        elif input_format == 5: formatted_input = (lambda x: [x[0], list(map(float, x[1:]))])(next_line.split())
        else: formatted_input = [next_line]

        return formatted_input

def log(*args):
    if testing_mode: print(*args)

def out(output_line, output_format = 0, newline = True):

        global final_output

        formatted_output = ""

        if output_format == 0: formatted_output = str(output_line)
        elif output_format == 1: formatted_output = " ".join(map(str, output_line))
        elif output_format == 1: formatted_output = "\n".join(map(str, output_line))

        if testing_mode: final_output += formatted_output + "\n" * newline
        else: print(formatted_output, end = "\n" if newline else "")

test_inputs = [
# Input 1
"""
5
1 1
999
1 1
1000
2 1
51 50
2 2
51 50
3 3
101 102 103

""",
# Input 2
"""
1
4 2
3 5 7 8
""",
# Input 3
"""
1
2 1
3 5
""",
# Input 4
"""
$$$
"""
]

test_outputs = [
# Output 1
"""
Yes
No
Yes
Yes
No

""",
# Output 2
"""
$$$
""",
# Output 3
"""
$$$
""",
# Output 4
"""
$$$
"""
]

#
#   >>>>>>>>>>>>>>> START OF SOLUTION <<<<<<<<<<<<<<
#

def q(x, e, o):
    if x < o:
        return x % 2 == 1 or e > 0
    else:
        if o == 0:
            return False
        elif o % 2 == 0:
            return e + o > x
        else:
            return True


def solve():
    for z in range(input(1)[0]):

        n, x = input(1)
        k = input(1)

        e = 0
        o = 0

        for i in k:
            if i % 2 == 0:
                e += 1
            else:
                o += 1

        out("Yes" if q(x, e, o) else "No")


    return


#
#   >>>>>>>>>>>>>>>> END OF SOLUTION <<<<<<<<<<<<<<<
#

def run_all(overwrite_testing = False):

    global testing_mode, final_output, test_data

    testing_mode = overwrite_testing and testing_mode

    if testing_mode:

        tests_failed = 0

        for test_number, (test_in, test_out) in enumerate(zip(test_inputs, test_outputs)):

            final_output = ""

            if test_in.lstrip()[:3] == "$$$": continue

            test_data = iter([i for i in test_in.split("\n") if i])

            print(f"Test Case #{test_number + 1}:")
            print("<" * 20)

            fail = False
            verdict = "\033[92m\033[1mPASS\033[0m"

            try:
                solve()
                final = final_output.rstrip("\n")
                raw_out = iter(map(str, final.split("\n"))) if final else iter(())
            except Exception:
                raw_out = ""
                fail = True
                print("\033[95m")
                traceback.print_exc()
                print("\033[0m")

            if raw_out:
                if test_out.lstrip()[:3] == "$$$":
                    verdict = "\033[94m\033[1mSKIP\033[0m"
                    print("\033[94m" + '\n'.join(list(raw_out)) + "\033[0m")
                else:
                    for line_out in [i for i in test_out.split("\n") if i]:
                        line_raw = next(raw_out, "% None %")
                        if line_raw == line_out.strip():
                            print(f"\033[92m{line_raw}\033[0m")
                        else:
                            print(f"\033[91m{line_raw}\033[0m")
                            fail = True

                    line_raw = next(raw_out, None)
                    while line_raw:
                        print(f"\033[91m{line_raw}\033[0m")
                        line_raw = next(raw_out, None)
                        fail = True

            print(">" * 20)

            if fail:
                verdict = "\033[91m\033[1mFAIL\033[0m"
                tests_failed += 1

            print(verdict + "\n")

        if tests_failed: print(f"\033[91m\033[1m{tests_failed} TEST{'S' if tests_failed > 1 else ''} FAILED!\033[0m")
        else: print(f"\033[92m\033[1mALL TESTS PASSED!\033[0m")

    else:

        test_data = False
        solve()

run_all(False)