A bitstring is a string consisting only of the characters 0 and 1. A bitstring is called k-balanced if every substring of size k of this bitstring has an equal amount of 0 and 1 characters (k/2 of each).

You are given an integer k and a string s which is composed only of characters 0, 1, and ?. You need to determine whether you can make a k-balanced bitstring by replacing every ? characters in s with either 0 or 1.

A string a is a substring of a string b if a can be obtained from b by deletion of several (possibly, zero or all) characters from the beginning and several (possibly, zero or all) characters from the end.

Input

Each test contains multiple test cases. The first line contains the number of test cases t (1 ≤ t ≤ 10^4). Description of the test cases follows.

The first line of each test case contains two integers n and k (2 ≤ k ≤ n ≤ 3 ⋅ 10^5, k is even) — the length of the string and the parameter for a balanced bitstring.

The next line contains the string s (|s| = n). It is given that s consists of only 0, 1, and ?.

It is guaranteed that the sum of n over all test cases does not exceed 3 ⋅ 10^5.

Output

For each test case, print YES if we can replace every ? in s with 0 or 1 such that the resulting bitstring is k-balanced, or NO if it is not possible.

Example

Input


9
6 4
100110
3 2
1?1
3 2
1?0
4 4
????
7 4
1?0??1?
10 10
11??11??11
4 2
1??1
4 4
?0?0
6 2
????00


Output


YES
YES
NO
YES
YES
NO
NO
YES
NO

Note

For the first test case, the string is already a 4-balanced bitstring.

For the second test case, the string can be transformed into 101.

For the fourth test case, the string can be transformed into 0110.

For the fifth test case, the string can be transformed into 1100110.
"""
// Author : snape_here - Susanta Mukherjee
     
 """
 
from __future__ import division, print_function
 
import os,sys
from io import BytesIO, IOBase
 
if sys.version_info[0] < 3:
    from __builtin__ import xrange as range
    from future_builtins import ascii, filter, hex, map, oct, zip
 
def ii(): return int(input())
def fi(): return float(input())
def si(): return input()
def msi(): return map(str,input().split())
def mi(): return map(int,input().split())
def li(): return list(mi())
 
 
def read():
    sys.stdin = open('input.txt', 'r')  
    sys.stdout = open('output.txt', 'w') 
 
def gcd(x, y):
    while y:
        x, y = y, x % y
    return x

def lcm(x, y):
    return (x*y)//(gcd(x,y))

mod=1000000007

def modInverse(b,m): 
    g = gcd(b, m)  
    if (g != 1):         
        return -1
    else:          
        return pow(b, m - 2, m) 

def modu(a,b,m): 

    a = a % m 
    inv = modInverse(b,m) 
    if(inv == -1): 
        return -999999999
    else: 
        return (inv*a)%m

from math import log,sqrt,factorial,cos,tan,sin,radians,ceil,floor

import bisect

from decimal import *

getcontext().prec = 8

abc="abcdefghijklmnopqrstuvwxyz"

pi=3.141592653589793238

import random

def main():

    for _ in range(ii()):
        n,k=mi()
        s=si()

        if n==k:
            if s.count('1')>k//2 or s.count('0')>k//2:
                print("NO")
            else:
                print("YES")
            continue

        x=y=0

        flag=1

        for i in range(k):
            c='2'
            for j in range(i,n,k):
                if s[j]!='?':
                    if c!='2' and s[j]!=c:
                        flag=0
                    c=s[j]
            if c!='2':
                if c=='1':
                    x+=1 
                elif c=='0':
                    y+=1 

            if x>k//2 or y>k//2:
                flag=0 
                break

        if flag:
            print("YES")
        else:
            print("NO")




# region fastio
 
BUFSIZE = 8192
 
 
class FastIO(IOBase):
    newlines = 0
 
    def __init__(self, file):
        self._fd = file.fileno()
        self.buffer = BytesIO()
        self.writable = "x" in file.mode or "r" not in file.mode
        self.write = self.buffer.write if self.writable else None
 
    def read(self):
        while True:
            b = os.read(self._fd, max(os.fstat(self._fd).st_size, BUFSIZE))
            if not b:
                break
            ptr = self.buffer.tell()
            self.buffer.seek(0, 2), self.buffer.write(b), self.buffer.seek(ptr)
        self.newlines = 0
        return self.buffer.read()
 
    def readline(self):
        while self.newlines == 0:
            b = os.read(self._fd, max(os.fstat(self._fd).st_size, BUFSIZE))
            self.newlines = b.count(b"\n") + (not b)
            ptr = self.buffer.tell()
            self.buffer.seek(0, 2), self.buffer.write(b), self.buffer.seek(ptr)
        self.newlines -= 1
        return self.buffer.readline()
 
    def flush(self):
        if self.writable:
            os.write(self._fd, self.buffer.getvalue())
            self.buffer.truncate(0), self.buffer.seek(0)
 
 
class IOWrapper(IOBase):
    def __init__(self, file):
        self.buffer = FastIO(file)
        self.flush = self.buffer.flush
        self.writable = self.buffer.writable
        self.write = lambda s: self.buffer.write(s.encode("ascii"))
        self.read = lambda: self.buffer.read().decode("ascii")
        self.readline = lambda: self.buffer.readline().decode("ascii")
 
 
def print(*args, **kwargs):
    """Prints the values to a stream, or to sys.stdout by default."""
    sep, file = kwargs.pop("sep", " "), kwargs.pop("file", sys.stdout)
    at_start = True
    for x in args:
        if not at_start:
            file.write(sep)
        file.write(str(x))
        at_start = False
    file.write(kwargs.pop("end", "\n"))
    if kwargs.pop("flush", False):
        file.flush()
 
 
if sys.version_info[0] < 3:
    sys.stdin, sys.stdout = FastIO(sys.stdin), FastIO(sys.stdout)
else:
    sys.stdin, sys.stdout = IOWrapper(sys.stdin), IOWrapper(sys.stdout)
 
input = lambda: sys.stdin.readline().rstrip("\r\n")
 
# endregion
 
 
if __name__ == "__main__":
    #read()
    main()