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.
import java.io.BufferedReader;
import java.io.*;
import java.util.*;

public class a {

    static BufferedReader br;
    static long mod = 1000000000 + 7;
    static HashSet<Integer> p = new HashSet<>();
     static boolean debug =true;
           //  Arrays.sort(time  , (a1,a2) -> (a1[0]-a2[0])); 2d array sort lamda
    public static void main(String[] args) throws Exception {
        br = new BufferedReader(new InputStreamReader(System.in));
        int tc = 1;
        PrintWriter pr = new PrintWriter(System.out);
        tc = cinI();
        int y=0;
        while (tc-- > 0) {
        	y+=1;
                   int  nk[]=readArray(2,0,0);
                   int n =nk[0];
                   int k=nk[1];
                   char[] ar=cin().toCharArray();
              boolean ans=true;
              // if(y==59){
              // 	System.out.println(String.valueOf(ar));
              // }
                   for(int i=0;i<k;i++){
                   	HashSet<Character> x =new HashSet<>();
                   
                   	for(int j=i;j<n;j+=k){
                   		//..System.out.println(i+" "+j);
                       if(ar[j]=='0'|| ar[j]=='1'){
                       	x.add(ar[j]);
                       }
                   	}
               //    	System.out.println(i +" "+x);
                   	if(x.size()==2){
                        ans=false;
                        break;
                   	}
                   	if(ar[i]=='?' && x.size()==1){
                        for(char c:x){
                        	ar[i]=c;
                        	break;
                        }
                   	}

                   }
                   if(ans==false){
                   	pr.println("NO");
                   	continue;
                   }
                     int one = 0;
                     int zero = 0;
                     int cnt=0;
                   for(int i=0;i<k;i++){
                         if(ar[i]=='1'){
                         	one+=1;
                         	continue;
                         }
                         if(ar[i]=='0'){
                         	zero+=1;
                         	continue;
                         }
                         cnt+=1;
                   }
                  
                   int mx = max(one,zero);
                   int mn = min(one,zero);
                   int requ  =mx-mn;

                   if(requ<=cnt){
                   	pr.println("YES");
                   }
                   else{
                   	pr.println("NO");
                   }
               
        }
        pr.close();
    }

    public static <E> void print(String var ,E e){
      if(debug==true){
      System.out.println(var +" "+e);
      }
    }
     private static long[]  sort(long[] e){
     ArrayList<Long> x=new ArrayList<>();
     for(long c:e){
       x.add(c);
     }
     Collections.sort(x);
     long[] y = new long[e.length];
     for(int i=0;i<x.size();i++){
       y[i]=x.get(i);
     }
     return y;
     }
    public static void printDp(long[][] dp) {

        int n = dp.length;
        for (int i = 0; i < n; i++) {
            for (int j = 0; j < dp[0].length; j++) {
                System.out.print(dp[i][j] + " ");
            }
            System.out.println();
        }
    }

    


  

    private static long gcd(long a, long b) {
        if (a == 0)
            return b;
        if (b == 0)
            return a;

        // base case
        if (a == b)
            return a;

        // a is greater
        if (a > b)
            return gcd(a % b, b);
        return gcd(a, b % a);
    }


    public static long min(long a, long b) {
        return Math.min(a, b);
    }

    public static int min(int a, int b) {
        return Math.min(a, b);
    }


    public static void sieve() {
        int[] pf = new int[100000000 + 1];
        //0 prime //1 not prime
        pf[0] = 1;
        pf[1] = 1;
        for (int j = 2; j <= 10000; j++) {

            if (pf[j] == 0) {
                p.add(j);
                for (int k = j * j; k < pf.length; k += j) {
                    pf[k] = 1;
                }
            }
        }

    }


    public static int[] readArray(int n, int x, int z) throws Exception {
        int[] arr = new int[n];
        String[] ar = cinA();
        for (int i = x; i < n + x; i++) {
            arr[i] = getI(ar[i - x]);
        }
        return arr;
    }

    public static long[] readArray(int n, int x) throws Exception {
        long[] arr = new long[n];
        String[] ar = cinA();
        for (int i = x; i < n + x; i++) {
            arr[i] = getL(ar[i - x]);
        }
        return arr;
    }

    public static void arrinit(String[] a, long[] b) throws Exception {
        for (int i = 0; i < a.length; i++) {
            b[i] = Long.parseLong(a[i]);
        }
    }

    public static HashSet<Integer>[] Graph(int n, int edge, int directed) throws Exception {
        HashSet<Integer>[] tree = new HashSet[n];

        for (int j = 0; j < edge; j++) {

            String[] uv = cinA();
            int u = getI(uv[0]);
            int v = getI(uv[1]);
            if (directed == 0) {

                tree[v].add(u);
            }
            tree[u].add(v);
        }
        return tree;
    }

    public static void arrinit(String[] a, int[] b) throws Exception {
        for (int i = 0; i < a.length; i++) {
            b[i] = Integer.parseInt(a[i]);
        }
    }


    static double findRoots(int a, int b, int c) {
        // If a is 0, then equation is not
        //quadratic, but linear


        int d = b * b - 4 * a * c;
        double sqrt_val = Math.sqrt(Math.abs(d));


        // System.out.println("Roots are real and different \n");

        return Math.max((double) (-b + sqrt_val) / (2 * a),
                (double) (-b - sqrt_val) / (2 * a));


    }

    public static String cin() throws Exception {
        return br.readLine();
    }

    public static String[] cinA() throws Exception {
        return br.readLine().split(" ");
    }

    public static String[] cinA(int x) throws Exception {
        return br.readLine().split("");
    }

    public static String ToString(Long x) {
        return Long.toBinaryString(x);
    }

    public static void cout(String s) {
        System.out.println(s);
    }

    public static Integer cinI() throws Exception {
        return Integer.parseInt(br.readLine());
    }

    public static int getI(String s) throws Exception {
        return Integer.parseInt(s);
    }

    public static long getL(String s) throws Exception {
        return Long.parseLong(s);
    }

    public static long max(long a, long b) {
        return Math.max(a, b);
    }

    public static int max(int a, int b) {
        return Math.max(a, b);
    }

    public static void coutI(int x) {
        System.out.println(String.valueOf(x));
    }

    public static void coutI(long x) {
        System.out.println(String.valueOf(x));
    }

    public static Long cinL() throws Exception {
        return Long.parseLong(br.readLine());
    }

    public static void arrInit(String[] arr, int[] arr1) throws Exception {
        for (int i = 0; i < arr.length; i++) {
            arr1[i] = getI(arr[i]);
        }

    }
}