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.ByteArrayInputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.Comparator;
import java.util.InputMismatchException;
import java.util.List;

public class Main {

	private static final String NO = "No";
	private static final String YES = "Yes";
	InputStream is;
	PrintWriter out;
	String INPUT = "";

	private static final long MOD = 1000000007;
	private static final int MAXN = 1000000;

	void solve() {
		int T = ni();
		for (int i = 0; i < T; i++) {
			out.println(solve(i) ? YES : NO);
		}
	}

	boolean solve(int T) {
		int n = ni();
		int k = ni();
		char a[] = ns().toCharArray();

		for (int i = k; i < n; i++) {
			if (a[i % k] == a[i])
				;
			else {
				if (a[i % k] == '?')
					a[i % k] = a[i];
				else if (a[i] == '?')
					;
				else
					return false;
			}
		}
//		tr(a);
		int cnt[] = new int[2];
		for (int i = 0; i < k; i++)
			if (a[i] != '?')
				cnt[a[i] - '0']++;
		return (cnt[0] <= k / 2 && cnt[1] <= k / 2);
	}

	// a^b
	long power(long a, long b) {
		long x = 1, y = a;
		while (b > 0) {
			if (b % 2 != 0) {
				x = (x * y) % MOD;
			}
			y = (y * y) % MOD;
			b /= 2;
		}
		return x % MOD;
	}

	private long gcd(long a, long b) {
		while (a != 0) {
			long tmp = b % a;
			b = a;
			a = tmp;
		}
		return b;
	}

	void run() throws Exception {
		is = INPUT.isEmpty() ? System.in : new ByteArrayInputStream(INPUT.getBytes());
		out = new PrintWriter(System.out);

		long s = System.currentTimeMillis();
		solve();
		out.flush();
		if (!INPUT.isEmpty())
			tr(System.currentTimeMillis() - s + "ms");
	}

	public static void main(String[] args) throws Exception {
		new Main().run();
	}

	private byte[] inbuf = new byte[1024];
	public int lenbuf = 0, ptrbuf = 0;

	private int readByte() {
		if (lenbuf == -1)
			throw new InputMismatchException();
		if (ptrbuf >= lenbuf) {
			ptrbuf = 0;
			try {
				lenbuf = is.read(inbuf);
			} catch (IOException e) {
				throw new InputMismatchException();
			}
			if (lenbuf <= 0)
				return -1;
		}
		return inbuf[ptrbuf++];
	}

	private boolean isSpaceChar(int c) {
		return !(c >= 33 && c <= 126);
	}

	private int skip() {
		int b;
		while ((b = readByte()) != -1 && isSpaceChar(b))
			;
		return b;
	}

	private double nd() {
		return Double.parseDouble(ns());
	}

	private char nc() {
		return (char) skip();
	}

	private String ns() {
		int b = skip();
		StringBuilder sb = new StringBuilder();
		while (!(isSpaceChar(b))) { // when nextLine, (isSpaceChar(b) && b != '
									// ')
			sb.appendCodePoint(b);
			b = readByte();
		}
		return sb.toString();
	}

	private char[] ns(int n) {
		char[] buf = new char[n];
		int b = skip(), p = 0;
		while (p < n) {
			if (!(isSpaceChar(b)))
				buf[p++] = (char) b;
			b = readByte();
		}
		return n == p ? buf : Arrays.copyOf(buf, p);
	}

	private char[][] nm(int n, int m) {
		char[][] map = new char[n][];
		for (int i = 0; i < n; i++)
			map[i] = ns(m);
		return map;
	}

	private int[] na(int n) {
		int[] a = new int[n];
		for (int i = 0; i < n; i++)
			a[i] = ni();
		return a;
	}

	private List<Integer> na2(int n) {
		List<Integer> a = new ArrayList<Integer>();
		for (int i = 0; i < n; i++)
			a.add(ni());
		return a;
	}

	private int[][] na(int n, int m) {
		int[][] a = new int[n][];
		for (int i = 0; i < n; i++)
			a[i] = na(m);
		return a;
	}

	private int ni() {
		int num = 0, b;
		boolean minus = false;
		while ((b = readByte()) != -1 && !((b >= '0' && b <= '9') || b == '-'))
			;
		if (b == '-') {
			minus = true;
			b = readByte();
		}

		while (true) {
			if (b >= '0' && b <= '9') {
				num = num * 10 + (b - '0');
			} else {
				return minus ? -num : num;
			}
			b = readByte();
		}
	}

	private long[] nl(int n) {
		long[] a = new long[n];
		for (int i = 0; i < n; i++)
			a[i] = nl();
		return a;
	}

	private long[][] nl(int n, int m) {
		long[][] a = new long[n][];
		for (int i = 0; i < n; i++)
			a[i] = nl(m);
		return a;
	}

	private long nl() {
		long num = 0;
		int b;
		boolean minus = false;
		while ((b = readByte()) != -1 && !((b >= '0' && b <= '9') || b == '-'))
			;
		if (b == '-') {
			minus = true;
			b = readByte();
		}

		while (true) {
			if (b >= '0' && b <= '9') {
				num = num * 10 + (b - '0');
			} else {
				return minus ? -num : num;
			}
			b = readByte();
		}
	}

	private static void tr(Object... o) {
		System.out.println(Arrays.deepToString(o));
	}

	static class CHT {
		long M[], C[];
		int ptr, idx;
		boolean slopeInc, queryMax;

		CHT(int n, boolean isSlopeIncreasing, boolean isQueryMax) {
			M = new long[n + 1];
			C = new long[n + 1];
			slopeInc = isSlopeIncreasing;
			queryMax = isQueryMax;
			ptr = idx = 0;
		}

		boolean bad(int i, int j, int k) {
			if ((slopeInc && queryMax) || (!slopeInc && !queryMax)) {
				return (C[k] - C[i]) / (M[i] - M[k]) <= (C[j] - C[i]) / (M[i] - M[j]); /// (slope dec+query min),(slope
																						/// inc+query max)
			} else {
				return (C[k] - C[i]) * (M[i] - M[j]) >= (C[j] - C[i]) * (M[i] - M[k]); /// (slope dec+query max), (slope
																						/// inc+query min)
			}
		}

		void add(long m, long c) {
			M[idx] = m;
			C[idx] = c;
			++idx;
			while (idx >= 3 && bad(idx - 3, idx - 2, idx - 1)) {
				M[idx - 2] = M[idx - 1];
				C[idx - 2] = C[idx - 1];
				idx--;
			}
		}

		long getY(int i, long x) { // y = mx + c //
			return M[i] * x + C[i];
		}

		/// (slope dec+query min),(slope inc+query max) -> x increasing
		/// (slope dec+query max), (slope inc+query min) -> x decreasing
		long query(long x) {
			if (ptr >= idx) {
				ptr = idx - 1;
			}
			if (queryMax) { // for maximum
				while (ptr < idx - 1 && getY(ptr + 1, x) >= getY(ptr, x))
					ptr++;
				return M[ptr] * x + C[ptr];
			} else { // for minimum
				while (ptr < idx - 1 && getY(ptr + 1, x) <= getY(ptr, x))
					ptr++;
				return M[ptr] * x + C[ptr];
			}
		}

		/// works for random query x
		long query_random_x(long x) {
			return bs(0, idx - 1, x, idx);
		}

		long bs(int st, int ed, long x, int idx) {
			int mid = (st + ed) >> 1;

			if (queryMax) { /// for maximum
				if (mid + 1 < idx && getY(mid + 1, x) > getY(mid, x))
					return bs(mid + 1, ed, x, idx);
				if (mid - 1 >= 0 && getY(mid - 1, x) > getY(mid, x))
					return bs(st, mid - 1, x, idx);
				return getY(mid, x);
			} else { /// for minimum
				if (mid + 1 < idx && getY(mid + 1, x) < getY(mid, x))
					return bs(mid + 1, ed, x, idx);
				if (mid - 1 >= 0 && getY(mid - 1, x) < getY(mid, x))
					return bs(st, mid - 1, x, idx);
				return getY(mid, x);
			}
		}
	}
}