Balanced Bitstring

题意翻译

给定一个二进制字符串 由0,1,?组成。 ?可以是1或者0，由你自由选择。 问你是否能构造出一个字符串，使得这个字符串每个长度为k的子串中0和1的个数相等。如果可以，输出"YES"，否则输出"NO" 注：a是b的子串，当且仅当b可以通过 从头删去若干个或0个字符，从末尾删去若干个或0个字符之后变成a。

题目描述

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 ( $ \frac{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.

输入输出格式

输入格式

Each test contains multiple test cases. The first line contains the number of test cases $ t $ ( $ 1 \le t \le 10^4 $ ). Description of the test cases follows. The first line of each test case contains two integers $ n $ and $ k $ ( $ 2 \le k \le n \le 3 \cdot 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 \cdot 10^5 $ .

输出格式

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.

输入输出样例

输入样例 #1

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

输出样例 #1

YES
YES
NO
YES
YES
NO
NO
YES
NO

说明

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.