You Are Given Two Binary Strings...

题目描述 给你两个二进制字符串$x$和$y$，将$y$左移$k$位，再与$x$相加，得到字符串$s_k$，最后将其反转得到$res_k$。求当$res_k$字典序最小时的$k$。 $PS:s_k = f(x) + f(y) * 2 ^ k$（$f(a)$为$a$的十进制形式） 输入格式 第一行为一个整数$T$——数据组数 接下来$2T$行每两行为一组数据，第一行为二进制字符串$x$，第二行为二进制字符串$y$。 字符串的长度均小于$10^5$且只由$1$或$0$构成，$1≤f(x)≤f(y)$ 输出格式 共$T$行，每行一个整数$k$，即当$res_k$字典序最小时的$k$。

You are given two binary strings $ x $ and $ y $ , which are binary representations of some two integers (let's denote these integers as $ f(x) $ and $ f(y) $ ). You can choose any integer $ k \ge 0 $ , calculate the expression $ s_k = f(x) + f(y) \cdot 2^k $ and write the binary representation of $ s_k $ in reverse order (let's denote it as $ rev_k $ ). For example, let $ x = 1010 $ and $ y = 11 $ ; you've chosen $ k = 1 $ and, since $ 2^1 = 10_2 $ , so $ s_k = 1010_2 + 11_2 \cdot 10_2 = 10000_2 $ and $ rev_k = 00001 $ . For given $ x $ and $ y $ , you need to choose such $ k $ that $ rev_k $ is lexicographically minimal (read notes if you don't know what does "lexicographically" means). It's guaranteed that, with given constraints, $ k $ exists and is finite.

The first line contains a single integer $ T $ ( $ 1 \le T \le 100 $ ) — the number of queries. Next $ 2T $ lines contain a description of queries: two lines per query. The first line contains one binary string $ x $ , consisting of no more than $ 10^5 $ characters. Each character is either 0 or 1. The second line contains one binary string $ y $ , consisting of no more than $ 10^5 $ characters. Each character is either 0 or 1. It's guaranteed, that $ 1 \le f(y) \le f(x) $ (where $ f(x) $ is the integer represented by $ x $ , and $ f(y) $ is the integer represented by $ y $ ), both representations don't have any leading zeroes, the total length of $ x $ over all queries doesn't exceed $ 10^5 $ , and the total length of $ y $ over all queries doesn't exceed $ 10^5 $ .

Print $ T $ integers (one per query). For each query print such $ k $ that $ rev_k $ is lexicographically minimal.

4
1010
11
10001
110
1
1
1010101010101
11110000

1
3
0
0

The first query was described in the legend. In the second query, it's optimal to choose $ k = 3 $ . The $ 2^3 = 1000_2 $ so $ s_3 = 10001_2 + 110_2 \cdot 1000_2 = 10001 + 110000 = 1000001 $ and $ rev_3 = 1000001 $ . For example, if $ k = 0 $ , then $ s_0 = 10111 $ and $ rev_0 = 11101 $ , but $ rev_3 = 1000001 $ is lexicographically smaller than $ rev_0 = 11101 $ . In the third query $ s_0 = 10 $ and $ rev_0 = 01 $ . For example, $ s_2 = 101 $ and $ rev_2 = 101 $ . And $ 01 $ is lexicographically smaller than $ 101 $ . The quote from Wikipedia: "To determine which of two strings of characters comes when arranging in lexicographical order, their first letters are compared. If they differ, then the string whose first letter comes earlier in the alphabet comes before the other string. If the first letters are the same, then the second letters are compared, and so on. If a position is reached where one string has no more letters to compare while the other does, then the first (shorter) string is deemed to come first in alphabetical order."