CF1694A Creep

Define the score of some binary string $ T $ as the absolute difference between the number of zeroes and ones in it. (for example, $ T= $ 010001 contains $ 4 $ zeroes and $ 2 $ ones, so the score of $ T $ is $ |4-2| = 2 $ ). Define the creepiness of some binary string $ S $ as the maximum score among all of its prefixes (for example, the creepiness of $ S= $ 01001 is equal to $ 2 $ because the score of the prefix $ S[1 \ldots 4] $ is $ 2 $ and the rest of the prefixes have a score of $ 2 $ or less). Given two integers $ a $ and $ b $ , construct a binary string consisting of $ a $ zeroes and $ b $ ones with the minimum possible creepiness.

The first line contains a single integer $ t $ $ (1\le t\le 1000) $ — the number of test cases. The description of the test cases follows. The only line of each test case contains two integers $ a $ and $ b $ ( $ 1 \le a, b \le 100 $ ) — the numbers of zeroes and ones correspondingly.

For each test case, print a binary string consisting of $ a $ zeroes and $ b $ ones with the minimum possible creepiness. If there are multiple answers, print any of them.

In the first test case, the score of $ S[1 \ldots 1] $ is $ 1 $ , and the score of $ S[1 \ldots 2] $ is $ 0 $ . In the second test case, the minimum possible creepiness is $ 1 $ and one of the other answers is 101. In the third test case, the minimum possible creepiness is $ 3 $ and one of the other answers is 0001100.