A15073. 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.